DEPARTMENT OF SCIENCE EDUCATION...Akor, A.E Pauline Prof. K.O. Usman (Student) (Supervisor) 7...

AKOR, A. E. PAULINE

PG/Ph.D/07/48424

EFFECT OF ACHIEVEMENT MOTIVATIONAL INSTRUCTIONAL

APPROACH ON PRIMARY SIX PUPILS’ NUMERICAL APTITUDE AND

RETENTION IN MATHEMATICS

DEPARTMENT OF SCIENCE EDUCATION

FACULTY OF EDUCATION

Fred Attah

Digitally signed by: Content manager’s

Name

DN : CN = Webmaster’s name

O= University of Nigeria, Nsukka

OU = Innovation Centre

EFFECT OF ACHIEVEMENT MOTIVATIONAL INSTRUCTIONAL APPROACH ON PRIMARY SIX PUPILS’ NUMERICAL APTITUDE AND

RETENTION IN MATHEMATICS

BY

AKOR, A. E. PAULINE

PG/Ph.D/07/48424

DEPARTMENT OF SCIENCE EDUCATION

FACULTY OF EDUCATION

UNIVERSITY OF NIGERIA NSUKKA

NOVEMBER, 2015

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TITLE PAGE

EFFECT OF ACHIEVEMENT MOTIVATIONAL INSTRUCTIONAL APPROACH ON PRIMARY SIX PUPILS’ NUMERICAL APTITUDE

AND RETENTION IN MATHEMATICS

BY

AKOR, A.E. PAULINE

PG/Ph.D/07/48424

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SUPERVISOR

PROF. K.O. USMAN

NOVEMBER, 2015

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A THESIS SUBMITTED TO DEPARTMENT OF SCIENCE EDUCATI ON

UNIVERSITY OF NIGERIA NSUKKA IN FULFILMENT OF REQUIREMENTS FOR THE AWARD OF DOCTOR PHILOSOPHY

(Ph.D) DEGREE IN MATHEMATICS IN EDUCATION

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CERTIFICATION

Akor, Awunghe-Ebuta Pauline a Postgraduate Student in the Department of

Science Education, with Registration Number PG/Ph.D/07/48424, has satisfactorily

completed the requirement for research work for the award of the degree of Doctor of

Philosophy (Ph.D) in Mathematics Education. The work embodied in this thesis is

original and has not been submitted in whole or part for any other degree of this or any

other university.

…………………………… ……………………… Akor, A.E Pauline Prof. K.O. Usman (Student) (Supervisor)

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DEDICATION

This work is dedicated to Almighty God for his grace and to my beloved family.

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ACKNOWLEDGEMENT

The researcher is thankful to Almighty God who made it possible for this study

to come to this stage. The researcher’s special thanks is to her Supervisor, Prof. K.O.

Usman for his interest and encouragement, God will pay you better Having spend all

her years of study in this University from Masters level till this moment, the researcher

appreciates mentors that have made her fit for the society. Mentors that easily come to

mind include; Prof. B.G. Nworgu, Prof. U.N.V. Agwagal, Prof. A. Ali, Late Prof. V.F.

Harbore Peters, Prof D.N. Ezeh and Prof. G. Offorma, may the Good Lord bless them

all.

The researcher cannot thank enough her readers at various stages of this work

especially Dr. (Mrs) Nworgu, L.N, Dr. Agah J., Dr. Nwabuku, and Dr. F.M. Onu who

painstakingly offered much of their time to see that the work was on correct course.

God bless you. To many others whose names are not mentioned, the researcher remain

thankful to you all.

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TABLE CONTENTS

Title Page i Approval Page ii Certification iii Dedication iv Acknowledgment v Table of contents vi List of appendices ix List of tables x Abstract xii

CHAPTER ONE: INTRODUCTION

Background of Study 1

Statement of the Problem 13

Purpose of the Study 14

Significance of the Study 15

Scope of the Study 17

Research Questions 19

Hypothesis 20

CHAPTER TWO: REVIEW OF RELATED LITERATURE

Conceptual Framework 22

� Teaching and learning mathematics 23

� Concept and components of achievement motivation 27

� Achievement motivational instructional approach 28

� Traditional teaching method 36

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� Mathematics Achievement 37

� Numerical Aptitude 39

� Gender and mathematics Achievement 42

� Retention and Mathematics Achievement 44

� Diagrammatical Representation of the Conceptual Framework 46

Theoretical Framework 47

� David McClelland’s Motivational Needs Theory 47

� Need Achievement Motivation Theory 51

Review of Empirical Studies 52

� Studies on teaching approaches on primary six pupils gender 52

� Studies on teaching approaches on primary six pupils retention 57

� Studies on the Effect of Achievement Motivational Instructional

Approach on Primary Pupils Achievement 58


Approach on Primary Pupils Retention 59


Approach on Primary Pupils Numerical aptitude 61

Summary of Related Literature 61

CHAPTER THREE: RESEARCH METHOD

Design of the Study 63

Area of the Study 64

Population of the Study 65

Sample and Sampling Technique 65

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Instruments for Data Collection 65

Validation of the Instrument 67

Reliability 68

Experimental Procedure 69

Control of Extraneous Variable 70

Training of Teachers 71

Method of Data Collection 73

Method of Data Analysis 74

CHAPTER FOUR: RESULTS 75

Summary of Findings 88

CHAPTER FIVE: DISCUSSION, CONCLUSION AND SUMMARY

OF THE STUDY

Discussion 90

Conclusions 96

Educational Implications 97

Recommendations 98

Limitations 99

Suggestions for Further Studies 100

Summary 100

REFERENCES 102

APPENDICES 110

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LIST OF APPENDICES

APPENDIX A: Mathematics Achievement Test (MAT) 110

APPENDIX B: Numerical Aptitude Test (NAT) 116

APPENDIX C: Lesson Plans (Experimental) 122

APPENDIX D: Lesson Plans (Control) 137

APPENDIX E: Table of Specification 153

APPENDIX F: Training Guide for Teachers 155

APPENDIX G: Primary Six Curriculum 158

APPENDIX H: Computation of the Reliability of MAT 179

APPENDIX I: Computation for reliability of NAT 181

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LIST OF TABLES

Table page

1: Mean and Standard deviation of pretest posttest score of pupils taught mathematics with achievement motivational instructional approach and those taught with traditional approach 75

2: Mean and Standard deviation of numerical aptitude score of pupils

taught mathematics with achievement motivational instructional approach and those taught with traditional approach 76

3: Mean and Standard deviation of pretest posttest score of male and female pupils taught mathematics with achievement motivational instructional approach 77

4: Mean and Standard deviation of numerical aptitude score of male and female pupils taught mathematics with achievement motivational approach 78

5: Mean and Standard deviation of retention score of pupils taught mathematics with achievement motivational instructional approach and those taught with traditional approach 78

6: Mean and Standard deviation of retention numerical aptitude score

of pupils taught mathematics with achievement motivational instructional approach and those taught with traditional approach 79

7: Mean and Standard deviation of retention score of male and female pupils taught mathematics with achievement motivational instructional approach 80

8: Mean and Standard deviation of retention numerical aptitude score of male and female pupils taught mathematics with achievement motivational instructional approach 81

9: Analysis of Covariance (ANCOVA) of the mean achievement

score of pupils taught mathematics with achievement motivational instructional approach and those taught with traditional approach 82

10: Analysis of Covariance (ANCOVA) of the mean numerical aptitude

score of pupils taught mathematics with achievement motivational instructional approach and those taught with traditional approach. 83

11: Analysis of Covariance (ANCOVA) of the mean retention of

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achievement score of male and female pupils taught mathematics with achievement motivational instructional approach. 85

12: Analysis of Covariance (ANCOVA) of the mean retention of numerical

aptitude score of male and female pupils taught mathematics with achievement motivational instructional approach. 86

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ABSTRACT This study sought to investigate the effect of achievement motivational instructional approach on primary six pupils’ numerical aptitude and retention in mathematic. Eight research questions and ten research hypotheses guided the study. The design of the study was quasi experimental pretest posttest equivalent control group design. The study was carried out in Calabar municipality Local Government Area of Cross River State in the present south-south zone of Nigeria. The population of the study was 2400 primary six pupils’ from the 24 public primary schools in Calabar municipality education zone of Cross River State. Two out of the 24 schools were randomly selected for the study. The sample size for this study was 241. 125 pupils were assigned the experimental group and 116 pupils constituted the control group for the experimental group 70 of the pupils were males and 55 pupils were females. The instruments used for data collection were Mathematics Achievement Test (MAT) and Numerical Aptitude Test (NAT).The MAT was developed by the researcher and the NAT was a standardized test from the state ministry of education. The MAT was subjected to both face and content validation. MAT and NAT were trial tested on 30 pupils and the data generated was used to determine the reliability coefficient of MAT to be 0.86 and of NAT to be 0.83 using Richardson (20) K – R20 formula. MAT and NAT was administered on the groups before treatment started while post-MAT and NAT was administered at the end of the 3 weeks treatment period. After 2 weeks of administration of post-test, the items of both MAT and NAT were reshuffled and again administered on the group as a retention test. Scores from the pretest of MAT and NAT, posttest of MAT and NAT and the retention test were analysed using means, standard deviation and analysis of covariance (ANCOVA). Some of the major findings from the analysis were (i) Achievement motivational instructional approach was found to be capable of enhancing pupils’ achievement, numerical aptitude and retention in Mathematics than the traditional approach. (ii) Achievement motivational instructional approach does not result in differences in achievement, numerical aptitude scores between male and female pupils. (iii) The use of achievement motivational instructional approach improved retention of male and female pupils. Based on the findings, the implication were highlighted and recommendation were made towards better achievements, numerical aptitude and retention of primary six pupils’ in mathematics

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CHAPTER ONE

INTRODUCTION

Background of Study

Mathematics has been described by many researchers and authors of different

times in different ways. While some tried to show its elegant precision, beauty and

brevity, others tried to show its structure and the training it provides. Ibrahim (2004)

said that among the training mathematics provides includes the ability to develop

powers of logical thinking, accuracy with figures and spatial awareness. The role of

mathematics in the field of science and technology is quite enormous and far-reaching

and the usefulness of mathematics in various fields of endeavors has been expatiated by

some writers including Usman (2002) and Agwagah (2004).

As a science subject, mathematics deals with counting, measuring and describing

shapes or objects. Mathematics can be regarded as a tool for basic science namely

physics, chemistry, biology, and even social sciences, for example geography,

economics, banking and finance. The role of mathematics is very important in everyday

life that its position is felt in all aspects of life. For instance, for the purpose of

economic survival, every citizen needs to be able to compare and estimate commodities

and cost of prices. The citizens requires some degree of competence in mathematical

computations for the purpose of carrying out routine daily businesses and for thinking

effectively. Akinsola and Popoola (2004), supported this fact when they said that

mathematics fosters intellectual skills that enable man analyze complex problems,

recognize logical relations between interdependent factors as well as formulate general

laws on their interrelationship in making precision statements. However it is necessary

for a person to have some knowledge of mathematics in order to become a useful and

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effective member of the society. Which follows that no Nation can develop

scientifically and technologically without proper foundation in school mathematics

(Ejakpovi and Uveruveh, 2014). Therefore any attempt to treat mathematics with levity

in the country’s educational system may have serious consequences for Nigerians.

All nations of the world should take mathematics studies seriously because it is

the precursor of scientific as well as technological breakthrough and there is no end to

the usefulness of mathematics. A strong background in mathematics is therefore critical

for many jobs and carrier opportunities in today’s increasingly technological society in

Nigeria. Mathematics has been made compulsory at both primary and secondary school

levels of education (Federal Republic of Nigeria, 2004). The primary objectives of

mathematics are as it was spelt out at the Benin conference of 1977 on mathematics and

mathematics education in Nigeria as follows.

• To lay a solid foundation for the concept of numeracy and scientific thinking.

• To develop in the child the ability to adapt to his changing environment.

• To give the child opportunity for developing manipulative skills that will enable

him function effectively in the society within the limits of his capacity.

• To provide the basic tools for further advancement as well as prepare him for

trades and crafts of his locality.

• At the secondary school level to build on the foundation of the primary level so

that the child can make a useful living professionally, economically, politically

and socially (FRN, 2004).

The inculcation of mathematical culture should therefore begin early in life. The

training of children to be competent in this very important subject should start in the

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primary school. The early years of primary experience with mathematics are very

crucial because they can affect the child’s attitude to mathematics for the rest of his or

her life. It is at this stage the child cultivates the understanding and application of

mathematics skills and concepts necessary to thrive in the ever changing technological

world (Ibrahim, 2004). The child at primary stage develops the essential element of

problem solving, communication, reasoning and connection within their study of

mathematics. If a child does not reach a satisfactory understanding of the basic

mathematical concept taught in primary school, he may find it difficult to assimilate

further concepts appropriately.

The teaching of primary mathematics therefore is necessary as it provide a solid

foundation for everyday living; develops the ability to recognize problems and to solve;

develop the ability of precision, logical and abstract thinking; and fosters the ability to

be accurate in solving both mathematical and real life problems among others

(Adedayo, 2001).

The primary mathematics curriculum is well designed to boost pupils’

achievements in cognitive and psychomotor capability. The content considered in the

revised curriculum for primary six are number and numeration, basic operation,

measurement, geometry and menstruation and everyday statistics (FME, 2007). The

curriculum provide maximal teaching aid for the teacher by prescribing topics,

objective or expected learning outcome stated in measurable terms, pupils and teachers

activities and adequate evaluation that will make the curriculum achieve its purpose.

The realization of good teaching and learning of primary mathematics lies in the hands

of teachers. The mathematics teacher should not merely impact information, but should

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try to develop in the pupils the ability to use these information to further their

knowledge in mathematics.

The quality and ability of secondary school students according to Offorma,

(2000) are largely determined by the type of training and academic instruction received

at the primary school. Teachers need to apply different approaches at different times.

Different content requires different approaches and different levels of intellectual

engagement. These approaches according to Reeve (2006) will provide a deeper

understanding of the subject matter. Teachers therefore can select from modern

innovative approaches that will promote better teaching process thereby improving

mathematics performance.

Primary mathematics is beset with many problems that causes poor performance.

Some of these problems include inadequate training facilities that can bring out the best

in the Nigerian child (Adedayo, 2001). Many scholars and other users of mathematics

had one time or the other complained about the decline in teaching and learning of

mathematics at primary level. Such complains among others are poor teaching

techniques that keeps the class dull (Willie and Bondi 2011). Besides, poor foundation

in primary school mathematics might be as a result of incompetent mathematics

teachers in the school system and psychological fear of mathematics as a subject, lack

of and inadequate instructional materials to teach some important practically oriented

topics at the primary school level (Eriaikhueman, 2003).

Much of the recent researches by Adeniji (2014), Agwagah (2013) on

mathematics teaching and learning identified teacher’s method of teaching as one major

reason for this persistent pattern of under-achievements and poor performance. Many

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teaching approaches that are not clearly specified are used in the teaching of

mathematics in primary schools. These approaches such as lecture methods, talk and

chalk method, individualistic method, sterile method, uninspiring and didactic

according to Adeniji (2014) are always combined and used in the teaching of

mathematics in the primary level. These methods according to Adeniji (2014) are

referred to as traditional method of teaching which the teachers primary roles is to

covey facts and procedures and the pupils role are to memorize the facts and practice

the procedure. This type of instruction according to Zakariyya (2014), emphasizes the

passive acquisition of knowledge and pupils become recipient of knowledge through

rote learning. In other words traditional teaching approach is an approach that lays no

emphasis on pupils constructing their own ideas. It is more of teacher centre and has

obvious and serious limitations (Agwagah, 2004).

Traditional methods does not give room for pupils’ activity and creative mind

that is required in the present day National development. Traditional mathematics

teaching is still the norm in our nation schools and has continued to dominate the

mathematics classrooms (Agwagah, 2004). Many scientific studies according to Adeniji

(2014) have shown that traditional methods of teaching mathematics not only are

inactive but also seriously stunt the growth of pupils’ mathematical reasoning and

problem solving skills. This implies that traditional teaching method has not been able

to sustain the development of children in mathematics, especially in the primary school

where a solid foundation is needed. The impact of low achievements in this all-

important subject is great, especially at the primary levels. Failure to learn mathematics

affects students’ performance at both secondary and tertiary level. According to

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Akinsola and Popoola (2004) many pupils who left primary school on admission into

the secondary levels of education in Nigeria continue to perform poorly because of their

poor mathematics background in the primary school level.

In order to compliment the use of traditional methods, current studies on how

pupils learn science and science related subjects such as mathematics have started

revealing new ideas and approaches that will improve primary mathematics teaching

and learning. By contrast, in a contextual classroom, the teacher’s role is expanded to

include creating variety of learning experiences with a focus on understanding rather

than memorization. Research shows that, when teachers design task for novelty and

variety, pupils’ interest, motivation, engagement and mastery of mathematics increases

(Santrock, 2011). One of these approaches that is geared towards achieving this is the

achievement motivational instructional approach. Achievement according to Santrock

(2011) is the outcome of level of accomplishment in a specified programme of

instruction in a subject area or occupation which a pupil had undertaken in the recent

past. Furthermore, achievement also refers to how much an individual or learner has

mastered in a given subject or learning experience (Okwajiako, 2002). The perceived

value of achievement according to (Coskun, 2013) varies; it may be valued primarily

for promoting future success (Schooling, Job) or for bringing honour to ones family.

There are differences in perception of what it takes to achieve, for example, efforts

versus ability (Fuligni, 2001), listening versus participating Greenfield (2000) and

collaborating versus working individually, Martin (2009). According to Obieyem

(2011), achievement is pupils’ academic standing in relation to those of other people

tested with the same instrument. It therefore implies that achievement improves when

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pupils set goals that are specific, proximal and challenging. These goals should be

optimally matched to the pupils’ skills. Okwajiako (2002) said achievement may be

influenced by motivation.

Motivation according to Rabideau (2013) can be defined as the driving force

behind all the actions of an individual. Motivation is based on ones emotions and

achievement related goals. In the view of Elliot, (1997) motivation is the dynamics of

our behaviour which involves our needs, desires and ambitions in life. In other words

motivation is the basic drive for all of our actions. Motivation in mathematics has two

aspects; that of creating or arousing interest and that of maintaining the interest after the

novelty of the work in hand have worn off. Pupils tend to remain interested in those

things they understand most completely (Ezeliora 2004).

A work group of the American Psychological Association Board of Education

Affairs (1997) considered learner centered principles as being very important in

enhancing pupils’ motivation and achievement. These principles according to

(Santrock, 2011) states that what and how much is learned is influenced by the learner’s

motivation to learn which is in turn influenced by the learner’s emotional states, beliefs,

interest, goals and habit. There are different forms of motivations which include

extrinsic, intrinsic, physiological and achievement motivation.

A renowned theorist McClelland (1961) in his theory of achievement motivation

said achievement motivation is seeking achievement and attainment of realistic but

challenging goals. This theory believe that there is a strong need for feedback as to

achievement and progress and a need for a sense of accomplishment. According to

Rabideau (2013), achievement motivation is the need for success or the attainment of

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excellence. Individuals will satisfy their needs through different means and are driven

to succeed for varying reasons both internally and externally. That is having an innate

need to succeed or to reach high level of attainment. It follows that achievement

motivation is the foundation for all human motivation. That is people who experience

great levels of success are motivated to strive for more success.

Pupils who are high in achievement motivation (Coskun, 2010) have the

tendency to solve strenuous exercises, retain what they had learnt, recall what they had

learnt in the past and are able to review certain properties of mathematical shapes. This

is largely dependent on the way and manner pupils are taught as to acquire the

competence.

Based on the ongoing discussions, achievement motivational instructional

approach is the teaching behaviour that leads pupils to have tasked goal that are focused

on improvement and mastery. According to Coskun (2013), pupils’ taught with

achievement motivational instructional approach strive for success, show active

participation, always show the willingness to work. While Jegede and Jegede (1990)

stated that achievement motivational instructional approach is an approach if fully

utilized in the teaching of school subjects including mathematics will make

mathematics more meaningful and interesting. Hence this approach may be possible in

mathematics.

Achievement motivational instructional approach is an instructional approach

which holds the view that knowledge or experiences must not be forgotten. In other

words, the learner constructs knowledge in an attempt to integrate the past existing

knowledge with the new experience. When a learner is presented with new information,

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the learner first tries to read, recall, review to understand the language before making

any precision statement. This is because in primary six classes, no information is

completely new. Every information is assumed to have been taught in the junior classes

and any new information should be connected to knowledge already in memory. The

pupils must actively construct knowledge from their existing mental framework for

meaningful learning to occur. At any point in time their ideas, knowledge and

experiences may be needed. Achievement motivational instructional approach offers

pupils an opportunity to activate their mental framework.

Achievement motivational instructional approach is organized into four categories,

namely

• Applying SQ3R meaning (scan questions, read, recall and review),

• Understanding the purpose of Mathematics Language instruction;

• Diagnosing and treating pupils difficulties and

• Using practical activities to aid studying.

Achievement motivational instructional approach is most appealing as it is an

actively learning approach engaged in thinking logically and quantitatively. The teacher

plays a critical role by guiding and providing the necessary directions to ensure that

mathematical ideas are recognized. Mcmillian, (2011) said if these processes are

adequately stimulated the pupils’ ability to think, retain, remember, read efficiently and

the speed of solving correct mathematical problems will be on the increase. While

Okwujioko (2002) had observed that pupils thought with achievement motivational

instructional approach tend to have higher numerical aptitude.

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Numerical aptitude refers to a person’s potential ability as it relates to numbers

or quantities. According to Santrocks (2011), numerical aptitude is a potential ability of

an individual in a particular area of study and also a measure of one’s ability. It

estimates one’s capability to profit from further training of experience. Willie and

Bondi (2011) stated that pupils with high numerical aptitude always stand out distinct

in all they do, they are good in mental sums, recalling mathematical concepts that have

been taught in the past and a high retention of ideas. Numerical aptitude has always

taken the form of aptitude test which is designated to predict pupils or an individual

ability to learn a skill or accomplish something with further education and training

irrespective of area of coverage. Primary six pupils’ are expected to be in the same age

bracket, and having attended lessons together, write their examinations together.

This final examination which is either state or federal common entrance

examination or as it is popularly called in Cross River State placement examination is

what is referred to in this study as the numerical aptitude test. This examination is

monitored and under strict supervision by the state or federal ministry of Education and

passing this examination qualifies the pupils for admission into the secondary school.

Numerical aptitude test therefore is an attempt to differentiate effectively among pupils

the extent to which pupils have mastered important basic concepts and skills in their

capacity to reason quantitatively and logically and their ability to retain what had been

leant in the past. Time for numerical aptitude test is not always sufficient. It is not how

many questions a pupil can answer or do but how many correct questions a pupil can

answer correctly. For a pupil to perform high in this examination, there is need for

pupils to possess high retention of ideas or information.

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Retention according to Okonkwo (2012) is the ability to store facts and remember what

you have learnt after a period of time and the ability to remember takes place more

effectively when experiences are passed across to pupils through an appropriate

instructional procedure which is capable of arousing pupils’ interest. (Ogbonna, 2007),

stated that retention is an important variable in learning mathematics and that

achievement last only when pupils are able to retain what they have learnt.

Many researchers such as Ogbonna (2007), Ezeh (2011), Okonkwo (2012) have

carried out studies in the past on retention in various fields, and all viewed retention as

important in sustenance of achievement. That is if a pupil performs well in a post test, it

is expected that the pupils perform very well in a retention test but if the reverse

happens, it is an indication that, the concepts and ideas did not register in the long term

memory. The teacher will then search for a better strategy that will make the pupil

retain what they have learnt in mathematics. Retention according to Teese, (2004) is a

vital factor in achievement motivational instructional approach on numerical aptitude

because without retention there will be no act of recalling, reviewing, understanding

mathematics language instruction, diagnosing and treating pupils difficulties and using

practical activities to aid studying. Both teachers and pupils must know the stuff stored

in the memory to be able to be active and function well. According to Nworgu, (2004),

Agwagah, (2013) boy’s increase interaction with teachers in class than girls and this

tend to influence better development of mathematics concepts among male pupils. Also

the pattern of interaction in class tends to make boys appear more confident in

mathematics than girls. It has been established that there is differential performance in

mathematical activities due to gender especially in favour of boys Agwagah (2004).

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The gender issue in mathematics according to Harbor-Peters (2001), has been a source

of aversion. The believe that mathematics is a male stereotype especially as it is

regarded as abstract and difficult with attributes which boys are attracted to.

Incidentally, evidence from researchers show that there is no significant difference in

the performances of boys and girls in mathematics before the age of 11 (Harbor-Peters

2001).

A number of studies have verified the influence of gender on mathematics

achievement of pupils. This has led to different types of findings on the role of sex on

the mathematics achievement. In the finding of Umar and Momoh (2001) there was no

statistical difference in the performance of boys and girls on quantitative and other

aptitude test. Intrinsically motivation for both genders differ which consequently

influence the type of problems pupils may like to answer in mathematics test. This is

evident in the emphasis made by Urdan (2010) that motivational condition influence

both sexes to perform equally well in mathematics test and examination. It is influenced

to some extent by the interest level of the pupils and the ability to remember what was

taught in the past. This evidence tends to agree with Gregory (2011) who viewed that

primary six pupils are in the same age bracket of plus and minus eleven years (11 yrs)

and achievement in mathematics at this age is not noticeable as to whether boys or girls

do better. This study will investigate the differential effect of achievements

motivational instructional approach on males and females pupils’ numerical aptitude

and retention in mathematics.

Some researchers have evaluated the effectiveness of achievement motivational

instructional approach in different subject areas. For instance, Jegede & Jegede (1990)

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carried out a study to ascertain if the use of achievement motivational instructional

approach could be found significantly effective in the teaching of English. A similar

study was conducted by Aydin and Coskun (2011), to ascertain if achievement

motivational instructional approach could better students’ performance in Geography.

Despite these significant results recorded in other subject areas, it becomes obvious that

much has not been done in the use of achievement motivational instructional approach

as a teaching approach in mathematics. This study therefore is aimed at finding if the

achievement motivational instructional approach will improve primary six numerical

aptitude and retention mathematics.

Statement of the Problem

The use of inappropriate instructional approach has been identified as the major

causes of pupil’s poor achievement. The persistence use of traditional teaching

approaches in primary schools has stunt the growth of pupils mathematical reasoning

and problem solving skills thereby instilling fears in pupils such that, they run out of

school or graduate from primary school without understanding the major concept in

mathematics. Thus, effort are being made by educators and researchers to see if there

will be improvement especially through the use of appropriate teaching approaches and

skills that will enable the pupils strive to achieve when solving problems, increase the

participation level and develop the willingness to work. This will increase interest and

at the end attain a level of excellence and success. Although, many approaches such as

guided discovery, target task, expository and traditional methods have been in use,

mathematics performances especially at the primary level have not really improved.

Some researchers have equally tried to find out the effect of achievement motivational

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instructional approach of subjects of other fields of endeavour and found the approach

useful and successful. This study therefore tries to investigate in the field of

mathematics.

Hence this study tries to investigate

• The effect of achievement motivational instructional approach on primary six

pupils’, numerical aptitude and retention in mathematics.

• If differences exist in the achievement of male and female primary six pupils

achievement, numerical aptitude and retention when achievement motivational

instructional approach is applied.

• The interaction effect of achievement motivational instructional approach and

gender on primary pupils’ achievement numerical aptitude, and retention in

mathematics.

Purpose of the Study

The main purpose of the study is to investigate the effect of achievement

motivational instructional approach on primary six pupils’ numerical aptitude

achievement and retention in mathematics in Cross River State.

Specifically the study is to

1. Determine the mean achievement score of pupils taught mathematics with

achievement motivational instructional approach and those taught with

traditional approach.

2. Ascertain the mean numerical aptitude score of pupils taught mathematics with



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3. Determine the mean retention scores of male and female pupils taught

mathematics with achievement motivational instructional approach.

4. Ascertain the mean retention of numerical aptitude score of male and female

pupils taught mathematics with achievement motivational instructional approach

5. Determine the mean achievement scores of male and female pupils taught

mathematics with achievement motivational instructional approach.

6. Determine the mean numerical aptitude score of male and female pupils taught

mathematics with achievement motivational instructional approach

7. Determine the interaction effect of approaches and gender on mean achievement

scores of pupils in mathematics.

8. Determine the interaction effect of approaches and gender on mean numerical

aptitude scores of pupils in mathematics.

9. Determine the interaction effect of approaches and gender on mean retention of

achievement scores of pupils in mathematics.

10. Determine the interaction effect of approaches and gender on mean retention of

numerical aptitude scores of pupils in mathematics.

Significance of the Study

The findings of this study will be of greater benefits to pupils/students, parents,

ministry of education, curriculum planners professional bodies and the entire society.

On the theoretical significance, the study provides an insight on the theories of

McClelland (1961) and McClelland and Atkinson (1953) which have been acclaimed as

promoting teaching and learning. On the practical significance, the achievement

motivational instructional approach will help in developing the mental processes of

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curiosity, and manipulation. Thus, this study has immense promise for improvement of

pupils’ performance in mathematics, since it is directed at finding the appropriate

teaching method, which could facilitate learning and retention of concepts, arousing of

curiosity and interest. The finding will also show the difference between achievement

motivational instructional approach and traditional teaching method. The finding will

provide in mathematics an alternative method of teaching mathematics, for easier

understanding and effective application by pupils. It will also help in overcoming

mathematics fear in pupils.

The study will help teachers to identify brilliant mathematics pupils and those

that need special attention on how they can improve. The study will provide useful

information to Teachers Training Institutions when publications on the work are made.

The institutions can then develop new programme of instructions based on achievement

motivational instructional approach. This study may help curriculum planners to plan

programmes that will encourage, develop and strengthen interest in pupils towards

solving mathematics.

All stake holders in education are required to contribute to the process of

achieving the objectives of mathematics teaching by studying the new approach and

implementing it. Other stake holders like the State Universal Basic Education Board

(SUBEB) and other school administrators should think more about the availability of

resource materials in the schools by devising ways of exposing the approach across the

schools. Since the state Universal Basic Education Board oversees every issue

pertaining to primary school, will bring about positive changes in schools by organizing

32

workshops, conferences and in-service training thereby encouraging the teachers. The

SUBEB take instructions and relate back to the state ministry of education.

Parents and guardians are committed to the success of the school. At state level

the Parents Teachers Association (P.T.A.) encourages hard work and innovation, when

a school is doing well academically, the P.T.A. will help in building classrooms and

provide resource materials and even pay for extra lessons to make the approach

successful. Since the Association is a major pressure group influencing government

policies for schools, will pressure rise the government. The government will take

necessary steps to make relevant books tailored towards the innovative methods and

approach like achievement motivational instructional approaches for teaching at

affordable prices. Professional bodies like (MAN) mathematics Association of Nigeria

and (STAN) Science Teachers Association of Nigeria will organize and write books on

these approaches and be as resource persons at workshops and seminars for teachers so

as to positively support the efforts of government.

Finally, the use of the appropriate teaching method in teaching primary

mathematics will enable pupils to build on their knowledge acquired by passing all final

mathematics examination with higher grades that will give them opportunity to do

mathematics related subjects and course in secondary and tertiary institution. Lastly this

study will serve as a source of literature to scholars and educational researchers.

Scope of the Study

The study will be limited to the effect of achievement motivational instructional

approach on primary pupils’ numerical aptitude, retention and achievement in

mathematics in Cross River State. Specifically the study will be conducted using

33

primary six pupils. The content is the entire primary six mathematics curriculum,

comprising of number & numeration, Basic operation, Geometry and menstruation,

statistics, and measurement. The content will be taught in accordance with achievement

motivational instructional approach. This takes the form of;

• Apply SQ3R (Scan Question, Read, Recall and Review) pupils must read

questions again and again to understand the area of mathematics the question is

taken from; Recall formulas, and Review properties of shapes and statistical

ideas.

• Understanding the mathematics language instruction for proper interpretation

e.g. write in figures, write in words, correct to decimal places, reduce to its

simplest term, work in standard form and many more.

• Diagnosing and treating pupils, difficulties teachers must diagnose the pupils to

know where and how to start, Definition of mathematical terms and concepts,

identification, solve logically or quantitatively.

• Using practical activities to aid studying example measurement, heights, angles,

and drawing.

The primary six curriculums has the details to make this approach effective

because it is subdivided into performance objectives, content, teacher activity, pupils’

activity, teaching and learning materials. The achievement motivational instructional

approach is chosen because it will expose all techniques involved in the solving of

primary mathematics and will give the pupils’ a sound ability to strive, participate

actively in mathematics classes and examinations and show the willingness to solve

mathematics problems at any time.

34

Research Questions

1. What is the mean achievement score of pupils taught mathematics with


traditional approach?

2. What is the mean numerical aptitude score of pupils taught mathematics with



3. What is the mean achievement score of male and female pupils taught

mathematics with achievement motivational instructional approach?

4. What is the mean numerical aptitude score of male and female pupils taught

mathematics with achievement motivational instructional approach?

5. What is the mean retention of achievement score of pupils taught mathematics

with achievement motivational instructional approach and those taught with


6. What is the mean retention numerical aptitude score of pupils taught

mathematics with achievement motivational instructional approach and those

taught with traditional approach?

7. What is the mean retention of achievement score of male and female pupils

taught mathematics with achievement motivational instructional approach?

8. What is the mean retention of numerical aptitude score of male and female

pupils taught mathematics with achievement motivational instructional

approach?

35

Hypothesis

H01: There is no significant difference between the mean achievement score of pupils

taught mathematics with achievement motivational approach and those taught with


H02: There is no significant difference between the mean numerical aptitude score of

pupils taught mathematics with achievement motivational approach and those

taught with traditional approach.

H03: There is no significant difference between the mean achievement scores of male

and female pupils taught mathematics with achievement motivational approach.


male and female pupils taught mathematics with achievement motivational

approach

H05: There is no significant difference between the mean retention of achievement

scores of male and female pupils taught mathematics with achievement

motivational approach.

H06: There is no significant difference between the mean retention of numerical

aptitude score of male and female pupils taught mathematics with achievement

motivational approach

H07: There is no significant interaction effect of approaches and gender on mean




36


retention of achievement scores of pupils in mathematics.


retention of numerical aptitude scores of pupils in mathematics.

37

CHAPTER TWO

REVIEW OF RELATED LITERATURE

The literature review related to this study is organized under the following sub-

headings:

1. Conceptual Framework

• Teaching and learning of primary school mathematics

• Concept and components of achievement motivation.

• Achievement motivational instructional approach

• Traditional teaching method.

• Mathematics achievement

• Numerical aptitude.

• Gender and mathematics Achievement.

• Retention and mathematics achievement

2. Theoretical Framework

• David McClelland’s motivational need theory.

• Need Achievement Theory of motivation

3. Review of Related Empirical Studies.

• Studies on teaching approaches on primary six pupils gender

• Studies on teaching approaches on primary six pupils retention

• Studies on the effect of achievement motivational instructional approach on

achievement


retention.


numerical aptitude.

38

Summary of Related Literature.

Teaching and Learning of Primary School Mathematics

Mathematics is all about finding solution to problems. All decisions taken are

based on such question as what and how this question is best answered by converting

every statement to mathematical statement before solution is sought (Eraikhuemen,

2003).

The depth of mathematical knowledge an individual has dictated is the level of

accuracy of his/her decision. This implies that before an individual can function in the

society, he/she must possess relatively good knowledge of mathematics. Obodo (1990),

noted that one contributory factor to teachers ineffectiveness in mathematics instruction

include lack of knowledge and interest in both teachers and pupils.

Another researcher Agyeman (1993) reported that a teacher who does not have

the academic and the professional teaching qualification would undoubtedly have a

negative influence on the teaching and learning of the subject and again, Coskun (2010)

added that a teacher who cannot demonstrate mastery of the concepts in a particular

subject matter area of mathematics is bond to having his/her pupils performing poorly

in mathematics. Teachers lack of knowledge of the mathematics concepts has remained

a very serious issue that needs attention. According to Betiku, (2002), Pupils

performance is a function of many variables including teacher characteristics, teacher

activities and pupils background which can either positively or negatively predict

pupils’ mathematics achievement.

But poor mathematics performance in Nigeria primary schools has generated an

over whelming need for a review of current teaching and learning approaches (Felix,

39

2009). The mathematical Association of Nigeria MAN (1977) once decleared a war

against poor achievement in mathematics (WAPAM). Unfortunately, WAPAM

achieve little in reversing the trend of poor mathematics achievement in Nigeria

schools. Poor achievement in mathematics in Nigeria primary schools has assumed an

alarming proportion and caused a lot of concern for many years. This study therefore is

to proffer a new approach towards reversing the trend. The effectiveness of a new

approach has to start from the foundation level which is the primary school level. The

primary level has its curriculum cutting across primary one to primary six.

Primary six mathematics curriculum comprises of mostly revision topics. At

primary six most topics have been taught at primary one to primary five. The primary

six mathematics curriculum emphasized on areas that need reading, recalling,

reviewing. The curriculum has been designed to take charge of topics, content

coverage, performance objectives, activities for teachers and pupils, materials to be

used where necessary and the evaluation. For a successful exposure of primary six

mathematics curriculum within the given time, the teachers should arrange the

curriculum to incorporate

i. The application of 3R (Read, Review, Recall)

ii. Understanding mathematics language instruction write in figures e.g. take to

decimal, significance etc reduce to simplest form with or without calculator,

calculate.

iii. Diagnose and treat pupils difficulties. E.g. define, state, mention, enumerate,

calculate etc.

40

iv. Using practical activities to ensure that learning takes place. E.g. measure, draw,

divide, locate etc. this will clearly expose the content of primary six mathematics

which when applied the achievement motivational instructional approach will

improve mathematics achievement and numerical aptitude which shows the

same mathematics content.

According to Yara (2009), attitudes of pupils can be influenced by the attitude of

the teacher and his method of teaching which agreed with Haigh (2008), who

emphasized on teaching learning process such that he gave what the teachers should do

to bring a lesson to a successful end as follows.

1. The teacher is to teach and the children learn –

• Remember that there are too levels of teaching ie shallow end teaching and Deep

end teaching.

• Use different approaches to teaching and learning.

• Apply different strategies at different times.

• Begin with the simple approach and progress from there

• Help children to make sense for themselves

• Don’t conflate content with process.

2. Guide children to discover for themselves

• Give children some ownership of their learning.

• Plan for children to discover what you want them to learn.

• Use questions to guide children to your teaching points.

• Decide whether you are questioning to assist or to assess.

• When you teach don’t test; when you test don’t teach

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• Don’t make children struggle.

• Teach off the children’s answers

3. Determine the pace of the lesson-

• Don’t talk too much

• Stick to the lesson objectives

• Don’t confuse speed with timing

• Refocus on the lesson objectives during the lesson.

4) Make the children independent

• -Teach children good learning behaviors

• First teach children to listen and then to speak

• Teach children to produce knowledge, not just to reproduce it.

• Create a classroom climate where children feel to question.

• Model the intelligent behaviours you are looking for.

5) Teach children to think

• Teach children to reason.

• Help children to behave more intelligently

6 Organize group work

• Train children to work in groups.

• Teach children to cooperate.

• Decide which your focus group for teaching is.

• Move around your group with purpose

• Help children to help each other with their learning.

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According to Amoo and Efumbajo (2004), despite these efforts mathematics has

not secured its rightful position in the mind of pupils due to lack of interest as a result

of poor teaching. This study is aimed at providing an effective achievement

motivational instructional approach that will enhance achievement in mathematics.

Concept and Components of Achievement Motivation

The architect of self determination theory Richard Ryan and Edward Deci

(2009) refer to teachers who create circumstances for pupils to engage in self

determination as autonomy supportive teachers. These type of teachers according to

Santrock (2011) often have positive expectation for high ability pupils; they show the

pupils concession in all they do, give pupils enough time to answer questions, respond

to such pupils with more information and in a more elaborate way, criticize them less

often, praise them more often, seat them closer to the teachers desk, and even give them

close calls in grading. Aydin (2013) also said teacher monitors the pupils expectations

to ensure that they have a positive expectation by helping the pupils set their own goals,

plan how to reach the goals and monitor their progress towards the goals. Anderman

(2011) in his own view said goal setting is a key aspect of achievement motivation. He

maintain that pupils who set their goals, do challenging exercises, answer difficult

questions and uses their time and energy to achieve the standard objectives set.

According to Aydin (2013) achievement motivated pupils show curiosity and interest in

class by actively participating in class and active in mental problems, e.g. mental sums,

and show willingness to work thereby striving to attain excellence. Okwajiako (2002)

found out that achievement motivation improves when pupils set goals that are specific

“I want to get an A in the next mathematics test”.

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Santrock (2011) observed that teachers monitors the progress of pupils who have

high ability to retain what they had earlier learnt. That such are the pupils teachers use

to represent schools in debates and quizzes because the pupils can remember at short

notices and time. He maintained that such pupils always have extra lessons to boost

their intellectual abilities for to such pupils do the schools depend on in inside and

outside competition, who bring trophies of success and excellence to the schools.

Cavazos (2011), therefore said that how hard pupils will work can depend on

how much they expect to accomplish the set goals and how hard pupils work is

influenced by the value they place on the goals they have set. Researchers have found

that pupils achievement internal motivation and intrinsic interest in school tasks

increase when pupils have some choice and some opportunities to take personal

responsibilities for their learning (Bella, 2009). A teacher giving a group of pupils’

opportunity to measure the classroom and be able to present it in their own way that can

be mathematically meaningful. Such type of self determination can enhance

achievement motivation and Maclelland (1961) said that the motivation to achieve an

attainment of realistic but challenging goals is known as achievement motivation.

Achievement Motivational Instructional Approach

Achievement Motivational Instructional approach is a pupils’ dominated approach

which is aimed at enabling pupils to remember what had been stored in their long term

memory. The approach is categorized into four namely (i) SQ3R which is scan

question, read, recall and review (ii) understanding mathematics language instructions

(iii) diagnosing and treating pupils difficulties and (iv) using practical activities to aid

solving mathematics.

44

Coskun (2010) qualifies achievement motivational instructional approach as an

approach that cattered for every mathematical concept and the application of the

concepts as stipulated in the mathematics curriculum. Achievement motivational

instructional approach is aimed at building a child’s intellectual and potential ability. A

primary pupil need proper nurturing as the knowledge gained at this level can never

depart from them unless they were not properly nurtured. Most pupils leave primary

schools without knowing how to read, talkless of solving problems. Teachers there fore

need to keep the pupils under check and balance by making sure that previous

knowledge of the pupils is not forgotten. Other wise the teacher will see himself

marking time and will be considered not teaching. If a child leaves primary three to

primary 4, what the pupil is going to meet is not completely new. The teacher must

always make reference to past knowledge by involving the pupils to remember. By so

doing the pupils will be actively involved. That is when the achievement motivational

approach comes. This approach keeps a child active, curious, and always alert, it is

pupils’ dominated approach. The achievement motivational instructional approach is

organized into four categories namely

The First Step: Applying SQ3R (scan question, Read, Recall and Review)

According to Halonen (2009), various systems have been developed to help

pupils remember what they had learnt and what they are still learning. This system he

maintained benefits pupils by getting them to meaningful organize information, ask

question, reflect and review while Oshibodu, (1998), stressed that success in solving

primary mathematics relies on understanding the problems. He noted that SQ3R

enables pupils’ remember what have been taught in the past.

45

• SQ (Scan Question): The pupils go through the question over and over to get the

sense of the over all organization of ideas. The pupils should look at the topic and

subtopics that will be covered and then ask themselves questions about the materials

as they read. Most children cannot read and if you cannot read, you cannot

understand mathematics.

• Read: This is the ability to read very well and be able to interpret. Reading is a very

important aspect in the study of mathematics because without this ability, a child

will not be able to comprehend mathematical terms and will not be able to solve

mathematics. The child needs to learn how to read very well and with understanding

first before learning how to interprete the mathematical language into mathematical

statements. This will help the child to recognize mathematical symbols and signs.

Santox, (2011). agues that the three main goals of reading instruction should be to help

children

i. Automatically recognize words

ii. Comprehend text, and

iii. Become motivated to read and appreciated reading.

These goals are inter-related in that if children cannot recognize words, automatically

their comprehension suffers and if they can not comprehend the text, they are unlikely

to be motivated to read it. (Pressley & Harris, 2006) gave some strategies that teachers

can help pupils use to improve their reading as

• Overview text before reading

46

• Look for important information while reading and pay more attention to it than

other information, ask yourself questions about the important ideas or relate them to

something you already know.

• Attempt to determine the meaning of words not recognized

• Monitor text comprehension

• Understand relationship between part of text.

• Recognize when you might need to go back and reread a passage (you didn’t

understand, to clarify an important idea, or to underline or summarized for study).

While Gunning (2010), observed that struggling readers can make tremendous progress

through programs that focus on learning letter-sound relationship which help in

decoding process that is so important to developing fluency; practices that facilitate

development of comprehension including summarizing and predicting; and teach

specific strategies to promote comprehension and retention of text material. Here

comprehension is extremely important because the focus in reading had shifted from

learning to read to reading to learn.

Reading more effectively therefore is by stressing reading for comprehension. The

teacher should help the pupils check for meaning that is whether it made sense or is

confusing, is understood and if the pupils know what was read, can summarize and

reflect. The teacher guides the pupils’ read the text and monitors the pupil to read with

understanding (checking their comprehension). This the teacher does by making sure

that they recognize important concepts and ideas. This will be done over and over to

enable the pupils determined the meaning of words. Example in writing and reading up

47

to one million teachers should guide the pupils’ to practice reading and writing up to

one million using Abacus and charts to aid them.

Teachers should encourage pupils to be active readers, the pupils should immerse

themselves in what they are reading and strive to understand what the author or the

problem is saying. The extent to which a solver understands the problem and the

nature of its solution depends largely on how rich and accurate his interpretation to

what he read is. According to Fuller (2003) success in solving mathematics

problems is due to the ability to read with understanding. That is the verbal

statement must be understood and the unknown must be detected by the pupils. For

example in open sentences, population, algebraic expression.

Recall: This according to Rabedeau (2013) is the ability to remember what was retained

in the long term memory. By occasionally reflecting and recalling on the materials and

questions, the pupils see its meaningfulness. The teacher now guides the pupils to

recall what they already know that is connected to the topic at hand. This can be done in

an interactive section or by writing simple problems for pupils to come out one after the

other to solve the problems on the board. This will enable the teachers know the ability

of the class and know how to plan the termly work. Example in counting in million

pupils should revise the previous work in counting to enable them remember how to

count up to even nine million with the aid of abacus and charts.

At this point, teachers should encourage the pupils to make up a series of questions

about what they had done and what they are still doing and try to answer them. e.g.

formulars, operations etc.

48

Review: The teacher guides the pupils to go over the work or problem and evaluate

what they know and what they do not know. Jegede and Jegede (1990) said at this

point pupils should re-read and study what they do not remember or understand well.

According to Sontrock (2011), SQ3R is a system that had worked well for elementary

high school pupils because it checks the pupils previous knowledge and their ability to

retain what they had learnt in the years past. Examples review properties, diagrams and

graphs.

The primary six mathematics curriculum emphasized on areas that need reading,

recall and review for proper teaching and learning. Rabedeau (2013) said that teachers

should always keep children on constant check by giving them surprise exercises such

as mental sums, dictation, classwork, assignments and from time to time check their

notebooks and even their test books. This he said will keep pupils alert in class and

after school. The pupils will always develop the ability to read and remember all they

had ever done that is their previous knowledge will always be updated.

The Second Step: Understanding the purpose of mathematics instruction.

According to Chukwu (2001), pupils fail mathematics examinations because of

their inability to recognize and follow the right instructions. Andermman (2010)

mentioned four mental operations important in solving mathematical problems as

• Recognize the problem and use definitions where necessary.

• Regroup as to transform the problem

• Remember known facts.

• Supplement by introducing auxiliary elements.

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He noted that instruction if followed correctly improve pupils achievement in

mathematics.

Examining some instructions such as

i) write in standard form

ii) Take to 2 significance figures

iii) Reduce to its lowest term

iv) Convert to decimals

v) Without the use of calculators, add, multiply and so on.

Pupils’ do not do what the instructions says but rather do the contrary and this leads

them in to a different method thereby arriving at different answers. Santrock (2011)

noted that mathematics is instructional in nature and succeeding in mathematics means

being able to interpret every mathematical statement to solvable problems before

solutions are sought. The teachers should explain this terms with specific example and

let the pupils examine the various mathematics instruction and solve accordingly.

The Third Step: Diagnosing and treating pupils difficulties.

According to Taiwo (1993), teachers should help pupils to actively construct

their understanding, set goals and plan, think deeply and creatively, monitor their

learning, solve real world problems. Alio in Akor (2005) noted that teachers should

closely guide the pupils as to discover answers to their instructional problems by using

investigating procedures. These procedures he maintained will enable pupils discover

or develop new rules and concepts. In an attempt to do this pupils should be asked to

define, evaluate, identify, solve, Recite and state. This according to Anderman (2010)

will enable the teachers know where pupils are lacking and the pupils will also know

50

what areas they have problems. Through the diagnoses the teachers will arrange for

extra lessons for pupils or device new ways to handle the problems. Thompson, (1995)

stressed that the teacher constantly monitors and verify flow of discussion and use

questions as informal assessment of pupils knowledge so that teachers can spot and

redirect errors and misleading immediately they occur.

The Fouth Step: Using practical activities to aid studying.

This is pupil centered activity oriented method of teaching which enables pupils

to work together. According to Adeniran,(2004), to learn mathematics and to use it

requires practice, repetition and drill. The teachers play a critical role in establishing a

rich environment to exploring and providing the necessary direction to ensure that

mathematical ideas are recognized. This procedure makes pupils use their minds to

think and reason together thereby building positive self concepts in them and promoting

interest. Harbor-Peters (2002) pointed out that practical method allows pupils to

discover for themselves and it is the most effective method of learning because it allow

learners to actively participate in the learning process. Also Karplus (1979) was of the

opinion that when doing practical exercises you are exposed to three types of methods

which are expository, Guided discovery and unguided discovery. Ahmed (2000) noted

that drilling and practices play an important roll in mastery of computational skills in

mathematics. This is achievement motivational instructional approach which gives the

pupils opportunity to brainstorm as they take active part in recalling and reviewing

concepts and facts they had learnt before in relation to what the teacher is teaching

presently. The achievement motivational instructional approach attempts to correct the

anomalies of the lecture and traditional teaching methods.

51

Traditional Teaching Approach

Agwagah (2004) said traditional teaching approach is a “transmission” model in

which teachers try to convey knowledge to pupils directly. In a traditional classroom,

the teacher begins the lesson by giving the pupils a fact or rule. The teacher then works

a text book example and assigns pupils to work exercise from the textbook to help them

remember the fact or process, without really minding whether the pupils could even

read what was written, or link what was taught with any previous knowledge that could

help make the concept or idea clearer. Various teachers apply various approaches.

The teacher is after ending the scheme of work, and so gives out lessons to

pupils to copy on the board and read on their own. The teacher never goes back to find

out if the pupils copied correctly and if they understood the note and so lives the pupils

in a more confused state whereas in achievement motivational instructional approach,

the teacher will remain very much involved in the learning process, coordinating and

monitoring pupils build their own knowledge. This is explain by Rabedeau (2013)

when he said that the teacher learns to guide, not to tell, monitors the pupils towards

achieving their goals. Babara (1994) gave a distinction between achievement

motivational instructional approach and a traditional instructional approach as

Traditional Achievement motivational instructional

Teacher directs Pupils explore

Instruction is didactic Instructional is interactive

Instruction on single subject Pupils perform extended and disciplinary work

Pupils is knowledge dispenser Teacher is facilitator

Pupils work individually Pupils work collaboratively

Pupils assessed on fact knowledge

and discrete skills

Pupils assessed on performance.

52

Koran (2001) observed that in a traditional lesson, the teacher is the master

source of knowledge and exercise control over the pupils. He does most of the talking.

Research studies has shown that average teacher does 70% talking in the classroom,

and the pupils get the impression that they can learn only when their teacher is present

and teaching. But Gbamanja (1991) observed that the traditional method makes pupils

to easily get bored, frustrated and easily loose interest in mathematics. Also it does not

take care of the individual differences of the pupils in terms of learning abilities.

Despite the ineffectiveness of the traditional method, most teachers are

sometimes force to use it. This is due to large class size, lack of instructional materials

or mathematics teachers and the urgent need to cover the syllabus so that pupils may

face their examination. In view of this, Azuka (2000) observed that pupils poor

performance in mathematics examination might be due to the teaching method adopted.

Hence the need to explore an effective teaching approach as achievement motivational

instructional approach.

Mathematics Achievement

Mathematics achievement is a measure of what the pupils had learned or what

skills the pupils had mastered (Gregory, 2011). Achievement that assess skills in

mathematics is known as mathematics achievement. Mathematics achievement serve a

wide variety of purpose from the informal quiz on a single facet of a topic to a formal

final examination which systematically samples the curriculum of the entire school year

and helps to rank pupils for the purpose of assigning grades and making

recommendations. According to Akinsola and Popoola (2004), mathematics

53

achievement carefully developed or selected to represent faithfully the major objectives

of instructions, provide pupils with information about these instructional objectives and

their best feed back on how well they have mastered what is expected of them. In the

same vain Koran (2001) said preparing pupils for mathematics achievement test and

reviewing with them the results of the test, will reinforce instruction and provide the

teacher with valuable information on where instruction has succeeded and where

additional efforts is needed.

Mathematics achievement tests according to Edestein (1985) are designed to

measure the knowledge and skills that individuals learn in a relatively well-defined area

through formal or informal educational experiences. Thus, mathematics achievement

tests include tests designed by teachers for use in the classroom and standardized tests

developed by school districts, states, national and international organizations, and

commercial test publishers. Harbor-Peter (2002), said mathematics achievement tests

have been used for: (a) summative purposes such as measuring pupils’ achievement,

assigning grades, grade promotion and evaluation of competency, comparing pupils

achievement, within the school system across states and nations, and also evaluating the

effectiveness of teachers programmes, and states in accountability programmes; (b)

formative purposes such as identifying pupils strengths and weaknesses, motivating

pupils, teachers, and administrators to seek higher levels of performance, and informing

educational policy; and (c) placement and diagnostic purposes such as selecting and

placing pupils, and diagnosing learning disabilities, giftedness, and other special needs.

Koran (2001) conducted a research on teachers and pupils motivation effects on

pupils’ mathematics achievement at junior secondary school level. The result of post-

54

test scores of the research showed that there is a significant difference in the

achievement levels of the two groups in favour of the pupils’ in motivated group which

is the experimental group.

Numerical Aptitude

According to Sontrock (2011) numerical aptitude are used by individuals to

measure ability to perform tasks involving the manipulation of numbers. The questions

on numerical aptitude range from simple arithmetic, for example, addition and

subtraction, to more intricate questions where you need to interpret numerical

information presented as graphs, tables and diagrams. As Edelstein (1985) put it that

there is no widely accepted definition of the difference between numerical ability and

numerical aptitude and as far as psychometric tests are concerned the two terms are

interchangeable. According to Gregory (2011) if one applying for a job which involves

working with figures on a day-to-day basis, the employer will regard ones numerical

aptitude as a valuable predictor of performance on the job. However, since most jobs

require someone to work with numbers at least some, numerical aptitude tests are

among the most widely used of psychometric tests. Okwajiako (2002) said there are

several hundred numerical aptitude tests from different suppliers in the market and they

all vary in both the number and difficulty of the questions that they contain. The

duration of the particular test will depend on the job/ purpose someone is applying for

and how many other tests he has taken on the day. Even though there are so many

ability tests available to teachers/employers, the types of questions used in these test

can be classified into:

55

Numerical Aptitude - Computation

These questions involve basic mathematics including: subtraction, addition,

division, multiplication, ratios, fractions, percentages and decimals. You will need to

practice making quick and accurate calculations if you want to score well on these

questions.

Numerical Aptitude - Estimation

These questions involves basically to make quick estimates. You do not have

time to actually calculate these answers.

Numerical Aptitude - Reasoning

These questions test your reasoning ability rather than your ability to do

calculations. They invariably include some number series questions where you need to

work out which number or numbers are missing from the series and may also include

questions where a mathematical problem is posed in words and your task is to apply the

necessary logic to find the solution. To also do well, one must have a high retentive

ability. This can be called quantitative aptitude.

Numerical Aptitude - Data Interpretation

These tests commonly use: line graphs, scatter-plots, pie charts and tables which

you need to understand and manipulate to answer the questions. Data is sometimes

shown in more than one format and you may need to understand how the data relate to

each other before you can begin to answer the question. Scores in the computation and

estimation tests will depend on someone ability to add, subtract, multiply and divide

quickly and accurately. Someone can practice the type of questions that will be given in

rival estimation practice tests. Data Interpretation and numerical reasoning tests require

56

to do fewer calculations than computation and estimation and someone may be allowed

to use a calculator. The achievement motivational instructional approach enables a child

face any numerical aptitude examination because a child that is trained with the

approach will certainly strive for excellence.

Numerical aptitude test

According to Edestein (1985), numerical aptitude test is designed to differentiate

among pupils with respect to their developed learning ability, and they are useful for

predictons, selection, guidance and grouping or for assessing the general academic

ability of a class or school population and tracing growth over a period of time.

Edestein maintained that aptitude test is not tied to a specific content, rather they are

required for a given age group only e.g. (primary six). From this base, aptitude test is

an attempt to differentiate effectively among pupils the extent to which they have

mastered important basic concepts and skills in their capacity to reason quantitatively

and logically and their ability to retain what they have learnt in the past. He maintained

that numerical aptitude tests are administered under exam conditions and strictly timed,

a typical test might allow 30-40 minutes for 30-40 questions. Okwajiako (2002)

observed that the questions are almost always presented in multiple-choice format and

may become more difficult as you progress through the test. These tests usually have

more questions than someone can comfortably complete in the time allowed, and so

advised pupils not to be worried if they do not finish the test - it is the number of

correct answers which counts.

To ascertain this the primary six placement examination to secondary schools is

used as numerical aptitude test. This examination comes at the end of their primary

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school year and it is an examination that will incorporate the entire curriculum running

from number and numeration to daily statistic the questions are asked in a way that

exhibits achievement motivational instructional approach on numerical aptitude and

retention. The aptitude test is said to cover areas of Computation, Estimation,

Reasoning which is the Quantitative Aptitude, Data Interpretation. It is a test that is set

by specialist outside the class. For instance Common Entrance or the placement

examination is not controlled by teachers teaching the pupils but by people unknown to

schools. It is controlled by the State Ministry of Education.

Gender and Mathematics Achievement

Pupils differ in their explanation of the cause of poor achievement especially in

mathematics. According to Ebeh (2000), individuals sometimes find themselves in

situation of feelings where they appear helpless about perceived events of threats or

problems and such a situation might affect normal function. This situation normally

comes during the process of test and evaluation especially in mathematics. Amoo and

Efumbajo (2004) said that most of the time, the teachers aids in the problems facing

pupils. Ezeudu (1998) observed that some of the problems centered on frequency and

type of teacher/pupils interactions, bias and views of staff, intimidation of girls by boys

within lessons, nature of mathematics, and assessment techniques used. In contrary to

the views of Ezeudu, Martin (2009) said, to learn mathematics and to use it requires

mastery, and to master to a skill requires practice, repetition and drill concentration.

Lack of concentration on the parts of pupils especially the female pupils. Female pupils

after school engage themselves in domestics work like cooking, plating of hairs, sowing

of cloths when they are through they get tired and will not be able to read. When they --

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are in class with their male counterparts, the male do far better than the girls because

the female never read the previous work.

In a study carried out by Nworgu, L.N. (2004) on gender gab in science

achievement reveled that gender gab between male and female students was reduced

and enhanced the overall achievement of boys and girls in science when gender

sensitization package was used. This implies that with enough sensitization and

motivation both boys and girls will perform equally. Boys and girls according to

Eraikhuemen (2003) if given equal opportunities will perform equally in mathematics.

Oftentimes usually feel withdrawn in mathematics and teachers do not care to motivate

and upgrade their willingness to work. This may contribute to gender inequality in

mathematics achievement but given the necessary encouragement the female are

capable of striving in mathematics as their male counterparts.

Al-Emadi, (2003) observed that boys exert better mathematics achievement than

the girls because the boys from the beginning are encouraged to be more independent

than the girls, therefore differential treatment of sex has given the boys more

confidence than girls and this enhances better performance in favour of boys, in

mathematics. There is always a belief that mathematics is difficult, abstract and a male

subject. Again Al-Emadi, asserted that teachers interact with male pupils more than

with the females. Franden (2003) advised teachers on how to avoid gender bias and

provide girls friendly mathematics and science education. In agreement with this

(Aydin 2013), in a primary class of 40 pupils, girls numbered 28 and males 12 showing

that girl children are outnumbering their male counterparts in school. Furthermore their

ability to strive and their level of participation in a mathematics lesson has not shown

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any significant difference. As a result, the views of the pupils about the scale of the

achievement in mathematics lesson has not shown any meaningful difference according

to the variable of gender. He concluded that female pupils these days are equally good

in mathematics as their male counterparts. The effect of achievement motivational

instructional approach will investigate the gap between males and females as it will

expose both sexes to things learnt in the past and in the present.

Retention and Mathematics Achievement

Aydin (2013) said retention is a necessary ability to primary six pupils and also

observed that primary pupils’ with well laid foundation are bound to do well in all

primary subjects because they always keep themselves busy, they strive to attain

success, and have the willingness to work. Also that such pupils do well because they

can afford to remember or reflect on their previous knowledge. Ali (2000) also viewed

that teaching mathematics using vernacular could improve retention thereby improving

mathematics achievement. Before a pupil gets to primary six, they have been taught

mathematics from primary one to five. So Ali added that the teachers of primary school

have a critical roll to play by establishing a rich environment to explore and provide the

necessary direction to ensure that mathematical ideas are recognized and retained such

that at primary six recalling, reviewing mathematics concepts and ideas becomes easy.

In the study of Eze, (2011)the students who were taught mathematics using

computer as tutor and tool performed better in mathematics achievement because they

could exhibit higher retention than those who were not taught with computer.

Retention in mathematics is engineered by the method used in teaching and

achievement in mathematics is enhanced when retention is highly exhibited. Similarly,

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Santrock (2011) said that pupils who are taught with achievement motivational

instructional approach exhibit high achievement and this high achievement is as a result

of their ability to retain mathematical ideas. This study therefore is geared towards

finding the effect of achievement motivational instructional approach on primary six

pupils numerical aptitude and retention in mathematics.

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Diagrammatical Representation of the Conceptual Framework

The diagram above shows the process of teaching and learning of primary school

mathematics using achievement motivational instructional approach as necessary

approach to pupils numerical aptitude, retention and achievement in mathematics.

Traditional teaching method

Achievement Motivational instructional method

Teaching method

Attributes/components of achievement motivation

Components of TM used (lecture, talk and chalk & didactic, etc)

Learning by male/female/Gender

Assessment instrument MAT x NAT

Achievement

Retention

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Theoretical Framework

Theory of Achievement Motivation

David McClelland's Motivational Needs Theory

Motivational needs theory was developed by American David Clarence

McClelland in 1961. McClelland is most noted for describing three types of

motivational needs:- achievement motivation denoted as (n-ach), authority/power

motivation denoted as (n-pow) and affiliation motivation denoted as (n-affil). These

motivational needs are found to varying degrees in all individuals, and this mix of

motivational needs characterizes a person's or manager's style and behaviour, both in

terms of being motivated and in the management and motivating others. The n-ach

person is 'achievement motivated' and therefore seeks achievement, attainment of

realistic but challenging goals, and advancement in the job. The theory believes that

there is a strong need for feedback as to achievement and progress, and a need for a

sense of accomplishment. The need for authority and power (n-pow) person is

‘authority motivated’. Such a person need to be influential, effective and to make an

impact. There is a strong need to lead and for their ideas to prevail. There is also

motivation and need towards increasing personal status and prestige. The n-affil person

is affiliation. To be liked and held in popular regard. These people are team players.

McClelland said that most people possess and exhibit a combination of these

characteristics. Some people exhibit a strong bias to a particular motivational need, and

this motivational or needs 'mix' consequently affects their behaviour and

working/managing style. McClelland suggested that a strong n-affil 'affiliation-

motivation' undermines a manager'? objectivity, because of their need to be liked, and

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that this affects a manager's decision-making capability. A strong n-pow 'authority-

motivation' will produce a determined work ethic and commitment to the organisation,

and while n-pow people are attracted to the leadership role, they may not possess the

required flexibility and people-centred skills. McClelland argues that n-ach people with

strong 'achievement motivation' make the best leaders, although there can be a tendency

to demand too much of their staff in the belief that they are all similarly and highly

achievement-focused and results driven, which of course most people are not.

McClelland particular fascination was for achievement motivation (n-arch)

McClelland identified the need for a 'balanced challenge' in the approach of

achievement-motivated people. McClelland contrasted achievement-motivated people

with gamblers, and dispelled a common pre-conception that n-ach 'achievement-

motivated' people are big risk takers. On the contrary - typically, achievement-

motivated individuals set goals which they can influence with their effort and ability,

and as such the goal is considered to be achievable. This determined results-driven

approach is almost invariably present in the character make-up of all successful

business people and entrepreneurs. McClelland suggested other characteristics and

attitudes of achievement-motivated people:

• Achievement is more important than material or financial reward.

• Achieving the aim or task gives greater personal satisfaction than receiving praise or

recognition.

• Financial reward is regarded as a measurement of success, not an end in itself.

• Security is not prime motivator, nor is status.

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• Feedback is essential, because it enables measurement of success, not for reasons of

praise or recognition (the implication here is that feedback must be reliable,

quantifiable and factual).

• Achievement-motivated people constantly seek improvements and ways of doing

things better.

• achievement-motivated people will logically favour jobs and responsibilities that

naturally satisfy their needs, ie offer flexibility and opportunity to set and achieve

goals, eg., sales and business management, and entrepreneurial roles.

McClelland firmly believed that achievement-motivated people are generally the

ones who make things happen and get results, and that this extends to getting results

through the organization of other people and resources, although as stated earlier, they

often demand too much of their staff because they prioritize achieving the goal above

the many varied interests and needs of their people.

McClelland (1953) postulated that participants high in achievement motivation

have a tendency to set realistic learning goals and consequently prefer tasks having

moderate difficulty than either easy or very difficult tasks while participants low in

achievement motivation have a tendency to avoid situation of uncertainty. They prefer,

consequently, easy and very difficult tasks that minimize uncertainty of failure and

success. This study in line with the theory of achievement motivation by McClelland

tries to find out the effect of achievement motivational instructional approach on

primary school/pupils’ numerical aptitude and retention in mathematics. According to

Aydin and Coskun (2011), achievement motivational instructional approach is capable

of increasing the achievement motivation of pupils that will reflect to their behaviour

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what they hard learned and achieved. They maintained that the achievement

motivational instructional approach gives pupils the disposition to participate actively

in the learning process thereby offering them opportunity to strive for success and

continue to show the willingness to work. Haigh (2008), in his view advice teachers to

teach meaningfully by helping pupils set goals that are challenging but realistic. This

he said will help the children attain high level of success and excellence. This theory is

based on the belief that pupils learn best when they gain knowledge through exploration

and active learning which are attributes of achievement motivational instructional

approach. In addition, one of the features of the theory that is relevant to this study is

the motion of teachers guiding pupils to set goals which they can influence with their

effort and ability which is in the character make up of all successful people. A

significant part of the theory is that it adopted the approach of reading, recalling,

reviewing, understanding mathematics language instruction, diagnosing and treating

pupils’ difficulties and using practical activities that keeps pupils busy and actively

solving mathematics problems, which a traditional classroom does not offer. The theory

seems to offer a means of investigating the growth of pupils understanding of the

concepts in mathematics in a very detailed way.

In conclusion McClelland’s motivational need theory in connection to

achievement motivational instructional approach presents clues and approaches to how

pupils activities in mathematics can be improved by applying reading, recalling,

reviewing and practical activities. Also uniquely draws the theories of achievement

motivation into classroom practices for meaningful learning. And finally beliefs that

there is a strong feedback as to achievement and progress.

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Need Achievement Motivation Theory

The need achievement motivation theory rests on the belief that most persons

want to achieve and experience levels of aspiration in a given environment.

Contributors of need achievement motivation theory are J. W, Atkinson and David

McClelland, (1953). According to Atkinson, (1953), when an individual is actively

involved on a task, he sets himself a standard to conquer. This standard is called the

level of aspiration. Caraway, (1985) pointed out that level of aspiration is a longing for

what is above one, with advancement as its goal. Aspiration has to do with the desire to

improve or to rise above one's present status. There are two set of factors which

interacts to determine the level of aspiration. They are the personal factors and the

cultural factor/environmental factors. Bella (2009) explained that personal factor relate

to such personality traits as intelligence, interest, gender, self concept, activity level,

socio-economic status and previous training experience. Cultural and environmental

factors include parental ambition, social values and social reinforcement. Need

achievement is more influenced by environmental factors. Some environmental factors

encourage the development of immediate aspiration.

According to Gregory (2011) the implication of need achievement theory is that

the teacher should create learning environment conditions that will help learners

adequately assess their abilities and opportunities available so that they can set realistic

and attainable goals. In this way learners will experience success in school activities

and thereby build positive self-concept which enhances need achievement motive.

Owing to the dominance of the teacher in the traditional teaching approaches, pupils are

not engaged in the classroom activities because such environment is not provided. This

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results into rote learning and memorization of facts with little transfer of knowledge.

Opara (2002) observed that the method hardly increased pupils enthusiasm and interest.

Meaningful learning activities built on prior knowledge motivate pupils and foster their

interest in their effort to executively control their own cognitive process. The fourth

stage of achievement motivational instructional approach which is using practical

activities to aid studying falls in line with the need achievement motivation theory since

it gives the pupils the opportunity to interact with themselves and the environment. The

achievement motivational instructional approach is an approach that McClelland called

‘balanced challenge’. It is on approach that exposes pupils to various ways of solving

problems.

Review of Empirical Studies

Teaching Approaches on Primary Pupils Gender

Amoo and Efunbanjo (2004) carried out a survey study on the attitudes of

primary school teachers to the teaching of mathematics. Two hundred and fifty primary

school teachers in Noforija-Ekpe, Lagos State irrespective of class taught participated

in the study. A self developed questionnaire that consisted of 20 items was used and

the method of analysis were t-test and multiple regression analysis were employed. The

results revealed that teaching of mathematics is beset with problem of non male and

female teachers to the teaching of mathematics. The characteristics of teachers that is

gender, qualification and area of specialization jointly contributes 76.5% to teachers

attitudes towards mathematics at primary school level. It suggests that there is strong

influence of the characteristics on attitude towards mathematics which was on how to

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teach mathematics in the primary schools as to enhance sustainable technological

development.

Ali (2000), investigated the effects of the use of Edo and Igbo for Teaching and

learning mathematics in Nigeria primary schools. Three groups of subjects participated

in the study. The groups were further broken down to primary 5 and primary 6. The

study made use of primary 5 and primary 6 pupils drawn from various states of Igbo

speaking and Edo speaking. The mode of instruction was that some were taught using

Edo and Igbo alone, some Edo and English and Igbo and English while the third

category which was the control group consisted of primary 5 and primary 6 selected

from various places of Igbo and Edo speaking areas who were taught mathematics in

English alone. All the primary 5 pupils were taught the same mathematics namely

practical and descriptive geometry drawn from the National primary mathematics

syllabus, the primary Education mathematics curriculum (PEMC).

Teachers who were involve for experimental group 1 and 2 were provided with

daily lesson plans prepared in Igbo and Edo languages. Those of the control group

taught mathematics with English alone had the lesson plan in English. Two respective

twenty item post-test, the Primary Mathematics Test (PMT) for primary five and

another for primary six drawn from the two respective mathematics topics. The validity

index was 0.79 and the reliability was 0.86. At the end of the five weeks of teaching,

the subjects were post-tested on the PMT and the PMT was scored and analyzed. The

results revealed that the use of vernacular in teaching primary 5 and 6 yielded feasible

results and both boys and girls had the same opportunities and no significance different

in their ability.

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Ife Centre for psychological studies (2010) examined whether there was a

significant gender gap in Mathematics achievement, and the nature of the gender gap.

It also investigated factors associated with the differential performance of girls and

boys and their retentive ability in mathematics class. The site for this study was a rural

primary school in Kwazulu Natal. Quantitative data was drawn from primary 6

mathematics achievement test results conducted in 2008 and 2009. In addition,

individual semi structured interviews and focus group interviews were conducted with

8 pupils (Male = 4, females = 4) from the 2009 cohort of primary six pupils. The

findings of the study revealed a gender gap in mathematics achievement in favour of

girls and that girls tend to remember what they have been taught more than the boys.

Sam, Joshua and Asim (2010) conducted a study to empirically verify the

existence or otherwise of gender inequality and retention in mathematics achievement

of rural male and female primary school pupils in Cross River State, Nigeria; and

whether parental socio-economic status and school proprietorship taken independently

are significant factors in the achievement of the pupils. By stratified and simple random

sampling, 2000 pupils 50% males, 50% females) were selected and a 30 items, four

options multiple choice mathematics achievement test (MAT) was constructed which

was pre-tested and post-tested. The independent t-test analysis of significance revealed

gender inequality and the girls having high retention over the boys. Researchers such as

Agwagah (2013), Korau (2008) have reported that boys out perform girls because boys

increase interaction with teachers and this influence better development of mathematics

concepts among male pupils. Also the pattern of interaction in class tends to make boys

appear more confident in mathematics than girls. The type of pattern of interaction

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mathematics teachers use in classroom matters because this will show the effectiveness

of teachers in teaching mathematics. Achievement motivational instructional approach

enables the teacher to exercise optimum interaction in a mathematics class. Pupils are

made to read, recall, review, use practical approach in solving problems. Teachers can

only achieve this when they have knowledge of content and can plan instructions for

pupils with different abilities and learning styles. By so doing pupils retention will be

upgraded and the issue of whether boys or girls do better will be taken care of.

Nnamani, (2010), investigated the effect of information and communications

Technology (ICT) Instructional package on, achievement of pupils with different

learning styles in primary science. The ICT instructional package used in this study

consists of prepared lessons on the two primary science topics taught in the study. The

study focused on two of the Felder Silverman’s dimensions of learning styles

(active/respective and visual/verbal) which have link with the learning process in a

classroom. The study also examined the influence of gender on achievements of pupils

with different learning styles in primary science. A quasi-experimental pretest posttest

non-equivalent control design was employed for the study. The study employed the

multi-stage sampling technique. A total of 177 primary five pupils who were clearly

demarcated on the two dimension of learning styles were investigated and sampled

from two schools in Nsukka Urban within Nsukka Educational Zone participated in the

study. Two instruments served the purpose which were learning style instrument and

achievement test tagged pupils achievement test in Primary Science (PATIPS). The

results of the study indicated that pupils made use of different learning styles during

learning and that gender influencing the learning styles of the pupils. The use of ICT in

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the delivery of primary science instruction enhance the achievement scores of pupils in

primary science and gender did not significantly influence the achievement scores of

pupils with different learning styles.

In the reference to the study conducted by Nworgu, L.N. (2004). The study was

designed to investigate the effect of gender sensitization of science teachers on gender

gap in science achievement and interest among students. The study was guided by four

research question and six hypothesis and adopted a non equivalent control group

design. The population comprise of all JS II students from six secondary schools

sampled from of seventeen co-educational schools in Nsukka Local Government Area.

The experimental Schools (3) were exposed to gender sensitization package while the

remaining three used conventional instructional approach (control). The reliability of

the instruments were established using Kudder Richardson formula 20 (K-R20) for

ISAT and Crombach’s alpha for ISIS. The reliability indices were found to be 0.84 for

ISAT and 0.76 for ISIS. Means and standard deviations were used to provide answers

to research questions while analysis of covariance (ANCOVA) was used to test the

research hypothesis at 0.05 level of significance. The result of the study showed that

gender sensitization package reduced gender gap that existed between male and female

students in science achievement and interest. Furthermore gender sensitization package

enhanced the overall achievement of boys and girls in science. Again the interactive

effect of sensitization and gender was statistically significant for achievement but not

for interest.

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Teaching Approaches on Primary Pupils Retention

Eraikhuemen (2003) also carried out a study on mathematics as an essential tool

for Universal Basic Education (UBE); implications for primary school mathematics that

can boost pupils ability to recall facts but cumulative evidence point to the fact that the

generality of pupils and teachers find mathematics uninteresting and pupils

unacceptable dimension. He pointed out that the needed involvement of the

mathematical association of Nigeria for effective teaching and learning of primary

school mathematics are Awareness campaign; for better methods. Problematic topics

identification, teachers retraining; and sourcing for fund. In conclusion Government

expects that the entire Nigeria populace will patriotically assume ownership of the

program by.

• Initiating and participating in continuing policy dialogues on the programme,

• Sensitizing all citizens to the need for all Nigerian children of school going age

to take full advantage of the free, compulsory UBE progrmame.

• Encouraging the out of school population to take advantage of the schooling

literacy and non-formal education programmes which will be an integral

ingredient of UBE.

• Mobilizing all and sundry to contribute (ideas-where possible, logistics, moral

support, etc). This was due to high retention of ideas. He also examine the

gender effect which he pointed out females tend to do better than boys this days

in mathematics.

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Furthermore, according to Ali (2000), because of the understanding of the

subject due to the use of vernacular, the level of retention increased thereby elevating

the interest and achievement in mathematics.

Ogbonna (2007) carried out a study on the effect of two constructivist

instructional models on students achievement and retention in Number and Numeration.

The study was carried in Abia State and a quasi experimental design was used. The

study used 290 JS III students. The findings revealed that the students who were taught

with the two constructivist instructional models (IEPT and TLC) achieved and retained

higher than those taught with the conventional method. Also female students

performed better than their male counterparts. The results from the studies conducted

by Aydin and Coskun (2011), and Perez, (2013) show significance difference in

mathematics achievement and retention between male and female students.

Studies on the Effect of Achievement Motivational Instructional Approach on

Primary Pupils Achievement

The relationship between achievement motivation and performance was

established in a study by Jegede (1990) whose work sought to determine the effect of

achievement motivational instructional approach and study habits on Nigeria primary

school pupils’ academic performance in English language learning. The experimental

variable (study habit and achievement motivation) were manipulated and their effects

on the dependent variable (English language performance) were observed. There were

four experimental groups for the study. All the groups were pre-and post-tested on the

measure of achievement motivation, study habits and English language performance.

The target population for the study was primary six pupils in mixed primary schools in

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Ilorin Nigeria. Four schools in that area were randomly selected and assigned to

treatment groups (three experimental and one control group) 40 pupils were selected in

each school (N = 160) for the study.

Bakare’s (1970) Academic Need Achievement motivation scale was used to tap

pupils achievement motivation. There were 36 standardized statements, to which the

pupils responded on a 5-point scale according to how true each statement is of him or

her. The validity and reliability were verified. Analysis of covariance (ANCOVA) was

used to test for the significance of the data. Thus there were significant differences

among the experimental groups performance in English. The findings lend further

support to the research hypothesis that pupils who were administered the combination

of improved study habit and higher achievement motivation would perform better in

English than any of the other groups as (study habit, achievement motivation and

control). The result also showed a significant different among the male and female

pupils where the boys performed better than the girls.


Primary Pupils Retention

Aydin and Coskun (2011) investigated the relationships between the

achievement motive of primary school pupils and the relationship between the

achievement motivational instructional approach. Class level”, parent, educational

level”, family income level. A total of 151 pupils took part in the study. A survey

model was used and the achievement motive scale develop by Fox, (2004) was used as

data collecting tool. t –test and one way analysis of variance (ANOVA) were used in

the analysis of data. At the end of the study the arithmetic mean of the views of pupils

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on the scale of achievement motivation has been determined to be 3.74. The views of

pupils about the scale of primary mathematic lesson achievement motivation has shown

significance difference according to class level but did not show any significant

difference according to ‘gender’ mother’s education level; father’s education level and

family income status”. Based on the findings of the study, suggestion for increasing the

achievement motivation of the pupils towards primary mathematics curriculum have

been developed to show that such pupils have the ability to strive for success,

participate actively in mathematics lessons, show the willingness to work, maintain

working and the ability to retain and be able to remember what they had learnt in the

past.

Pe rez, (2013) worked on a framework for understanding what might influence

children’s retention. She employed the framework of individualism and collectivism in

the bridging of cultures project and saw it as a source of understanding why the star

chart may have bombed as a motivational tool. She started learning about the success of

groups collectively and to use the power of the group to help everybody succeed.

Equipped with a new understanding of culture and in particular the collectivism of her

pupils, Pe’rez reconceptualized the chart from the means of encouraging pupils to earn

more stars for themselves to a visual aid that stimulated and encouraged the children to

think about achievement motivation as a group issue. The pupils all looked at the chart

together and talked about it and asked questions. From the children’s collectivistic

perspective, the chart seem to be a potential motivator for group achievement rather

than individual achievement. The study also revealed that both boys and girls can work

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effectively well given the same opportunity and the system made them to understand

better thereby giving them high retention.


Primary Pupils Numerical aptitude

Okwajiako (2002) took up a research to investigate the relationship between

achievement motivational instructional approach and numerical aptitude among

primary six pupils in Abia State. In this study, a total of 1024 pupils were randomly

selected across the primary schools in the state. The design used was ex-post facto and

three measurement instruments were used in collecting data; the achievement

motivation questionnaire, numerical aptitude test which was designed as quantitative

aptitude and mathematics achievement test. At the end, the result of the study showed

no significant difference in achievement motivational instructional approach and

numerical aptitude of the primary school pupils. Also no significant difference in the

achievement motivational instructional approach and mathematics achievement. The

study again viewed that there was a significance difference in gender where the males

performed better than the female.

Summary of Related Literature

The poor achievement in primary mathematics was attributed to poor

foundation, poor teaching methods, lack of interest in both teachers and pupils, lack of

knowledge of the subject. These have continued to pose a great concern to mathematics

educators, researchers, parents and even Government. It is in the basis to find a solution

to poor achievement of primary pupils in mathematics that made researchers to search

for methods that will improve pupils’ achievement in the subject. Hence, the

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introduction of achievement motivational instructional approach in teaching

mathematics. Many methods of solving primary mathematics had been in use.

However, research finding indicated that pupils’ are lacking in ability of solving

numerical aptitude problems and retention. The achievement motivational instructional

approach exposes the gymics in solving primary mathematics. It gives the pupils the

opportunity to work closely with the previous knowledge, affording the pupils the

ability to remember or recall all that was taught in the past thereby making their

reasoning, and retentive abilities very active also exposing the pupils aptitude

potentials. It is an approach that systematically unfold how to approach any

mathematical problem.

The review also revealed that gender disparity has long been a problem in our

researches and up till date it has not been clear on issues of gender because there is no

clear distinction as to which sex perform better than the other in mathematics

achievement. Under the framework for the study, McClelland’s motivational need

theory and need achievement theory of motivation were considered relevant and

suitable for this study. A lot of related empirical studies were reviewed in order to guide

the researcher in selecting appropriate design for the study, statistical tools and other

procedures for achieving the purpose of the study. Hence the effect of achievement

motivational instructional approach on primary six pupils numerical aptitude, on

gender, retention and achievement as mathematics.

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CHAPTER THREE

RESEARCH METHOD

In this chapter, the method to be used are presented under the following

headings, Research design, area of study, sample and sampling techniques, instrument

for data collection, validation of the instrument, trial testing, reliability of the

instrument, experimental procedure, control of extraneous variable, scoring of the

instrument, and method of data analysis.

Design of the Study

Quasi-experimental design was adopted in this study. Specifically, the pretest-

post test non-equivalent control group design. According to Gall, Gall and Borg (2007)

quasi-experimental design can be used when it is not possible for the researcher to

randomly sample the subjects and assign them to treatment groups without disrupting

the academic program of the schools involved in the study. Therefore, this design is

considered suitable for this study because intact classes (non-randomized groups) were

assigned to the two different groups in order to determine the effect of achievement

motivational instructional approach on primary school pupils numerical aptitude,

achievement and retention in mathematics. The design is symbolically represented

thus:

E O1 X1 O2 O3

C O1 X2 O2 O3

Where E - experimental group

C = control group

O1 = pretest

X1 = treatment experimental

X2 = treatment control

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O2 = Post test

O3 = Retention test

Area of the Study

This study was conducted in Calabar municipality Education Zone of Cross

River State Nigeria. The State is bounded by the North by Benue State, East by Akwa

Ibom and Abia States, North East by Ebonyi State, West and Southwest by Cameroun

and in the South by Atlantic ocean. The State is divided into 3 senatorial districts;

North, central and southern senatorial districts. The State comprises of 18 local

government areas of which Calabar municipality local government area is one of them.

Each local government area of the state has education authority zonal offices that

overseas the management of both public and private schools in the local government

areas.

The major languages spoken there are Efik, Ejachem and English. The local

government area is bounded by Odukpani local government area in the north south by

Calabar South local government area, in the west by Akpabuyo local government area

and in the east by the ocean and Odukpani.

Calabar municipality is one of the last local governments in the southern

senatorial districts of Cross River State and the education authority controls more

schools than any other local government because of its position as the centre of

business and as head quarters of the State. This area was chosen due to its position as

the centre and head of all educational activities where large number of pupils and

teachers reside and frequent supervision is carried out by education authority zone. This

will enable the researcher to supervise the workability of achievement motivational

instructional approach on primary school pupils in this zone.

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Population of the Study

The population of the study consist of all primary six (6) pupils in Calabar

municipality Education zone. The zone is made up of twenty four (24) public primary

schools (from the education authority zone of Calabar municipality local government

area of Cross River State as of March 2014) all of which are mixed. The schools joined

together has a population of about 2400 primary six pupils with boys numbering about

1,180 and girls about 1,220 (from the examination unit of State Ministry of Education

of Cross River State as of March 2014) where all primary six pupils are registered.

Sample and Sampling Technique

The sample for the study consisted of 241 public primary six pupils drawn from

24 public primary schools of Calabar Municipality education zone of Calabar

Municipality Local Government Area of Cross River State. Purposive sampling

technique was used to select Calabar Municipality education zone out of 18 education

zones in Cross River State. The Calabar Municipality education zone comprises of 24

public primary schools with 2,400 primary six pupils. Two schools of sample size

241primary six were selected using simple random sampling technique from 24 public

primary schools. All the schools are mixed each having 3 classes of A, B, C. One of the

schools was assigned experimental with 125 pupils and the other assigned control with

116 pupils and are used as intact classes.

Instruments for Data Collection

Two instruments were used for this study. The Mathematics Achievement Test

(MAT) (Appendix A, pg 110) and Numerical Aptitude Test (NAT) (Appendix B pg

116). The Mathematics Achievement Test (MAT) consist of 50 multiple choice test

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items and was developed by the researcher. The Mathematics Achievement Test (MAT)

consists of two sections. Section A shows the demographic variables which are name

of school, gender: Male [ ] Female [ ] and candidate register number. Section B

contain the main items which are made up of four (4) clusters.

Cluster A comprising of application of SQ3R question meant to guide a pupils reading,

recalling and reviewing. Total items in this cluster are 10 items.

Cluster B Comprising understanding mathematics language instruction with the total of

15 items meant to guide the pupils in understanding and interpretation of mathematical

statements.

Cluster C Diagnosing and treating pupils difficulties comprising of 15 items meant to

investigate areas of difficulties as to intensify strategy for solving mathematics.

Cluster D using practical activities to aid studying comprising of 10 items meant to

guide pupil working in teams practically.

The 50 multiple choice items using options A to E and are divided according to

the steps involve in achievement motivational instructional approach. The objective of

each topic (or section) guided the researcher on the depth the MAT items should cover.

The test blue print used in constructing the instrument was developed by the researcher

based on the relative emphasis in each of the sub-topic in primary six mathematics

curriculum appendix G pp. 158.

The question in each of the sections were classified into the three (3) cognitive

levels namely knowledge (K), comprehension (C), and Application, (A) which is the

lower cognitive process (LCP) for primary level of Education. The MAT items were

used to assess pupils’ cognitive achievement in primary mathematics topics.

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The Numerical Aptitude Test (NAT) was made up of two section A and B.

section A comprising of candidates name, number and gender: Male [ ] Female [ ]

while section B comprises of the main items from 1 to 50 which are in multiple choice

The NAT was a placement examination into Junior Secondary one developed by the

state ministry of education Cross River State. NAT is also a 50 multiple choice items

which is used to test the numerical aptitude of the pupils. The NAT was also used to

assess pupils’ cognitive achievement in primary six mathematics after being taught with

achievement motivational instructional approach. It is expected that the knowledge

gained from the approach will be applied to answer questions in numerical aptitude,

both in pre-testing and post-testing.

The researcher developed unit lesson plans appendix (C pp. 122) in all the

primary six mathematics topics to be used based on the test blue print using

achievement motivational instructional approach which will be used to teach

experimental group. The traditional lesson plan was also developed in all the primary

six mathematics topic to be used without involving achievement motivational

instructional approach. appendix (D pp. 137)

Validation of the Instrument

The MAT was face validated by two experts in curriculum and instructions and three

experts in mathematics education. Two of these experts from university of calabar and

three from University of Nigeria Nsukka. The validators were requested to

(a) check the suitability and clarity of the test items.

(b) Add any other items(s) which is/are relevant but had not been included in the

instrument.

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(c) Remove ambiguous or irrelevant statements in order to improve the structure of

the items. Based on the comments and suggestion of these experts, some of the

items were modified.

(d) To check the lesson plans if necessary informations were included

To ensure content validity of MAT, a test blue print or table of specification was

constructed based on the emphasis placed on each objective and content area of

Primary Six curriculum. The table of specification was based on the lower cognitive

processes; knowledge, comprehension and application. A total of fifty (50) multiple

choice items were drawn for MAT based on the lower cognitive processes. In addition

to the validation of the instrument, the lesson plans for the effective teaching of primary

six mathematics curriculum were face validated by experienced mathematics teachers.

The NAT was not validated because NAT was a standardized test from the state

ministry of education.

The MAT and NAT were trial tested to determine their stability using test-retest

method of administration on an intact class of 30 pupils at Government Primary School

Akpabuyo, Akpabuyo Local Government Area of Cross River State. This school is not

part of the sampled area for the study but have some similarities like the composition of

the pupils (mixed), the structural facilities and the same curriculum. The test retest was

carried out within an interval of two weeks.

Reliability

The data obtained from the trial testing of MAT and NAT was used to determine

the reliability coefficient of MAT and NAT. Kuder-Richardson formula (K-R20) was

found most appropriate. The reliability for MAT was 0.86 and NAT was 0.83. The

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reason for the choice of K-R20 was because the items are multiple and dichotomously

scored. K – R 20 was also to check the internal consistency of the instrument. (see

appendixes, H and I, pp. 175 and 181 respectively).

Experimental Procedure

The Numerical Aptitude Test (NAT) which is an intelligence test though not

structured by the researcher was adopted from the State Ministry of Education and also

tested alongside the Mathematics Achievement Test (MAT). The pretest of both

instruments were first conducted before the commencement of the treatment. The

pretest exercise provided the base line data that was used to compare pupils in both

groups (experimental and control). The pupils from both experimental and control

groups were taught primary six work using primary six curriculum. The experimental

group were specifically taught using achievement motivational instructional approach.

The approach was used for the purpose of mathematics achievement test and for the

purpose of any numerical aptitude test. The NAT was mostly to test the level of their

intelligence.

Furthermore, the experimental group were taught 5 lessons of 80 minutes each

(2 days at 40 minutes each) using the lesson plans based on achievement motivational

instructional approach likewise the control group were taught 5 lessons of 80 minutes

each (2 days at 40 minutes each) using the traditional teaching method. The training

lasted for 2 weeks at the end of the treatment; posttest was administered on the two

groups. Experimental group was administered with posttest of MAT and NAT and the

control group with MAT and NAT too. After the posttest, two weeks later the same

MAT and NAT were reshuffled and renumbered and re-administered to the same pupils

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(experimental and control groups) to test their level of retention. The scores obtained

from the two groups recorded and compared to determine the achievements of the

groups.

Control of Extraneous Variable

1. Experimental Bias: To avoid experimental bias, the regular class teachers in the

participating schools taught their own pupils in their group. The researcher was

therefore not directly involved in administering the instrument. To control invalidity

that could be caused by teacher variability and to ensure uniform standard in the

conduct of the research, the researcher personally prepared the teaching lesson plans

(Achievement motivational instructional approach and a traditional lesson plan

appendix C and D pp. 122 and 137 respectively). The researcher trained the

participating teachers and they were not allowed access to the test instruments until the

time it was to be administered. A three day intensive training programme was organized

for the participating teachers in the experimental school. The experimental group

teachers were trained giving detailed explanation.

2. Maturation: While the experimental treatment is in progress, changes in the research

participants (pupils) are likely to occur. Pupils might become more proficient, more

self-confident or more independent in solving mathematics problem. We might attribute

this gainful development to exposure of achievement motivational instructional

approach. It may not be clear whether the improvement was due to the approach or to

maturation. To tease out the effect of maturation, the control group of pupils who

received no exposure on achievement motivational instructional approach is equally

observed. If the group that received exposure perform better than control group that did

86

not receive exposure, it will be reasonable to say that the achievement motivational

instructional approach not maturation led to the growth in the ability to think and solve

mathematical problems. To control this, the effective use of achievement motivational

instructional approach should be encouraged in schools by organizing workshops and

seminars that can make the approach clearer to teachers. These will irrespective of the

child’s age (maturity) will make a child grow in ability to think and solve problems in

mathematics.

3. Testing: In this research the two test (MAT and NAT) used the same format. Pupils

might show improvements simply as an effect of their experience with the pretest. In

other words, they have become “test-wise”. But to control this, the items in the test

should be alternated.

4. Experimental mortality or Attrition: This is a phenomenon of losing research

participants during the course of the experiment. Some pupils either from the

experimental or control groups may drop out of the study, miss pretesting or posttesting

or are absent during some sections, attrition might result from factors such as illness,

the study is too demanding or threatening. This threatens an experiment’s internal

validity. In order to control those who missed either pretest or posttest should not be

considered. That is there will be no results for them and should be removed from the

study.

Training of Teachers

The training on achievement motivational instructional approach was conducted

in the experimental school. The teachers of the experimental classes were used for the

training. There are three (3) classes with one teacher a class therefore three teachers

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were trained for the programme. The programme of the activities for the three days was

as follows.

Day One

1. Introduction of participants on the purpose of the training exercise

2. Discussion focusing on teachers’ experiences on pupils’ inability to solve

mathematics problems correctly.

3. The researcher request to know the various approaches teachers have been

applying in the teaching and learning of mathematics.

4. The researcher tries to find out from the teachers why primary pupils exhibit

incompetencies in solving mathematics.

Day Two

The researcher went straight to the application of the achievement motivational

instructional approach to solving mathematics

5. The teachers should guide the pupils to read every mathematical statement

correctly and be able to recall and review what the child had done in the past i.e.

Application of (3R) e.g. properties of shapes, Differentiate currencies,

multiplication…,

6. Every verbal statement in mathematics must be understood and converted to a

mathematical statement that is understanding mathematics language instruction.

For instance pupils should be able to translate. Write in figures; write in words;

take to 3 decimal place; convert to percentage and so on.

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7. Diagnosing and treating pupils difficulties by giving them first simple problems

to solve as to find out areas they have problems. Give mental sums everyday to

check their ability to reason and calculate problems at a short possible time.

8. Teachers should divide their classes into groups to allow for practical exercises

and competition among themselves. The pupils should be allowed opportunity

of using appropriate instructional materials.

Day Three

9. Discussion of the unit lesson plans according to the topics.

10. Class interaction through groups performance and by coming out to the board to

teach themselves and solve problems while the researcher guides.

11. Teacher evaluate group by group and individually.

12. Closing

At the end of the training, the researcher organized a micro teaching session for the

experimental teachers to ensure that they have mastered the application of the different

stages of the instructional approach, expected of them. The teacher training guide are

reflected in (Appendix F pp. 155).

Method of Data Collection

There are 50 multiple choice items in both MAT and NAT. Each item was

scored one (1) mark. The pretest and posttest scores of both MAT and NAT were

collected for all the pupils who sat for the test except those whose results were

incomplete for final analysis.

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Method of Data Analysis

The pretest and posttest scores that were obtained from the administration of the

MAT and NAT instrument (Appendix A & B pp. 110 and 116) were analysed using

mean, standard deviation for the research questions and Analysis of Covariance

(ANCOVA) for testing of the hypotheses at 0.05 level of significance.

90

CHAPTER FOUR

RESULTS

This chapter is concerned with the presentation of result from data analysis. The results

are presented in tables according to the research questions and hypotheses that guided

the study.

Research Question 1:

What is the mean achievement score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach?

Table 1: Mean and Standard deviation of pretest posttest score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach

Variable Pre test Posttest Mean gain

N SD SD

Achievement motivational approach

125 15.44 5.22 33.65 5.56 18.21

Traditional approach 115 14.94 3.58 15.42 4.80 0.48

The result presented in Table 1 show that the achievement motivational approach

(experimental group) had a pretest mean 15.44 with a standard deviation of 5.22 and a

posttest mean 33.65 with a standard deviation of 5.56. The difference between the

pretest and posttest mean for achievement motivational approach (experimental group)

was 18.21. The Traditional approach (control group) had a pretest means 14.94 with a

standard deviation of 3.58 and a posttest mean 15.42 with a standard deviation of 4.80.

The difference between the pretest and posttest mean for Traditional approach (control

group) is 0.48. For both achievement motivational approach (experimental group) and

Traditional approach (control group), the posttest means were greater than the pretest

mean with achievement motivational approach having higher mean gain. This is

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indicative that achievement motivational approach improved pupils’ achievement in

mathematics.


What is the mean numerical aptitude score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach?

Table 2: Mean and Standard deviation of numerical aptitude score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach


N SD SD


125 14.98 5.44 39.08 7.09 24.10



(experimental group) had a pretest mean 14.98 with a standard deviation of 5.44 and a

posttest mean 39.08 with a standard deviation of 7.09. The difference between the

pretest and posttest mean for achievement motivational approach (experimental group)

was 24.10. The Traditional approach (control group) had a pretest means 10.47 with a

standard deviation of 5.91 and a posttest mean 16.56 with a standard deviation of 5.98.

The difference between the pretest and posttest mean for Traditional approach (control

group) is 6.09. For both achievement motivational approach (experimental group) and

the Traditional approach (control group), the posttest means was greater than the pretest

mean. This is indicative that achievement motivational approach improved pupils’

mean numerical aptitude score.

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What is the mean achievement score of male and female pupils taught mathematics with achievement motivational approach?

Table 3: Mean and Standard deviation of pretest posttest score of male and female pupils taught mathematics with achievement motivational approach


Gender N SD SD

Male 70 15.28 5.72 34.89 5.22 19.61

Female 55 15.65 4.55 33.09 5.97 17.44

The result presented in Table 3 show that the male group had a pretest mean 15.28 with

a standard deviation of 5.72 and a posttest mean 34.22 with a standard deviation of

5.22. The difference between the pretest and posttest mean for male group is 19.61. The

female group a pretest means 15.65 with a standard deviation of 4.55 and a posttest

mean 33.09 with a standard deviation of 5.97. The difference between the pretest and

posttest mean for female group is 17.44. For each of the two groups, the posttest means

are greater than the pretest means with male group having slightly higher mean gain.

This is indicative that achievement motivational approach appears to have improved

male pupils’ achievement in mathematics more than that of female.


What is the mean numerical aptitude score of male and female pupils taught mathematics with achievement motivational approach?

93

Table 4: Mean and Standard deviation of numerical aptitude score of male and female pupils taught mathematics with achievement motivational approach


Gender N SD SD

Male 70 14.66 4.85 39.40 7.82 24.74

Female 55 15.38 6.13 38.67 6.09 23.29

The result presented in Table 4 show that the male group had a pretest mean 14.66 with

a standard deviation of 4.85 and a posttest mean 39.40 with a standard deviation of

7.82. The difference between the pretest and posttest mean for male group is 24.74. The

female group a pretest means 15.38 with a standard deviation of 6.13 and a posttest

mean 38.67 with a standard deviation of 6.09. The difference between the pretest and

posttest mean for female group is 23.29. For each of the two groups, the posttest means

are greater than the pretest means with male group having slightly higher mean gain.

This is indicative that achievement motivational approach appears to have improved the

numerical aptitude score of both male and female pupils.


What is the mean retention of achievement score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach?

Table 5: Mean and Standard deviation of retention score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach

Variable Post test Retention score Mean gain

N SD SD


125 33.65 5.56 37.43 4.75 3.78


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(experimental group) had a posttest mean 33.65 with a standard deviation of 5.56 and a

retention mean score of 37.43 with a standard deviation of 4.75. The difference between

the posttest and retention mean score for achievement motivational approach

(experimental group) was 3.78. The Traditional approach (control group) had a posttest

means score of 14.42 with a standard deviation of 4.80 and a retention mean score of

16.21 with a standard deviation of 4.00. The difference between the posttest and

retention mean score for Traditional approach (control group) is 1.79. For achievement

motivational instructional approach (experimental group) and the Traditional approach

(control group), the retention means score were greater than the posttest mean score

with achievement motivational approach having higher mean retention gain. This is

indicative that achievement motivational approach enhanced higher retention than the

Traditional approach.


What is the mean retention numerical aptitude score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach?

Table 6: Mean and Standard deviation of retention numerical aptitude score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach

Variable Post test Retention score Mean gain

N SD SD


125 39.08 7.09 41.48 4.65 2.40


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(experimental group) had a posttest numerical aptitude mean 39.08 with a standard

deviation of 5.56 and a retention mean score of 41.48 with a standard deviation of 4.65.

The difference between the posttest and retention mean score in numerical aptitude for

achievement motivational approach (experimental group) was 2.40. The Traditional

approach (control group) had a posttest numerical aptitude means score of 16.56 with a

standard deviation of 5.98 and a retention mean score of 17.05 with a standard

deviation of 6.10. The difference between the posttest and retention mean score in

numerical aptitude for Traditional approach (control group) is 0.49. For both

achievement motivational approach (experimental group) and Traditional approach

(control group), the retention means score were higher than the posttest mean score

with achievement motivational approach having higher mean retention gain. This is

indicative that achievement motivational approach enhanced retention more than the

Traditional approach.


What is the mean retention of achievement score of male and female pupils taught

mathematics with achievement motivational approach?

Table 7: Mean and Standard deviation of retention score of male and female pupils taught mathematics with achievement motivational approach

Variable Post test Retention test Mean gain

Gender N SD SD

Male 70 34.09 5.22 45.83 4.57 11.74

Female 55 33.09 5.97 44.47 4.91 11.38

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The result presented in Table 7 show that the male group had a post test mean 34.09

with a standard deviation of 5.22 and a retention test mean 45.83 with a standard

deviation of 4.91. The difference between the post test and retention test mean for male

group is 11.74. The female group a post test means 33.09 with a standard deviation of

5.97 and a retention test mean 44.47 with a standard deviation of 4.91. The difference

between the post test and retention test mean for female group is 11.38. For each of the

two groups, the retention mean scores were greater than the post test means. This is

indicative that achievement motivational approach appears to have improved both male

and female pupils’ retention in Mathematics.


What is the mean retention of numerical aptitude score of male and female pupils

taught mathematics with achievement motivational approach?

Table 8: Mean and Standard deviation of retention numerical aptitude score of male and female pupils taught mathematics with achievement motivational approach

Variable Post test Retention test Mean gain

Gender N SD SD

Male 70 39.40 7.82 46.79 4.78 7.39

Female 55 38.67 6.09 44.09 4.50 5.42

The result presented in Table 8 show that the male group had a post test mean 39.40

with a standard deviation of 7.82 and a retention test mean 46.79 with a standard

deviation of 4.78. The difference between the post test and retention test in numerical

aptitude for male group is 7.39. The female group had a post test means 38.87 with a

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standard deviation of 6.09 and a retention test mean 44.09 with a standard deviation of

4.50. The difference between the post test and retention test mean for female group is

5.42. For each of the two groups, the retention mean scores were higher than the post

test means. This is indicative that achievement motivational approach appears to have

improved the retention of numerical aptitude score of both male and female pupils.

Hypotheses 1

H01: There is no significant difference between the mean achievement score of pupils



Table 9: Analysis of Covariance (ANCOVA) of the mean achievement score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach

Source Type III Sum

of Squares

df Mean Square F Sig.

Corrected Model 22183. 263a 4 5545.816 202.633 .000

Intercept 11307.820 1 11307.820 413.164 .000

Preachievement 0.071 1 0.071 0.003 .959

Group 21755.839 1 21755.839 794.914 .000

Sex 24.108 1 24.108 .881 .349

Group * Sex 7.543 1 7.543 .276 .600

Error 6431.671 235 27.369

Total 171892.000 240

Corrected Total 28614.930 239

a. R Squared = .775 (Adjusted R Squared = .771)

The result in Table 9 shows that an F-ratio of 794.914 with associated probability value

of 0.000 was obtained with regards to the mean achievement score of pupils taught

mathematics with achievement motivational approach and those taught with traditional

approach. Since the associated probability (0.000) was less than 0.05, the null

hypothesis (H01) was rejected. Thus, there was a significant difference between the

98

mean achievement score of pupils taught mathematics with achievement motivational

approach and those taught with traditional approach. This implies that the use of

achievement motivational approach improves achievement of pupils in mathematics.

Hypotheses 2




Table 10: Analysis of Covariance (ANCOVA) of the mean numerical aptitude score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach

Source Type III Sum

of Squares



Intercept 23257.323 1 23257.323 533.128 .000

Preaptitude 11.321 1 11.321 0.260 .611

Group 24893.149 1 24893.149 750.626 .000

Sex 41.366 1 41.366 .948 .331

Group * Sex 1.164 1 1.164 .027 .870

Error 10251.699 235 43.624

Total 232733.000 240



The result in Table 10 shows that an F-ratio of 174.430 with associated probability

value of 0.000 was obtained with regards to the mean numerical aptitude score of pupils


traditional approach. Since the associated probability (0.000) was less than 0.05, the

null hypothesis (H02) was rejected. Thus, there was a significant difference between the

mean numerical aptitude score of pupils taught mathematics with achievement

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motivational approach and those taught with traditional approach. This implies that the

use of achievement motivational approach improves the mean numerical aptitude score

of pupils in mathematics.

Hypotheses 3

H03: There is no significant difference between the mean achievement scores of male

and female pupils taught mathematics with achievement motivational approach.

. The result for this hypothesis is presented in Table 9

The result in Table 9 shows that an F-ratio of 0.88 with associated probability value of

0.349 was obtained with regards to the mean achievement score of male and female

pupils taught mathematics with achievement motivational approach. Since the

associated probability (0.349) was greater than 0.05, the null hypothesis (H03) was not

rejected. Thus, there was no significant difference between the mean achievement score

of male and female pupils taught mathematics with achievement motivational approach.

This implies that the use of achievement motivational approach does not result in

difference in achievement between male and female pupils in mathematics.

Hypotheses 4



approach

The result for this hypothesis is presented in Table 10


0.331 was obtained with regards to the mean numerical aptitude score of male and

female pupils taught mathematics with achievement motivational approach. Since the


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rejected. Thus, there was no significant difference between the mean numerical aptitude

score of male and female pupils taught mathematics with achievement motivational

approach. This implies that the use of achievement motivational approach does not

result in difference in the numerical aptitude score between male and female pupils in

mathematics.

Hypotheses 5

H05: There is no significant difference between the mean retention of achievement

scores of male and female pupils taught mathematics with achievement


Table 11: Analysis of Covariance (ANCOVA) of the mean retention of achievement score of male and female pupils taught mathematics with achievement motivational approach.

Source Type III Sum

of Squares



Intercept 7132.551 1 7132.551 369.528 .000

Postachievement 0.438 1 0.436 0.023 .880

Group 4945.824 1 4945.824 256.236 .000

Sex 1.702 1 1.702 .088 .767

Group * Sex 84.685 1 84.685 4.387 .037

Error 4535.923 235 19.302

Total 189998.000 240




0.767 was obtained with regards to the mean retention of achievement score of male

and female pupils taught mathematics with achievement motivational approach. Since

the associated probability (0.767) was greater than 0.05, the null hypothesis (H05) was

not rejected. Thus, there was no significant difference between the mean retention of

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achievement score of male and female pupils taught mathematics with achievement

motivational approach. This implies that the use of achievement motivational approach

does not result in difference in retention of achievement between male and female

pupils in mathematics.

Hypotheses 6

H06: There is no significant difference between the mean retention of numerical


motivational approach

Table 12: Analysis of Covariance (ANCOVA) of the mean retention of numerical aptitude score of male and female pupils taught mathematics with achievement motivational approach.

Source Type III Sum

of Squares


Corrected Model 22972.555a 4 5743.139 205.567 .000

Intercept 5904.934 1 5904.937 211.358 .000

Postaptitude 340.330 1 340.330 12.193 .001

Group 3551.091 1 3551.091 127.106 .000

Sex 0.552 1 0.552 0.020 .888

Group * Sex 25.794 1 25.794 0.923 .338

Error 6565.441 235 27.938

Total 206719.000 240




0.888 was obtained with regards to the mean retention of numerical aptitude score of

male and female pupils taught mathematics with achievement motivational approach.

Since the associated probability (0.888) was greater than 0.05, the null hypothesis (H06)

was not rejected. Thus, there was no significant difference between the mean retention

of numerical aptitude score of male and female pupils taught mathematics with

achievement motivational approach. This implies that the use of achievement

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motivational approach does not result in difference in the retention of numerical

aptitude score between male and female pupils in mathematics.

Hypotheses 7





0.600 was obtained with regards to the interaction effect of approaches and gender on

the mean retention of achievement scores of pupils in mathematics. Since the associated

probability (0.600) was greater than 0.05, the null hypothesis (H07) was not rejected.

Thus, there was no significant interaction effect of approaches and gender on mean


Hypotheses 8





of 0.870 was obtained with regards to the interaction effect of approaches and gender

on the mean numerical aptitude scores of pupils in mathematics. Since the associated

probability (0.870) was greater than 0.05, the null hypothesis (H08) was not rejected.

Thus, there was no significant interaction effect of approaches and gender on mean


Hypotheses 9



103




on the mean retention of achievement scores of pupils in mathematics. Since the

associated probability (0.037) was less than 0.05, the null hypothesis (H09) was rejected.

Thus, there was significant interaction effect of approaches and gender on mean


Hypotheses 10






on the mean retention of numerical aptitude scores of pupils in mathematics. Since the


rejected. Thus, there was no significant interaction effect of approaches and gender on

mean retention of numerical aptitude scores of pupils in mathematics.

Summary of Findings

The summary of the findings is presented below:

• There was a significant difference between the mean achievement score of



• There was a significant difference between the mean numerical aptitude score of



104

• There was no significant difference between the mean achievement score of


approach.

• There was no significant difference between the mean numerical aptitude score

of male and female pupils taught mathematics with achievement motivational

approach.

• There was no significant difference between the mean retention of achievement

score of male and female pupils taught mathematics with achievement


• There was no significant difference between the mean retention of numerical



• There was no significant interaction effect of approaches and gender on mean




• There was significant interaction effect of approaches and gender on mean




105

CHAPTER FIVE

DISCUSSION, CONCLUSION AND SUMMARY OF THE STUDY

This chapter presents the discussions, conclusions, educational implications,

recommendations, limitations and suggestions for further researchers and summary of

the study. The discussions were done according to the following re-stated findings:

DISCUSSION

This study sought to investigate the effect of achievement motivational

instructional approach on primary six pupils’ numerical aptitude and retention in

mathematics. The results revealed that there was a significant difference between the

mean achievement score of pupils taught mathematics with achievement motivational

approach and those taught with traditional approach. This implies that the use of

achievement motivational instructional approach improves achievement of pupils in

mathematics. Evidence from the results revealed that the mean gain for the achievement

motivational instructional approach group was 18.21 in table 1 and the traditional

approach group was 0.48 same table 1. The findings of this study is similar to those of

Jegede & Jegede (1990) who found out that, there was significant difference in the

performance of pupils in English taught with achievement motivational instructional

approach.

It is interesting to note that the traditional approach group which was the control

for the experiment lost some mean value based on the difference between the posttest

and pretest means. It is evident that other factors other than methods of instruction can

lead to some changes in the achievement of pupils (Rothman, 2004).

106

The second finding of the study was that, there was a significant difference

between the mean numerical aptitude score of pupils taught mathematics with

achievement motivational approach and those taught with traditional approach. This

implies that the use of achievement motivational instructional approach improves the

mean numerical aptitude score of pupils in mathematics. The findings showed that the

mean gain of pupils taught mathematics with achievement motivational instructional

approach group was 24.10 and is higher than that of the traditional approach group

(6.09) in table 2. This result indicated that the achievement motivational instructional

approach group improved their numerical aptitude score better than the traditional

approach group.

The result on methods of instruction and numerical aptitude score negates that of

Okwuajioko (2002) who found out that there was no significant difference in

achievement motivational instructional approach and numerical aptitude of the primary

school pupils. The use of achievement motivational instructional approach enhances in-

depth and proper connection, organization and integration of concepts into pupils’

knowledge structure through Scan Question, Read, Recall and Review practice. This in

turn may have aided improved numerical aptitude score of pupils

The third finding of the study revealed that there was no significant difference

between the mean achievement score of male and female pupils taught mathematics

with achievement motivational instructional approach. This implies that the use of

achievement motivational approach does not result in difference in achievement

between male and female pupils in mathematics. This finding differs from that of

Agwagah, (2000) who established that there is differential performance in mathematical

107

activities due to gender especially in favour of boys. It also varies from the opinion of

Harbor-Peters (2001) who observed that mathematics is a male stereotype especially as

it is regarded as abstract and difficult with attributes which boys are attracted to. Also

Al-Emadi, (2003) observed that boys exert better mathematics achievement than the

girls because the boys from the beginning are encouraged to be more independent than

the girls, therefore differential treatment of sex has given the boys more confidence

than girls and this enhances better performance in favour of boys, in mathematics.

However, the findings is in line with that of Aydin (2013) who concluded that

female pupils these days are equally good in mathematics as their male counterparts.

Also, Urdan (2010) stated that motivational condition influence both male and female

to perform equally well at all levels in mathematics test and examination. The use of

achievement motivational instructional approach will help to bridge the gap between

males and females observed by other researchers in the past and in the present.

The fourth findings from table 4 was that there was no significant difference

between the mean numerical aptitude score of male and female pupils taught

mathematics with achievement motivational instructional approach. This implies that

the use of achievement motivational instructional approach does not result in difference

in the numerical aptitude score between male and female pupils in mathematics. This

finding is in line with that of Umar and Momoh (2001) who stated that there was no

statistical difference in the performance of boys and girls on quantitative and other

aptitude test. The achievement motivational instructional approach used in this study

was taught to both male and female equally and also the equality in the achievement of

male and female pupils in table 3 and 4 agrees with Gregory (2011) who viewed that

108

primary six pupils are in the same age bracket of plus and minus eleven (11) years and

achievement in mathematics at this age is not noticeable as to whether boys or girls do

better. This was probably responsible for equality in the observed achievement of male

and female pupils used in this study. This implies that when male and female pupils are

given similar condition to operate they perform equally.

The fifth finding was that there was no significant difference between the mean

retention of achievement score of male and female pupils taught mathematics with

achievement motivational instructional approach. This implies that the use of

achievement motivational instructional approach does not result in difference in

retention of achievement between male and female pupils in mathematics. The result

presented in Table 5 indicates that both achievement motivational instructional

approach and traditional approach appears to have similar retention influence. The

achievement motivation instructional approach in table five had a higher retention

influence. This appears to be consistent with the studies conducted by Aydin and

Coskun (2011), and Pe’rez, (2013) that showed no significance difference in

mathematics achievement and retention between male and female students. The

similarity in the retention of male and female pupils was in agreement with that of

Aydin and Coskun (2011), and Perez, (2013) whose respective works did not show any

significant difference according to gender. This could be attributed to the fact that the

pupils were given enabling environment to work together effectively. They were

equally given the same opportunity and conditions that made them to understand better

thereby obtaining similar retention.

109

The sixth findings in table 7 and 8 were that there was no significant difference

between the mean retention of numerical aptitude score of male and female pupils

taught mathematics with achievement motivational instructional approach. This implies

that the use of achievement motivational instructional approach does not result in

difference in the retention of numerical aptitude score between male and female pupils

in mathematics. This finding appears to be inconsistent with the study conducted by

Okwuajioko (2002) whose findings shows that there is a significance difference in the

numerical aptitude of the primary school pupils due to gender with males performing

better than the female. The work of Sam, Joshua and Asim (2010) on the other hand

revealed significant gender inequality and the girls having high retention over the boys.

The contradicting findings may not be far from the different conditions under which the

studies were conducted. The no significant difference between male and female pupils

in the mean retention of numerical aptitude score might have been caused by the fact

that the treatment was equally appealing to both males and females.

Other findings revealed that there was no significant interaction effect of

instructional approaches and gender on mean achievement scores of pupils in

mathematics. The result therefore implies that the combined effect of instructional

approaches and gender on mean achievement scores of pupils did not influence their

achievement in mathematics. In other words, the effectiveness of the interaction was the

same for males and females groups with respect to their achievement. The no

interaction effect between instructional approaches and gender on mean achievement

scores of pupils in mathematics could be attributed to the fact that instructional

approaches are school factors while gender is a biological and socio-cultural factors.

110

This finding tends to agree with Gregory, (2011) who found out that there was no

significant interaction effect between instructional approaches and gender on mean


Again, no significant interaction effect of instructional approaches and gender on

mean numerical aptitude scores of pupils was detected. The no significant interaction

effect between instructional approaches and gender on mean numerical aptitude scores

of pupils could be attributed to the impact of extra-cognitive numerical aptitude tasks

due to the treatment on male and female pupils. Both male and female pupils

experienced and enjoyed the treatment atmosphere in different ways. This might have

resulted in the combined effect of the treatment and gender not influencing any change

in the numerical aptitude scores of pupils. This result is inline with Okwujiako (2002)

who also acknowledged that there was no significance interaction effect of instructional

approach and gender on mean retention of numerical aptitude.

Significant interaction effect of instructional approaches and gender on mean

retention of achievement scores of pupils in mathematics was evidential. The result

therefore implies that the combined effect of instructional approaches and gender on

mean retention of achievement scores of pupils influence their achievement in

mathematics. In other words, the effectiveness of the interaction was not the same for

males and females groups with respect to their achievement. This implies that when

instructional approaches interaction with gender, male and female pupil appears to

retain what they have been taught in mathematics differently. This result agreed with

Eze (2011) who found out that there was a significance interaction effect of

111

instructional approaches and gender on mean retention of achievement scores of

students in mathematics.

Finally no significant interaction effect of instructional approaches and gender

on mean retention of numerical aptitude of pupils was detected. The result therefore

implies that the combined effect of instructional approaches and gender on mean

retention of numerical aptitude scores of pupils did not influence their retention in

numerical aptitude. In other words, the effectiveness of the interaction was the same for

males and females groups with respect to their numerical aptitude. This implies that

when instructional approaches interaction with gender, male and female pupil appears

to retain what they have been taught in numerical aptitude equally.

CONCLUSIONS

The study set out to investigate the effect of achievement motivational


mathematics. Based on the findings of this study, the following conclusions have been

made; the achievement motivational instructional approach was found to be capable of

enhancing pupils’ achievement and retention in mathematics and numerical aptitude.

Consequently, achievement motivational instructional approach could revamp teaching

and learning of mathematics and numerical aptitude with reasonable functionality.

Another conclusion drawn from the results of this study is that achievement

motivational instructional approach narrowed the gap that existed between the

achievement of male and female pupils as reported by Aydin and Coskun (2011). The

instructional approach provided male and female pupils with the opportunities to solve

mathematical and numerical aptitude tasks well. The use of achievement motivational

112

approach does not result in difference in the numerical aptitude score between male and

female pupils in mathematics.

The results of this study also lead to the conclusion that the use of achievement

motivational instructional approach improved the retention of numerical aptitude score

between male and female pupils in mathematics.

It can also be concluded that no significant interaction effect of instructional

approaches and gender on mean achievement scores of pupils in mathematics. The

combined effect of instructional approaches and gender on mean achievement scores of

pupils did not influence their achievement in mathematics.

Lastly the results of this study lead to the conclusion that when instructional

approaches interaction with gender, male and female pupil appears to retain what they

have been taught in mathematics differently.

EDUCATIONAL IMPLICATIONS

The results of this study have some implications to mathematics education,

especially in the area of teaching and learning. For instance, achievement motivational

instructional approach provided a framework for integration of how to Scan Question,

Read, Recall and use Review practice into pupils’ knowledge structure. A deficiency on

Scan Question, Read, Recall and use Review practice on the part of the pupil may have

accounted for persistent failure in mathematics and students hating mathematics.

Therefore, proper use of achievement motivational instructional approach may help

pupils to effectively solve mathematics problems

113

With the achievement motivational instructional approach, pupils’ retention in

mathematics can be improved. This in turn will make the teaching and learning of

mathematics as well as problem solving better than it has been. If this is done, it will

not only increase achievement of pupils but will help them understand mathematics

concepts better.

For curriculum designers, these results will guide them in the development and

designing of the primary school curriculum for mathematics and numerical aptitude. It

might in turn influence them to plan curriculum documents in relation to the strategies

for solving problems associated with the content

The results will help pupils have a better understanding of how to handle several

tasks in mathematics and numerical aptitude. This will consequently improve their

achievement in mathematics and numerical aptitude. In this respect, pupils will be

motivated to put in extra efforts on their own part to improve their achievement without

waiting on what the other stakeholders will do.

RECOMMENDATIONS

Based on these findings, it was recommended that achievement motivational

instructional approach should be part of mathematics education curriculum

implementation programme. This will enhance achievement and retention in

mathematics and numerical aptitude.

Teachers of mathematics need to be periodically given orientation course on the

use of achievement motivational instructional approach to help them get used to this

instructional approach.

114

Achievement motivational instructional approach activities need much time. The

preparation of official school time-table should take into cognizance of that and make

provisions for extra time to accommodate the use of this method.

Mathematics teachers should also be motivated so as to persist when they encounter

obstacles and difficulties in applying this approach as it is very demanding and time

consuming.

Teachers should make efforts to direct the presentation of mathematics lessons from the

traditional approach to a more learner centered approach which is achievement

motivational instructional approach.

LIMITATIONS

The generalizations drawn from this study are subject to the following limitations;

The teachers were all trained for the teaching of the research lessons, and the

researcher ensured that the same teaching materials, teaching methods and pupil

activities were used, but other intervening variables like mastery of content, teaching

experience, communication skills, and classroom environment skills of the teachers

might have affected the results of the study.

The achievement motivational instructional approach if well applied is time consuming

and normally required more time than the normal school time-table could tolerate.

The achievement motivational instructional approach is relatively strange to the

mathematics teachers and there are no available textbooks on the approach for teachers

to refer to and even for pupils to use.

115

Suggestions for Further Studies

• This study is limited to the mathematics and numerical aptitude achievement, a

similar study could be carried out in different subject area and the results

compared to this results.

• A study on the effect of Achievement motivational instructional approach with

other innovative approaches on the mathematics and numerical aptitude

achievement could be carried out.

• Another investigation could be carried out with variables like, interest, school

location, larger sample size etc.

SUMMARY

This study sought to investigate the effect of achievement motivational


mathematics. Eight research questions and ten hypotheses guided the study.

Discussions of findings were done according to the hypotheses that guided the study.

conclusions were drawn from the results of the investigation. It was concluded that the

achievement motivational instructional approach was found to be capable of enhancing

pupils’ achievement and retention in mathematics and numerical aptitude. It was also

concluded that achievement motivational instructional approach does not result in

difference in the numerical aptitude score between male and female pupils in

mathematics, it was equally concluded that when instructional approaches interaction

with gender, male and female pupil appears to retain what they have been taught in

mathematics differently among others.

116

Some recommendations were made to the Government, education authorities

and teachers, the educational implications that stem from this study were also outlined

by the researcher, and lastly the limitations and suggestions for further studies based on

the results of the study were proposed.

117

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Work group of the American Psychological Associations Board of Education Affairs (1995). Learner-centered psychological principles: A framework for school reform and redesign. Washington, D.C: American Psychological Association.

Yara, P.O. (2009). Students attitude Towards Mathematics and Academic Achievement in some selected Secondary Schools in Southwest Nigeria European Journal of Scientific Research, 136 (3), 336-341.

Zakariyya, A.A. (2014). Effects of Metacogintive skills on Achievement and Attitude of Senior Secondary Students ABACUS: The Journal of the Mathematical Association of Nigeria, 39(1), 64-73.

125

APPENDIX A

Mathematics Achievement Test (MAT)

Section A

Name of School ----------------------------

Class – Primary Six (6) Gender: Male [ ] Female [ ]

Time allowed 1 ½ hrs Candidate No: -------------------------------------

Section B

Cluster A: (Application of SQ3R)

(1) An equilateral triangle has the following properties except.

(a) All the 3 sides of an equilateral triangle are equal in length

(b) All the 3 angles are equal

(c) All the 3 lines of symmetry meet at a point.

(d) Each line of symmetry bisects the base at right angles, and also bisects the

angle at the vertex

(e) All of the above.

2. Write in figures Eight billion, seven hundred and sixty-five million, four

hundred and thirty-two thousand, five hundred and forty three.

(a) 8765432543 (b) 8756432543 (c) 876532443

(d) 8755431588 (e) 856, 432 54321

3. In a class the ratio of the number of boys to the number of girls is 3: 4. There

are 18 boys in the class. How many girls are in the class

(a) 24 (b) 25 (c) 23 (d) 28 (e) 26

4. Correct 2.992 to 2 decimal places

(a) 2.99 (b) 29.9 (c) 2.10 (d) 299 (e) 3.0

5. Express 45 as a product of prime factors

(a) 3 × 3 × 5 (b) 2 × 3 × 5 (c) 4 × 3 × 3 (d) 9 × 5 (e) 3 × 3 × 6

6. Convert 100

15 to percentage

(a) 25% (b) 15% (c) 75% (d) 30%

7. What does the letter d represent in the expression 81-d = 32

(a) 49 (b) 42 (c) 38 (d) 113 (e) 1.25

126

8. There are 40 pupils in the class. If 25% are absent, how many pupils are present

(a) 30 (b) 10 (c) 40 (d) 20 (e) 15

9. By how much is (3/4 + 1/12 + 2/3) greater than 1.

(a) ½ (b) ¾ (c) 1/5 (d) 2/5 (e) 4/20

10. Arrange 0.306, 0.7, 0.089 in ascending order.

(a) 0.306 , 0.7, 0.089 (b) 0.7, 0.306, 0.089 (c) 0.089, 0.7, 0.306

(d) 0.306, 0.089, 0.7 (e) 0.089, 0.306, 0.7

Cluster B: (Understanding the mathematics language instruction)

11. Write 5 ×5×5×5×5×5 in index form

(a) 510 (b) 56 (c) 55 (d) 57 (e) 5×52

1.2 what fraction is shaded

(a) 6

5 (b)

6

2 (c)

6

1 (d)

8

3 (e)

8

2

13. The number of people in a group is known as

(a) census (b) figure (c) population (d) demograph (e) frequency

14. What is the correct formular for finding simple interest

(a) S.I = R

100 T P ×× (b) S.I =

100

T R× (c) S.I =

100

R T P ××

(d) S.I = RP

T R 100

×××

(e) S.I P100

T R

××

15. If the current rate of £1 = N225.00, by calculation convert £12.00 to Naira

(a) N4800 (b) N2700 (c) N6800 (d) N3300 (e) N4500 16. How many odd numbers are between 1 and 20

(a) 2, 4, 6, 8, 10 (b) 10 (c) 5 and 10 (d) 8 (e) 12

17. How many degrees does the hour hand of a clock make as it moves from 1 to 2

O’clock.

(a) 450 (b) 600 (c) 150 (d) 300 (e) 900

18. Write down your finishing direction starting at North, turn clockwise 900

(a) South West (b) South South (c) North South (d) East (e) West

19.

(a) 5.5km/h (b) 3.6km/h (c) 4.5km/h (d) 2.5km/h (e) 6.6km/h

110km/h 20km/h ?

127

20. Reduce 75

15 to its simplest fraction

(a) 5

1 (b)

5

3 (c)

15

5 (d)

15

1 (e)

4

3

21. If the number of people infected with HIV in Nigeria is 2900 000 and Ghana is

320,000. By how much is Nigeria greater than Ghana.

(a) 2, 580, 000 (b) 2, 560,000 (c) 1,250,000 (d) 320,000

(e) 2900, 000

22. If a = 5, b = 6 and C = 1 without calculator find a

c b a ××

(a) 10 (b) 6 (c) 8 (d) 5, (e) 4

23. Find the square root of 81

16

(a) 81

16 (b)

9

4 (c)

9

2 (d)

8

4 (e)

9

3

24. Find the sum of 2 ½ and the product of 1 ¼ and 1/3 and leave the answer in its

simplest form

(a) 32

1 (b) 2

12

11 (c) 3

12

11 (d) 4

12

11 (e) 3

5

5

25. Find the missing number in the box 9

4

3 =

(a) 16 (b) 12 (c) 15 (d) 21 (e) 18

Cluster C: (Diagnosing and treating pupils difficulties.)

26. Write 209 in Roman numerals

(a) CCIX (b) CMX (c) XXIV (d) CIXC (e) XCIV

27. What is the median of an even distribution

(a) Average of the number (b) the middle number

(c) the average of the two middle numbers (d) the last number

(e) the first number.

Use the figure below to answer question 28 and 29

C

D E

B

P

F

G

Q

A

H

I R I

128

28. What type of triangle is ABC

(a) Equilateral (b) Isosseles (c) Right-angled (d) obtuse (e) acute.

29. In the triangle side BC is called

(a) Adjacent (b) Hypotenuse (c) opposite (d) Parallel

(e) Longitudinal.

30. Reduce the figure below to a smaller size using a scale of 1: 5

(a) (b)

(c) (d) (e)

31. If the scale is 1cm = 10m, what will be the measurement of 10m on the ground

(a) 100m (b) 120m (c) 150m (d) 125m (e) 90m

32. By folding a rectangle along its lines of symmetry. How many lines of

symmetry does a rectangle have

(a) 3 (b) 2 (c) 4 (d) 5 (e) 1

33. Use your protractor and measure the angle X and y and their sum will be equal

to

(a) 900 (b) 1800 (c) 3600 (d) 450 (e) 800

34. What was the highest number thrown

(a) 3 and 4 (b) 3 and 5 (c) 2 and 5 (d) 4 and 2 (e) 4 and 5

35. If find

(a) 3

2 (b) 0.25 (c) 0.5 (d)

5

3 (e) 0.75

2

0.25

8 3

?

6

20cm

15cm 15cm

20cm

5cm

3cm

4cm

3cm 3cm

5cm

4cm

2cm

5cm

2cm

6cm

4cm

y

x

129

36. If Find

(a) 18 (b) 16 (c) 12 (d) 24 (e) 48

37. 14 × [ ] = 504 find [ ]

(a) 40 (b) 50 (c) 36 (d) 46 (e) 35

38. What is the value of 49 - 9 16 +

(a) 6 (b) 7 (c) 0 (d) 3 (e) 21

39. A boy got 50 marks out of 75 in a test. What percentage is this

(a) 66% (b) 65% (c) 68% (d) 66.67% (e) 55%

40. A factory uses 35 tonnes of coal every 5 days, how many tones are used in 15

days

(a) 15 tonnes (b) 65 tonnes (c) 12 tonnes (d) 105 tonnes (e) 48 tonnes

Cluster D: (Using practical activities to aid studying)

Use the data given to answer questions 41 and 42 i.e. 10, 9, 8, 13, 17, 16, 13, 13, 9

41. What is the mode

(a) 10 (b) 9 (c) 13 (d) 16 (e) 17

42. What is the median score

(a) 9 (b) 16 (c) 13 (d) 10 (e) 8

43. What is the sum of the interior angle of a hexagon

(a) 6000 (b) 4200 (c) 1350 (d) 7200 (e) 1500

44. A polygon whose sides and angles are equal is called

(a) A regular polygon (b) square (c) equilateral triangle

(d) convex polygon (e) concave polygon

45. All are example of cuboid except

(a) box of sugar (b) match box (c) building block

(d) All of the above (e) maggi

46. By measurement, what do you discover about the length of the diameter of a

circle.

(a) All diameter of a circle are equal in length

35

21

3:5

36

?

3:1

130

(b) All diameters of a circle are different in length

(c) All diameter of a circle are shorter

(d) All diameters of a circle are round

(d) None of the above.

47. If find

(a) (b) (c)

(d) (e)

48. The sum of two numbers is 24. one of the numbers is twice the other, find the

two numbers

(a) 4 and 5 (b) 6 and 8 (c) 12 and 15 (d) 16 and 8 (e) 15 and 12

If

49. What is the correct name of the angle

(a) < AOB (b) < OBA (c) <OAB (d) <BOA

(e) < BAO

Use this information to answer questions 50.

Thirty pupils in a class throw dice. The number each pupil got is

4 6 4 1 5 5 4 3 2 5

6 3 5 2 4 3 6 2 1 3

4 1 3 6 5 2 3 1 5 2

50. What was the median number

(a) 5.5 (b) 6.5 (c) 4.5 (d) 3.5 (e) 6.2.

15 2

30 45

16 ?

48 ?

16 2

48 32

16 3

48 35

16 3

48 30

16 4

48 40

16 5

48 35

180km/h 45km/h 4 km/h

B

A

O

131

APPENDIX B

Numerical Aptitude Test (NAT)

132

SECTION NUMERICAL APTITUDE TEST NAT

OBJECTIVES

INSTRUCTION: Each question carries one mark. Choose the correct answers from

OPTIONS A-E for each question and work write down the letter on your answer

booklet

1. Express 400102 in words

(a) Four thousand one hundred and two

(b) Four million one hundred and two

(c) Four hundred thousand one hundred and two

(d) Four thousand and two

(e) Forty thousand one hundred and two

2. Write in figure Eighty-Six thousand, Seven Hundred and Sixty-Four

(a) 68784 (b) 87764 (c) 80064 (d) 86764 (e) 860764

3. What is the place value of 5 in 47.015? (a) 5 tens (b) 5 units

(c) 5 thousandths (d) 5tens (e) 5 hundredths

4. Express 940 in Roman Numerals

(a) XLXC (b) CMXL (c) MCLX (d) CDML (e) MCLX

5. Find the sum of the following numbers 348, 25,1425 and 113

(a) 1921 (b) 1911 (c) 1081 (d) 1231 (e) 1913

6. Which of the following is a prime number?

(a) 1(b) 4 (c) 10 (d) 15 (e) 2

7. The difference between 0.0754 and 1 is

(a) 0.9246 (b) 0.2946 (c) 1.0754 (d) 0.4296 (e) 1.0292

8. Which of the following numbers cannot be divided by 3 without any reminder?

(a) 30 (b) 42 (c) 54 (d) 69 (e) 74

9. Calculate 2013-2015+2002-2000

(a) 0 (b) 4 (c) 2 (d) 2013 (e) 2006

10. Find the sum of 1/3 of 18 and ¼ of 4

(a) 6 (b) 12 (c) ½ (d) 4 (e) 7

11. What is the cost of 5kg of carrots if two kg of carrots cost 80?

(a) 120 (b) 150 (c) 200 (d) 400 (e) 800

133

12. Express 40 Kobo as a fraction of 3 naira.

(a) 40 (b) 15 (c) 1/15 (d) 3/40 (e) 2/15

13. Reduce 21/28 to its lowest terms

(a) 7/14 (b) 7/14 (c) 3/7 (d) ¾ (e) 2/15

14. Find the value of y it 4/7y=22/3

(a) 42/3 (b) 22/3 (c) 52/3 (d) 11/3 (e) 4/7

15. Three-Quarters of a certain number is 12. What is the number?

(a) 24 (b) 20 ( c) 16 (d) 8 (e) 36

16. What fraction of 2m is 25cm?

(a) 1/5 (b) 1/8 (c) 2/25 (d) ¼ (e) 2/5

17. Change 151/100 to a decimal number

(a) 0.151 (b) 1.51 (c) 15. 1 (d) 15.2 (e) 01.51

18. Obi and Doreas shared 120 stamps in the ratio 2:3 how many stamps was Obi’s

share?

(a) 60 (b) 40 (c) 72 (d) 48 (e) 20

19. What must be added to 1/8 to make5/6?

(a) 17/24 (b) 7/8 (c) 20/24 (d) 12/28 (e) 21/8

20. Find the product of 81/2 and 6

(a) 17 (b) 51 (c) 84 (d) 33 (e) 34

21. Change 2.75 to an improper fraction

(a) 55/2 (b) 11/4 (c) 275/10 (d) 9/2 (e) 3/35

22. How many 200ml glasses can you fill from a l5litres container of fruit juice?

(a) 10 (b) 20 (c) 25 (d) 30 (e) 50

23 What is 2/3 of N=45.00

(a) =N=30.00 (b)=N=20.00 (c) =N=60.00 (d) =N=50.00 (e) =N=25.00

24. Divine’s father is 36 years old. If divines’ age is one third of the father’s age,

what is Divine’s age?

(a) 24yers (b) 18years (c) 12years (d) 9 years (e) 30 years

25. 4men take 5days to dig a trench. How many men will dig the same trench in 2

days?

(a) 4 men (b) 10 men (c) 8 men (d) 6 men (e) 12 men

134

26. Find the area of a square with length 9cm long.

(a) 18cm2 (b) 36cm2 (c) 45cm2 (d) 36cm2 (e) 81cm2

27. Simplify 3 1/3 +4 12+7/18

(a) 73/2 (b) 123/4 (c) 82/9 (d) 45/36 (e) 754/36

28. What is the average seed of a motorist who covered 50 km in 30 minutes?

(a) 50 km/h (b) 100km/h (c) 300km/h (d) 45km/h (e) 150km/h

29. Find the area of the shape below

(a) 31cm2 (b) 40 cm2 (c) 48cm2 (d) 36cm2 (e) 60cm2

30 Find the simple interest on=N=600.00at 3% after 3years

(a) =N=54.00 (b)=N=60.00 (c) =N=36.00 (d)=N=72.00 (e)=N=18.00

31. How many cubes of side 1 1/3 cm can be contained in a box whose internal

Measurement is a cube of sides 8 cm?

(a) 512 (b) 216 (c) 1.33 (d) 826 (e) 270

32. The volume of a rectangular box is 101/2cm3. if it is 31/2 cm long ande 11/3 cm

wide How high is the box?

(a) 21/4 cm (b) 41/2 cm (c) 202/3 cm (d) 11/3 cm (e) 51/3cm

33. Find the volume of a cylinder whose radius is 7 cm and height 4cm. (take π

=22/7).


34. Express 4 cubic meters in cubic centimeters.

(a) 0.004cm3 (b) 4000cm3 (c) 160000cm3 (d) 40000000cm3 (e) 4cm3

35. There are 6 packet of sweets. Each packet contains 36 sweets. How m any

sweets will each of 18 pupils receive?

(a) 140 sweets (b) 120 sweets (c) 180 sweets (d) 12 sweets (e) 24 sweets.

36. Reduce 12:48:60 to its simplest form.

2cm

5cm 7cm

3cm

135

(a) 4: 3:6 (b) 1:4:5 (c) 2:3:4 (d) 1:3:4 (e)2:6:10

37. Decrease 35 by 25%

(a) 61.25 (b) 26.25 (c) 21.10 (d) 75.24 (e) 8.15

38. Add together 4044+44+4+440

(a) 4532 (b) 5432 (c) 2453 (d) 4453 (e) 4523

39. What is the least common multiple of 18,24and 84?

(a) 1512 (b) 2152 (c) 5121 (d) 1521 (e) 84

40. What is the square root of 225?

(a) 25 (b) 15 (c) 35 (d) 51 (e) 52

41. How many days are there in 96 hours?

(a) 3days (b) 5days (c) 6 days (d) 8 days (e) 4 days

42. Given that Q =6, P=5,M=4,N—2. Evaluate Q × P

(a) 10 (b) 3 (c) 5 (d) 15 (e) 4 M+N

43. Correct 0.0074 to two-significant figures.

(a) 0.0 (b) 0.00 (c) 74 (d) 0.0074 (e) 0.74

44 Simplify3.2691x104

(a) 32961 (b) 32691 (c 326910000 (d) 32.691 (e) 32.96

45 What is the mode in 0,1.2 4,0,3,7and 10?

(a) 7 (b) 17 (c) 1 (d) 0 (e) 3and2

46. What fraction of the rectangle below is shaded?

(a) 1/5 (b) 2/5 (c) ¼ (d) 1/3 (e) 1/2

47. Given that the perimeter of a square is 40cm. find the area.


48. What is the index form of 2x2x2x2x3x3? (a) 8x6x3 (b) 24x32 (c) 26x33 (d) 23x34 (e) 25x32

136

49 Find angle P in the figure below

(a) 1800 (b) 540 (c) 630 (d) 900 (e) 600

50. Simplify the ratio 20g: 11/4kg

(a) 1.16 (b) 152:2 (c) 2:125 (d) 10:25 (e) 20:250

P Q

R 126

0

S

137

APPENDIX C

UNIT LESSON PLAN (1) FOR EXPERIMENTAL GROUP.

Name of School:

Subject: Mathematics

Title: Number and Numeration

Class: Primary Six (6)

Average Age: 11 years

Sex: Male ( ) Female ( )

Duration: 40 mins (2 periods in 2 days)

Specific objectives:

At the end of the lesson, the pupils should be able to:

1. Read and write numbers up to one billion

2. Add, subtract in place value

3. Give the place value of digits with decimal and identification of fractions

4. Read and compare population of cities HIV infected persons

5. Express in ratio, percentages and proportion

6. Solve problems on quantitative aptitude on numbers, direct and indirect

proportion and open sentence.

Previous knowledge:

It is expected that the pupils familiar with areas taught in primary 3,4 and 5 and as such

can

1. Count in English up to one million and also in Roman numerals

2. Writes in figures and in words

3. Do some addition and subtraction

4. Identify population charts

Instructional materials:

1. Abacus and charts for numbers

2. Charts of factors and multiples of numbers, population charts and HIV/AIDS

charts.

138

Instructional procedures:

CONTENT TEACHER ACTIVITY PUPILS ACTIVITY APPROACH E valuation

Whole

numbers

The teacher involves the pupils

to do some previous exercises on

board on numbers by making the

pupils read and write numbers up

to one million

He guides the pupils to recall

counting in place value. To be

sure whether the pupils

understand mathematics

language, instruction, the teacher

engage the pupils to write in

words and figure one after the

other on the board.

The teacher guides the pupils to

recall writing numbers in

standard form 100 10 x 101

The teacher ensure the effective

use of 3R.

The pupils recall counting

up to 1 billion. The pupils

count and write in various

place values and filling the

missing numbers.

The pupils writes in words,

figure and standard.

NUMERALS WORD

FORM

1,000,000 One million

10,000,000 Ten million

50,000,000 Fifty million

100,000,000 One hundred

millions

500,000,000 Five hundred

million

1000,000,000 One billion

The approach

involves

reading,

recalling,

receiving,

understanding

of mathematics

language and

instruction.

Mental

sums, class

work and

home work

Fraction


divide and oranges to identify

fractions and reduce fractions to

its simplest form and to add and

subtract fraction

The pupils recalls and

review fractions by relating

it to sharing

The pupils do many

exercises.

1/4

1/4

1/4

1/4

1 /41 /4

The approach

used were

practical

activity

reading,

recalling,

reviewing and

understanding

mathematics

language and

instruction

Group

presentatio

n and home

work

Multiplication


identify multiples e.g

1. List the multiples of 10

and 12

2. Find the LCM of 10 and

The pupils try to provide

answers multiple of

10=,10,20,30,4050,60

Multiples of 12 = 12, 24,

36,48,60,72.

Diagnosing and

treating pupils

difficulties

139

12

3. Write numbers in index

form

4. Solve some quantitative

aptitude problems.

Factor of 10 =2x5

LCM= 2x2x3x5 = 60 and 27

= 33

64 = 20

1000 = 103

Population

The teacher gives suitable

information that will keep pupils

in the construction of population

data. He guides pupils to define

population and leads the pupils to

give the population of their

houses, churches, towns.


read and compare the population

of families in a village. Read and

compare the population of HIV

infected people by looking at

different charts presented in the

class..

The pupils goes home to

carry out the experiment by

counting the number of

people in their houses,

church and by getting

information from records

and data.

Reading and

using practical

activity to aid

studying

Percentage

ratio

proportion

The teacher guides the pupil to

express ratio in its simplest form.

Find the percentage. Identify

direct and indirect proportion e.g

1. Reduce to its simplest

form 20:28:32

2. Find the cost of a articles

at N125.25 each.

The pupils solves many

exercises. Direct proportion

as xxy

x=ky

and indirect as x x 1/y

x=k/y

The pupils solves the

problems 5:7:8

1 article cost N125.25

9 xN125.25

=N1127.25 Use 4 to

divide all

Recall

Review

And

Understanding

Mathematics

Language

Instruction

Open sentences


solve problems on open

sentences by making use of 3R

read recall review and solve

problems the teacher guides the

The pupils recall solving

problems in open sentences.

1) add the same number

both side

2) subtract the same number

Recall

Review

And

Understanding

Mathematics

Mental

sums,

group by

group

presentatio

140

pupils understand the

mathematics language before one

can solve problems in open

sentences.

both side

3)multiply both side by the

same number

4) divide both sides by the

same non-zero number.

e.g., 5 + [ ] = 25

∴ 25 - = 20

∴ 5 + 20 = 25

3

y = 9 y = ∴ 9 × 3

y = 27

language

instruction

Diagnosing

And treating

Pupils

Difficulties.

n in class

and class

work.

UNIT LESSON PLAN 2 EXPERIMENTAL GROUP


Class: Primary 6

Topic: Geometry and Mensuration

Duration: 40 minutes

Sex: Male [ ] - Female [ ]

Behavioural objectives:

At the end of the lesson the pupils should be able to:

1. Identify Heights, Distance, time and speed.

2. Name features of given shapes and polygons.

3. Identify lines of symmetry, edges, phases and vertices of various plane shapes.

4. Identify basic properties of shapes

5. Solve quantitative aptitude problems.

Previous knowledge:

1. The pupils are familiar with travelling from one place to another.

2. The pupils can identify planeshapes.

Instructional Materials:

1. Metre rule, wall metre rule.

2. Measuring tapes or rope

141

3. Different types of shapes ranging from three dimensional shapes to polygon

CONTENT TEACHER ACTIVITY PUPILS

ACTIVITY APPROACH

EVALUATION

Measuring of

height and

distance

1. The teacher uses practical

activity to aid studying.

2. The teacher divides the

pupils into groups and

leads them to obtain

readings of their heights.

3. The teacher guides the

pupils to read

measurement of things in

the class and home.

The pupils in

group by group

actively participate

in the various

measurement of

their height,

materials in the

classroom and at

home.

Using

Practical

activities to

aid studying


ACTIVITY APPROACH

EVALUATION

Polygons and

shapes angles

The teacher divides the class

into groups. The teacher guides

the pupils to identify and recall

the names and features of

different shapes given:

i. Rectangle

ii. Square

iii. Circles

iv. Shapes and

v. Polygons


review properties of plane

shapes.

The teacher also uses practical

activity to aid studying by using

paper cut outs and by folding to

determine the lines of

symmetry.

The pupils:

1. Identify, recall

the different

shapes using 3R.

2. Reviewed the

properties of

shapes. Do a

practical exercise

by folding paper

cutouts to

determine the lines

of symmetry of

various shapes.

The pupils fold

many papers

cuttings to

different shapes

and polygons.

Reading to

understand,

Recall area of

simple shapes

and review

shapes and

their

properties

By folding of

paper and

cutting to

determined

lines of

symmetry

Pupils’ cut

paper to

various shapes

guided by the

teacher also

fold paper to

show various

lines of

symmetry.

142

Engage the pupils to give the

number of vertices, edges and

phases of shapes.

The teacher engage the pupils to

measure angles with the use of

a protractor e.g. angle in a

triangle = 180

He teacher guides the pupils in

the application of 3R

The pupils

measure angles

from triangles

drawn by them.

Measure the

angles of some

triangles.

A Square

By folding a square to

get four lines of symmetry .

The pupils fold

paper cutting a

square to get its

line of symmetry.

Boys and girls

mixed together

and divided

into groups.

Mental sums,

group by group

presentation in

class and class

work.

Collaborative

learning to

folding and

cutting paper to

get lines of

symmetry.

Hexagon

The sum of the interior angles

of a triangle = 180 :- 180 x 4 =

720

The pupils

divides the

hexagon into 4

triangles.

Collaborative

143

UNIT LESSON PLAN (3) FOR EXPERIMENTAL GROUP


Title: Measurement

Class: Primary 6

Duration: 40 minutes (2 periods)


Behavioural objectives: At the end of the lesson, the pupils should be able to:

1. Identify a right angled triangle

2. State Pythagoras rule

3. Define area, volume and perimeter

4. Read and tell time in seconds, minutes and hours.

5. Define distance, speed and time solve some quantitative aptitude problems.

Previous knowledge:

1. The pupils can find area of rectangles, squares and circles

2. The pupils tell time and days in a week or months up to one year

3. The pupils are familiar with entering a car and travelling a distance.


1. Cardboards showing rectangles of equal areas but different perimeters.

2. Nail boards, rubber band, balls,cylindrical tins, charts containing word problem

watch, second pendulum stop watch

.

Instructional procedure

CONTENT TEACHER ACTIVITY PUPILS ACTIVITY APPROACH E valuation

Right angle

triangle

The teacher guides the

pupils to identify right angle

triangle


pupils on the application of

3R. Then to draw a right

angle triangle of sides 3cm,

The pupils identifies a right

angle triangle

3cm

4cm

5cm

The pupils calculate many

more right angle triangle

problems.

The approach

used by the

teacher will

involve

reading,

recalling,

reviewing

Pupils

come out

one after

the other

to draw

and solve

on the

144

4cm, 5cm


pupils to identify the sides as

hypotenuse, opposite and

adjacent and he then guide

the pupils to state

Pythagoras rule

a2 +b2 = c2 where a and b are

the adjacent and opposite

and c the hypotenuse.


pupils to construct squares

on each of the 3 sides, then

divide the squares into unit

squares to get the square of

each.

The teacher guides the pupil

in guides of 3R.

The pupils count the unit

squares to get the actual

squares.

54

3

This is showing 9 + 16 = 25

The pupils applied the use

of 3R.

Understanding

the language

instruction

and using

practical

activities to

aid studying

board

Areas

perimeter

andvolume


pupils to calculate area,

perimeter and volume by

applying the appropriate

formula

Area of rectangle = Lxb

Perimeter = 2(lxb)

The pupils activity

participate in the

calculations of what the

teacher wrote by correctly

reviewing the formula and

recalling some facts.

Area of triangle = ½ base x

height e.g

Area of parallelogram

b x h

Recalling and

reviewing

The approach

used here is

diagnosing

and treating

pupils

instructions

Recalling and

reviewing

Time, speed

and

distance

The teacher leads the pupils

to define time, speed and

distance as speed = Distance

The pupils recall telling

time. The pupils calculate

problems with time, speed

Recall,

review,

understand the

7cm

10cm

Base of parallelogram = 10cmHeight = 7cmArea = 10cmx7cm = 70cm2

145

Time

Distance = Speed x Time

Time = Distance

Speed

The teacher guide the pupils

to solve problems. An

aeroplane travelled to Lagos

at 839km/hr for 4 hours what

distance was covered by the

aeroplane.

and distance. The pupils try

more examples

The pupils copy down.

Time taken to cover the


= 839 x 4

= 3356km

language

instruction

and

diagnosing

and treating

their

difficulties

Using

practical

activity

Quantitative

aptitude


pupils in the use of 3R to

solve quantitative aptitude

problems.

The pupils apply 3R to

understand the instructional

225km 50km/h ?4.5h

Time = = = 9/2 = 4.5hr SP 50

D 225

Understanding

mathematics

language

instruction

before

solving.

Mental

sums, group

by group

presentation

in class and

class work.

146

UNIT LESSON PLAN 4 FOR EXPERIMENTAL GROUP


Topic: Statistics

Class: Primary 6


Age: 11 years

Duration: 40 minutes

Objectives:- At the end of the lesson the pupils should be able to

1. Define mean, median and mode of a set of data.

2. Form set of data from given numbers of items

3. Read and interpret pictograms and bar charts

4. Represent information on bar charts

Previous Knowledge

1. The pupils are familiar with numbers.

2. The pupils can name in the class, at home, in school

3. The pupils can do addition, multiplication and division.


Pencils, graph paper, coin/dice, pack of cards and charts.

Instructional Procedures:

CONTENT TEACHER ACTIVITY PUPILS ACTIVITY APPROACH Evaluation

Mean,

median,

mode


pupils in the use of 3R as to

define mean, median and

mode of a set of data.

Mean of a set of data means

average median means the

middle number depending

if the set of data is add or

even and mode means the

number that occurs most.

The pupils recall various

definitions and write them

down with examples.

The pupils collects the data

into number and frequency.

NO 8 9 10 11

FREQ 4 4 8 4

Total = 20

Mean=8x4+9x4+10x8+11x4 4+4+8+4

Read

Recall

Review

Diagnosing

and treating

pupils

difficulties

147

The teacher presents a set of

data representing the ages

of 20 primary 6 pupils as 8,

10, 9, 11, 10, 9, 8, 8, 8, 10,

10, 11, 9, 10, 11, 10, 10, 10,

9, 11.


pupils to calculate mean,

median and mode ages. As

the pupils recalls and

review their formulars.

= 32+36+80+44 20

= 192 = 48 = 93/5

20 5 = 9.6

Median

88889999101010101010101

011111111

Since there are 20 numbers

½ of 20 = 10 each

Median = middle number

= 10th+11th numbers

10+10 = 20 = 10

2 2

Median = 10

Modal No. = 10 (occur

most) has the highest

frequency.

Using

practical

activities to

aid studying

Pupil’s give

their different

ages and use

to find mean,

median and

mode. A

teacher

guides the

pupils to read

and write the

numbers in an

ungrouped

data in

ascending or

descending

order

Data

collection

and

presentation

Bar graph

Pictogram

The teacher in the effective

application of 3R to collect

guides the pupils to collect

data by performing some

experiment like tossing a

coin once or twice and

collect the information.

The teacher divides the

pupils into groups and

encourage them to work in

group.

The teacher encourage the

pupils to collect data by

The pupils with the use of

graph books represents the

resulting experiment on data

which is translated to charts

e.g bar chart.

The pupils participate

actively in the experiment

by throwing a dice and

tossing coins to get their

readings and practice many

more examples with tossing

a coin many times

Throwing a dice once to six

Using

practical

activity to aid

studying

The pupils

work in

groups to

achieve better

results

Recalling,

Read

Revising

understanding

148

using tallies after which a

frequency table is gotten

and then represent the

information on a bar chart.

The teacher solves a

problem of tossing of coin

10 times e.g TH TH, HH,

TH, HT, HT HTTT,TT, HT

Outcomes Tallies Freq

HT IIII 4

TH III 3

HH I 1

TT II 2

10

No. of outcomes

0

1

2

3

5

HH HT TH TT

times and also use pack of

cards. The pupils do this

exercises to generate data

which they use to draw the

bar graph.

mathematics

language

instruction.

Diagnosing

and treating

pupils

difficulties

and using

practical

activities to

aid studying

149

UNIT LESSON PLAN (5) FOR EXPERIMENT GROUP

Subject: Mathematics (1)

Topic: Basic Operation



Duration: 40 mins (2 days)

Behavioural objectives: At the end of the lesson the pupils will be able to:

(1) Identify the different operational signs

(2) Write and interoperate BODMAS

(3) Write numbers in index form

(4) Write in significance figure

(5) Identify squares and square root of numbers

(6) interpret words in open sentence

(7) solve problem on qualitative aptitude involving three or more operations.

Previous Knowledge

(1) The pupil can add subtract, multiply and divide

(2) They can interpret words in open sentences

(3) Identify square roots of numbers

Instructional Materials

Sum cards, Multiplication facts and charts, Flash cards

Procedure:

150

CONTENT Teacher Activity Pupils Activity Approach E valuation

Squares,

Square notes

numbers


pupils in the proper use

of 3R to identify square

of numbers and square

roots of numbers. The

teacher also guides the

pupils to solve some

exercises.

The pupils identify

squares of numbers

and square roots and

solve some exercises

e.g.

52 = 25

82 = 64

102 = 100

152 = 225

Applying

3R

Read,

Recall and

Review


ACTIVITY APPROACH Evaluation

Multiplication

The teacher drills pupils

on multiplication. The

teacher guides the pupils

in the effective use of 3R

recall the multiplication

time table by making them

recite and write down 2

times table to 12 x

timetable

To diagnose their

difficulties, the teacher

tests the pupils mentally

by giving mental sums

and finds out the

important of

multiplication and its

application.

The teacher multiplies 3

digit numbers decimal by

decimal

The pupils recall

the

multiplication

time table

starting from 2

times table to 12

times table.

Pupils solve

problems on

multiplication

using three digit

numbers and

decimal to

decimal. The

pupils solve

mental sum

while they

quickly provide

the answers at a

limited time.

Read, Recall,

Review

Active

participation

in solving

diagnosing

pupils

difficulties.

Recall and

reviewing

Application

of 3R and

understanding

mathematics

language

instruction

The teacher

guides pupils

in the use of

Abacus to

write numbers

in millions,

billions,

trillions and do

the necessary

multiplications.

151

= 5, = 4

= 8, = 10

The pupils identify

the numbers in square

root.

Addition and

Subtraction


pupils in the use of 3R

to identify place value

in addition of whole

numbers and decimal.

The teacher guides

pupils to solve problems

on addition and

subtraction

The pupils recall

whole numbers,

fractions and decimal.

Solve problems in

addition and

subtraction

Read

Recall

Review

Order of

operations


pupils in the use of 3R

to understand the

meaning of BODMAS

as

B = Bracket 1st

O = of 2nd

D = Division 3rd

M = Multiplication

A = Addition

S = Subtraction

Guides pupils to apply

the order in solving

basic operational

problems.

The pupils apply the

order in solving

exercises on order of

operations

5 of (3 + 8) – 2

5 of 11 – 2

5 x 11 – 2

55 – 2

= 53

Read

Recall,

Review,

Diagnosing

and

treating

pupil’s

difficulties.

Mental sums,

group by

group

presentation

in class and

class work.

152

APPENDIX D

UNITY LESSON PLAN (1) FOR CONTROL GROUP


Title: Number and Numeration

Class: Primary 6

Duration: 40 minutes (2 days)

Sex: Male [ ], Female [ ]

Specific objection:

At the end of the lesson, the pupils should be able to:

1. Read and write numbers up to one billion

2. Add, subtract in place value

3. Give the place value of digits with decimal and identification of fractions

4. Read and compare population of cities HIV infected persons

5. Express in ratio, percentages and proportion

6. Solve problems on quantitative aptitude on numbers, direct and indirect

proportion.

Previous knowledge:

It is expected that the pupils had been taught works on primary 3,4 and 5 and as such

can

1. Count in English up to one million and also in Roman numerals

2. Writes in figures and in words

3. Do some addition and subtraction

4. Identify population charts


1. Abacus and charts for numbers

2. Charts of factors and multiples of numbers, population charts and HIV/AIDS

charts.

153

Instructional procedures:


ACTIVITY APPROACH

Evaluation

Whole

numbers


to count up to one million. He

also leads the pupils to write

in words e.g

NUMERALS WORD FORM

1,000,000 One million

10,000,000 Ten million

50,000,000 Fifty million

100,000,000 One hundred millions

500,000,000 Five hundred million

1000,000,000 One billion

The pupils count

up to one million.

They write in

words and

figures up to one

billion

The pupils copy

what the teacher

writes into their

notebooks.

What is the

difference

between one

million and

one billion.

How can you

write

25million in

words.

Fractions


to identify fractions, reduce

fractions to its simplest form

and to add and subtract

fractions.

The pupils

identify fractions

such as ½ , 1/3

¾ , ¼

As the teacher

does

1/4

1/4

1/4

1/4

1 /41 /4

Divide the

circle into

five and write

the fraction

Multiples


to

i. List the multiples of

10 and 12

The pupils

copy’s what the

teacher had

written on the

154

ii. Find the LCM of 10

and 12

The teacher solves for the

pupils to copy.

Multiple of 10=10,20,30,40

Multiple of 12=12,24,36,48

Factors of 10=2 x5

Factors of 12= 2 x 2 x 3

LCM = 2 x 2 x 3 x 5= 60

Write in index

27 = 33

64 = 26

100 = 103

board into their

notebooks

Practice

solving on

their own

Population

The teacher leads and guides

the pupils in the construction

of population data. The

teacher leads the pupils to

define population and to give

the population of their

classes, houses, towns and

churches.

Population is the number of

persons in a locality.

The pupils do

what the teachers

had done in class

by writing down

population and

goes home to

find the answers

to others on their

own

Pupils ask

questions on

how they can

read and

write

population

Ratio

Proportion


to express ratio in its simplest

form, find percentage and

identify direct and indirect

proportion.

The teacher solves the

following:

(1) Reduce to its simplest

form 28:32 5 7 8

The pupils copy

what the teacher

has written on

the board

Pupils ask

questions on

how to solve

direct and

indirect

proportion.

155

(2) Find the cost of a

articles at N125.25

each.

1 article cost N125.25

9 articles cost 9 x N125.25 =

N1127.25

Open

sentences


to revise open sentences by

reading recalling reviewing

and solving problems the

teacher makes the pupils

understand the mathematics

language before one can solve

problems in open sentences.

Pupils copy from

the board what

the teacher has

written

The pupils

ask questions

Teacher

ask pupils

questions.

156

UNIT LESSON PLAN 2 FOR CONTROL GROUP


Class: Primary 6

Topic: Geometry and Mensuration

Duration: 40 minutes each (2 days)

Sex: Male [ ] - Female [ ]

Behavioural objectives:

At the end of the lesson the pupils should be able to:

1. Identify Heights, Distance, time and speed.

2. Name features of given shapes and polygons.

3. Identify lines of symmetry, edges, phases and vertices of various plane shapes.

4. Identify basic properties of shapes

5. Solve quantitative aptitude problems.

Previous knowledge:

1. The pupils are familiar with travelling from one place to another.

2. The pupils can identify plane shapes.


1. Metre rule, wall metre rule.

2. Measuring tapes or rope

3. Different types of shapes ranging from three dimensional shapes to polygon


ACTIVITY APPROACH

Evalu-

ation

Measuring of

height and

distances

The teacher leads the

pupils to obtain reading

of their heights .


pupils to read

measurement of things

in their class or home

The pupils will

copy what the

teacher does in

the class.

The pupils

ask questions

157

Polygons

plane shapes

and angles


pupils to identify:

i. Rectangles

ii. Squares

iii. Circles, other

shapes and

polygons


pupils to name the

properties of

planeshapes.


pupils to identify lines

of symmetry, vertices,

edges and phases of

shape


pupils to measure

angles with the use of

protractor as to find out

that the sum of angles

in a triangle is equals

1800

A square 4 lines

of symmetry

Hexagon

The sum of the interior

angles of hexagon = 4 x

180 = 7200

The pupils

writes the

properties of the

various shapes

and polygons

The pupils listen

to the teacher

and copy’s what

the teacher

writes on the

board.

The pupils copy

into their books.

Without

knowing how

lines of

symmetry of a

square are

gotten.

Questions

The pupil ask

questions

such as why

is the answer

720.

Teacher ask pupils questions.

158

UNIT LESSON PLAN (3) FOR CONTROL GROUP


Topic: Statistics

Class: Primary 6


Age: 11 years







Previous Knowledge








ACTIVITY APPROACH

Evalu-

ation

Right angle

triangle


to draw a right angled

triangle with sides 3cm, 4cm

and 5cm

3cm

4cm

5cm

The pupils

draw the

diagram as

drawn by the

teacher.

Questioning

159


to identify hypotenuse,

opposite and adjacent. He

guides the pupils to state the

Pythagoras rule as a2 + b2 =

c2. The lead pupils to use the

formula to solve problems.

The pupils

copy all that

the teacher

writes on the

board into

their

notebooks.

Area

perimeter

and volume

The teacher guides the pupils

to calculate Area perimeter

and volume by applying

approximate formula Area of

rectangle = L xb

Perimeter = 2 (L+b)2

Area of parallelogram b x h

Area of triangle ½ base x

heighte.g

7cm

10cm

Base of parallelogram = 10cmHeight = 7cmArea = 10cmx7cm = 70cm2

The pupils

write down

the different

formulas into

their

notebooks

and copy the

problem.

Questioning

Time

Distance

and Speed


to define time, distance and

speed as Speed = Distance

Time


Time = Distance

Speed

The teacher leads and guides

the pupils to solve a problem

e.g iAn aeroplanetravelled to

Lagos at 839km/hr for 4

hours what distance was

The pupils

follow what

the teacher

did and copy

into their

notebooks

The pupils

copy what the

teacher had

done

Questioning

Teacher

ask pupils

questions.

160

covered by the aeroplane.

Time taken to cover the

distance = 4 hrs

Distance = speed x time

= 839km/hr x 4 hrs

= 3356km

161



Topic: Statistics

Class: Primary 6


Age: 11 years







Previous Knowledge








ACTIVITY APPROACH

Evalu-ation

Mean median

and mode

The teacher leads pupils to define mean,

median and mode of a set of a data as

mean is average of a set of numbers,

median is the middle number depending

on the set of data, whether it is odd or

even while mode is the number that

occurs most e.g the teacher presents a

set of data representing the ages of 20

The pupils

defines

mean,

median and

mode and

write it

down as

defined by

The pupils

ask questions

to enable

them

understand.

Teacher

ask pupils

questions.

162

Data

representation

Bar graph

pictogram

primary 6 pupils as

8, 10, 9, 11, 10, 9,8, 8, 8, 10, 10, 11, 9,

10, 11, 10, 10, 10, 9, 11.

The teacher leads and guides them to

solve as follows

8+10+9+11+10+9+8+8+8+10+10+11+9

+10+11+10+10+10+9+11.__________

20

192 = 48= 93/5 = 9.6

20 5

The teacher leads the pupils to toss 2

coins 100 times.

Leads the pupils to prepare bar graphs

to represent the resulting scores.

Guides the pupils to represent the result

on bar graph

The teacher solves a problem of tossing

2 coins 10 times as

TH TH, HH, TH, HT, HT HTTT,TT,

HT

Outcomes Tallies Freq

HT IIII 4

TH III 3

HH I 1

TT II 2

10

the teacher

The pupils

copy into

their note

books as the

teacher

writes.

10+10 = 20 2 2

= 10

Mode = 10

The pupils

do as

instructed

by the

teacher.

Represent

the

information

on a bar

graph.

The pupils

copy the

problem

and the

solution

into their

note books

Questioning

Questioning

163

No. of outcomes

0

1

2

3

5

HH HT TH TT

164


Subject: Mathematics (1)

Topic: Basic Operation



Duration: 40 mins each (2 days)

Behavioural objectives: At the end of the lesson the pupils will be able to:

(8) Identify the different operational signs

(9) Write and interoperate BODMAS

(10) Write numbers in index form

(11) Write in significance figure

(12) Identify squares and square root of numbers

(13) interpret words in open sentence

(14) solve problem on qualitative aptitude involving three or more operations.

Previous Knowledge

(1) The pupil can add subtract, multiply and divide

(2) They can interpret words in open sentences

(3) Identify square roots of numbers

Instructional Materials

Sum cards, Multiplication facts and charts, Flash cards


ACTIVITY APPROACH

Evalu-

ation

Multiplication


to multiply 3 digit numbers

by solving some examples on

the board e.g.

(1) 0738 x 50

x 7.38 36900

(2) The teacher again takes

The pupils

identifies the

numbers in squares

and copy what has

been given on the

board into their

notebook

165

an example on

multiplication by decimal

2.8 or 28 X 3.1 31 28 84 868 = 8.68 (3) Multiplication by fraction

3/8 x 8/9

= 3 x 8 = 1/3 8 x 9

Or

½ x 4/5 = 1 x 4 = 4/10 2 x 5 = 2/5

Indices

The teacher drills the pupils

on numbers in index form

9 = 3 x 3 = 32

27 = 3 x 3 x 3 = 33

125 = 5 x 5 x 5 = 53

The teacher uses mental sums

to make the pupils read,

recall and review all about

powers of numbers

The pupils respond

to the teachers

instruction by

copying what the

teacher writes on

the board.

Questioning

Order of

Operation

The teacher makes the

meaning of BODMAS

understood by the pupils by

explaining the order as B

(Bracket) is done first O (of)

done next D (Division) next

M (Multiplication) next A

(Addition) next S

(Subtraction) last the teacher

The pupils copy

what the teacher

writes on the board.

questionings

166

leads the pupils to solve 5 of

(3 + 8) – 2

Fractions by fractions

multiplications of 3 digits

(1) (738 x 10) x 5

=7380 x 5

=36900

(2) 4597

* 8000

367,7600

(3) Multiplication of decimal

by decimal by decimal

2.8 x 3.1 = 28

* 31 (considering 2p.d)

28

+ 84 868 = 8.68

(4) Multiplication by

Fractions by Fraction

3/8 x 8/8 =3 x 8 = 1/3 Or ½ x 4/5 = 1 x 4 = 2/5 2 x 5

Leads pupils to add and

subtract

The pupils copy

what the teacher

writes on the board.

Questioning

Addition and

subtraction

squares and

square roots

of numbers

The teacher explains the

meaning of squares of

numbers as multiplying the

number to itself.

He leads the pupils to

produce numbers with perfect

square and guides the pupils

The pupils copy

what the teacher

writes on the board

Questioning

167

to solve problems and square

roots

52 = 5 x 5 = 25

82 = 8 x 8 = 64

102 = 10 x 10 = 100

152 = 15 X 15 75 15 225

Division

The teacher led pupils to

recall, review division by

doing some mental drills in

division e.g. 10 : 2, 100 : 5

25.5 : 5

The pupils copy

what the teacher

writes on the board

Questioning

Teacher

ask pupils

questions.

168

APPENDIX E

Table of Specification

CONTENT DIMENSION ABILITY PROCESS DIMENSION

Class Lower cognitive processes

S/

N

Topics % 30%

K

30%

Com.

40%

APL

100%

1 APPLY SQ3R (SCAN Question)

i) Read, recall and review open

sentence, interprete mathematical

sentences

ii) Recall Basic operation

(BODMAS), Basic statistics,

percentages

iii) Review: properties of shapes,

counting in place value and

quantitative reasoning.

20%

3

3

4

10

2 Understanding the purpose of

mathematics language instruction

i) write in words

ii) Express decimal to fractions and

vise versa

iii) Reduce to its lowest term.

iv) Give answer to 3 significance

figures

v) Without calculator add, multiply,

divide

vi) Express in percentage.

30%

4

5

6

15

3 Diagnosing and treating pupils

difficulties:

i) Definition of concepts

30%

169

ii) Identification of concepts

iii) Solve mathematical problems.

iv) Time, Distance and speed

4 5 6 15

4 Using practical activities to aid

studying:

i) measurement; length Distance,

angles

ii) Converting given lengths, distance

iii) Drawing of circle, graphs and

review their properties.

iv) Data collection mean, media,

mode range, Bar chart

v) Solve quantitative problems

20%

3

3

4

10

Total 100% 14 16 20 50

Topics considered in the construction of the table of specification are: number and

numeration, basic operation, measurement, geometry and menstruation and statistics.

170

APPENDIX F

Training guide for Mathematics Teachers on Achievement Motivational

Instructional Approach.

Introduction

This training is to familiarize you with the achievement motivational

instructional approach. We know as teachers we are conversant with many teaching

methods such as demonstration, discussion, laboratory, lecture, target task, discovery,

expository traditional and enquiry. Although these methods have been in use for years,

pupils performance in internal and external examination continues to be poor. This is a

fact that every mathematics teacher can bear witness. Research studies have identified

teaching methods used by teachers as the main contributing factor to pupils poor

performance. Therefore, there is the need for primary school teachers to look for better

and rewarding methods of teaching mathematics in the primary schools that will give

the pupils a better foundation in mathematics.

In this training exercise, the possibility of using achievement motivational

instructional approach in teaching mathematics to primary six pupils will be considered.

This is to investigate whether achievement motivational instructional approach could

facilitate learning, enhance retention, and the ability to manipulate numbers and

achievement in mathematics in the primary schools. Operationally, achievement

motivational instructional approach is a method where pupils are trained to be mentally

coordinated by making sure that previous knowledge is updated, it is a method that

ensure that pupils can read questions very well to their proper understanding;

1. Recall and review facts and knowledge previously done that is related to what is

treated at hand.

2. Understand Mathematics Language instruction.

3. Diagnosing and treating pupil’s difficulties.

4. Using practical activities to aid studying.

The method is time consuming and demands patience from both the pupils and the

researchers. This method gives the pupil’s satisfying intellectual reward. This in-turn,

helps in better memory, facilitate retention arouse interest and transfer of knowledge.

171

The success of this method highly depends on the teachers. As such your cooperation is

highly solicited throughout the period of this investigation.

Teachers and Pupils role in Achievement Motivational Instructional Approach

In achievement motivational instructional approach, the teacher acts as a

facilitator of learning. He over-sees all the activities of the pupils. He directs and

constantly monitors pupils to understand every verbal statement made in mathematics

by reading the statement over and over as to device a workable plan. The teacher

should use simple and related procedures that could give clue and understanding to

getting the correct procedure that will lead to the correct answer. The teacher does not

respond negatively to pupil’s wrong attempts to question, as not to frustrate their effort.

Instead, the teacher encourage them through the use of rewarding work such as

try again, you can do it, etc. this will make the pupils constantly think of the problem at

hand and try to find solution to it.

In a situation where the class size is large, the teacher starts off the lesson with

mental sums. This will spur everybody in class thereby making the pupils show active

concentration and participation because they must finish within a limited time. Again if

the class is large and there is inadequate supply of instructional materials, effective

supervision becomes very difficult. As such, the teacher should divide the pupils into

small working groups, each with enough instructional materials, for easier and effective

supervision. That will enable each pupil participate and be involved throughout the

lesson”

At the beginning (at entry behaviour), of each lesson approach, the teacher

should diagnose the productivities of the pupils by giving simple tasks that majority can

attempt. This will enable the teacher find out their problems and stimulate their

curiosity to learn. The objectives of the activities in the lesson should be explained to

the pupils as well as the guide lines on the use of the instructional approach especially

where it involves instructional materials. At the end of every activity, an interactive

session, should follow to find out if the activity has helped in providing the required

method or formular to the instructional problem and getting the correct solution. The

way and manner, and formular used in solving problem should be such that anywhere

such a problem is seen, the approach goes. The pupils should be encouraged to express

172

their views to their teachers and amongst themselves, so as to exchange ideas. This will

improve interaction between themselves, the teacher and the learning materials. Hence

the pupils communication skills, computational and intellectual ability, retentive ability

are improved. Pupils should feel free to learn, ask questions on ideas they did not

understand especially in understanding mathematics language instruction. The teacher

on the other hand, should attend to all their problems and difficulties they encounter in

carrying out their activities. Thus the teacher should guide, reinforce, motivate and

stimulate the pupils effort to work harder towards achieving the objectives of the

lesson. The teacher does this by providing feedback on their performance.

Traditional Method

The teachers of the control group will be presented with unit lesson plan of all

the areas offered in primary six. The teachers will use the plans with the textbook. They

first use solved examples from the textbook, write on the board for pupils to copy. After

which the teacher takes one or two simple problems from the exercises in the textbook

and then give classwork in the textbook. The teachers do not mind whether the pupils

understand what he did or not and most teachers do not even mark the classwork or

homework.

Pupils ask questions to get clarification but teachers use lecture methods to give

the answer which in most cases is not understood by pupils. Teachers out of laziness

give their notebook to pupils to copy for others on the board and most of these pupils

can neither read well nor spell as to copy rightly. In a control class pupils are always

writing, no interaction of any kind. The class is always dull and uninteresting. Pupils

hardly know each other’s ability. They are lazy and weak in solving problems. The

teachers do not really try to arouse pupils by giving them mental sums that will act as a

stimulant to thinking.

For the experimental and control groups, the teaching will be done in 10 teaching

periods of 40 minutes each. That will last for three (3) weeks at 5 periods per week. On

the last day of the two weeks the posttest will be administered. Lastly, the pupils will

not be informed of the purpose of this investigation. This may influence their

performance in the posttest at the end of the exercise.

Thank you.

173

APPENDIX G

PRIMARY SIX CURRICULUM

THEME EVERYDAY STATISTICS

TOPIC PERFORMANCE OBJECTIVES

CONTENT ACTIVITIES TEACHING AND

LEARNING MATERIALS

EVALUATION GUIDE

TEACHER PUPILS

1.

Population

Pupils should be

able to:

1. interpret,

pictograms and

bar graphs.

2. state the

meaning of

population

3. appreciate the

use of

pictograms and

bar graphs in

representing

population of

people or data.

Pictograms

and bar

graphs

1. Brings teaching materials to

the class.

2. Introduces the topic and

guides the pupils to define

population.

3. Presents a bar graph chart of

population of a town showing

men, women, boys and girls and

leads the pupils to examine the

graphs and deduce the

population of men, women, boy

and girls.

4. Displays the population chart

of a village as:

men - 20,000

women – 30,000

boys - 40,000

1. Brings pencil,

ruler, exercise

book, eraser to

the class.

2. Define

population.

3. Give the

population of

men, women,

boys and girls in

the bar graph.

4. Represent the

information on a

pictogram and

bar graph.

5. Work in

group.

Population

data chart

pictogram

chart bar

graph

Pupils to:

1. prepare

pictogram

and bar

graph of

given data.

2. prepare

pictogram

and bar

graph using

data gotten

from the

need of the

population of

boys, men,

women and

girls in his

174

girls - 36,000

and guides the pupils to prepare

a pictogram and bar graph of

cows needed by the population

where 2000 men need 1 cow

women need 1 cow 4000 boys

need 1 cow 4000 girls need 1

cow.

5. Encourage the pupils to work

in groups.

6. Leads the pupils to appreciate

the use of pictograms and bar

graphs in representing

population of people or any

data.

6. Appreciate

the use of

pictograms and

bar graphs in

representing

population of

people or any

given data.

environment.

2.

Measurem

ent of

Central

Tendency

Pupils should be

able to:

1. find the mode

of data.

2. appreciate the

use of mode in

analyzing

population of

i. mode 1. Brings teaching materials to

the class.

2. Gives colours of 2,000 cars

as follows

green - 448

red - 452

white - 562

blue - 538 and leads pupils to

1. Observe and

study the

teaching

materials

brought by the

teacher.

2. Represent the

given

175

people or data

and in daily

activities

find the modal colour and to

represent the information on a

bar graph

3. Leads the pupils to appreciate

the use of mode in analyzing the

population of people or data

information in

bar graph and

finds the mode.

176


THEME: NUMBER AND NUMERATION



LEARNING MATERIALS

EVALUATION GUIDE

TEACHER PUPILS

1. Whole

Numbers

Pupils should to

able to:

1. count in

millions and

billions

i. Counting

in millions

and billions

1. Revise the previous work in

counting up to counting in

million

2. Guides pupils to count in

millions up to nine hundred

millions

1. Revise

counting up to

one million

2. Count in

millions up to

nine hundred

million.

Abacus and

Charts of

numbers

Pupils to:

1. count in

millions up

to a specified

number.

2. write and read

up to one

million

ii. Writing

and reading

up to one

million

3. Guides pupils to read up to

one billion as shown below

Numeral Word form

1,000,000 one million

10,000,000 ten million

50,000,000 fifty million

100,000,000 one hundred

million

500,000,000 five hundred

million

1000,000,000 1 billion

1. Practice

reading and

writing of

numbers up to

one million

2. Devise other

practices or

methods to write

and read up to

one billion

Abacus and

Charts of

numbers

2. write and

read up to

one million

177

2. Devises other practices or

methods to write and read up to

one billion.

3. solve

problems

involving

quantitative

reasoning

iii.

Quantitativ

e reasoning

Guides pupils to answer

question in quantitative

reasoning

3. do given

exercise on

quantitative

reasoning.

178


THEME: NUMBER AND NUMERATION



LEARNING MATERIALS

EVALUATION GUIDE

TEACHER PUPILS

4. solve problem

on quantitative

reasoning

iv.

Quantitativ

e reasoning

Leads pupils to solve problems

on quantitative aptitude e.g.

Find the missing number such

that the resulting fraction is

expressed as 0.25

Solve problems

on quantitative

aptitude

4. solve

problems on

quantitative

aptitude.

3.

Demograp

hy

Pupils should be

able to:

1. read, write

and compare

population of

big cties

i.

population:

• Families

• Classes

• Towns and

cities etc.

1. Guides pupils to define

population.

2. Leads pupils to give the

population of:

• Their houses

• Classes

• Town etc.

3. Guides pupils to read and

1. Define

population.

2. Give

population of

their houses,

classes, towns

etc.

3. Read and

write

Demography

map of

Nigeria

video of

populations

Pupils to:

1. define

population.

2. read and

write the

population of

big cities in

Nigeria.

3. read and

2

0.25

?

179

write populations of some cities

e.g. Lagos, Kano, Aba in the

country using map of Nigeria.

populations of

some cities e.g.

Lagos, Kano,

Aba in the

country using

the map of

Nigeria.

compare

population.

2. read and

compare

population of

HIV positives in

different

countries.

ii. Reading

and

comparing

of

populations

Guides pupils to read and

compare population of HIV

positive from different countries

of the world

Participate in

reading and

comparing

populations of

HIV positives in

different

countries in the

world

World Atlas

and some

published

information

from WHO

on

HIV/AIDS

etc.

4. read and

compare

population of

HIV

positives in

some given

countries in

the world.

3. appreciate the use of counting in thousands and millions and population in demography, epidemiology, etc.

Guides pupils to appreciate the

importance of population

studies in demography,

epidemiology, etc.

Appreciate the

study of

population in

demography and

epidemiology.

180





LEARNING MATERIALS

EVALUATION GUIDE

TEACHER PUPILS

4. Ratio

and

proportion

Pupils should be

able to:

1. solve

problems on

ratio

2. appreciate the

application of

ratio in everyday

life.

3. solve

quantitative

reasoning

problem

involving ratio

i. Ratios 1. Leads pupils to revise

previous work done on ratios

2. Guides pupils to solve

problems on population e.g.

In a city of 10,000 people 100

of them are HIV positive. Find

the ratio of those infected to the

total population.

Total population 100,000

Infected population – 100

The ratio of infected to total

population is 100: 10,000 or

1:100 or 1/100.

3. Leads pupils to appreciate the

application of ratio in everyday

life.

4. Leads pupils to solve

quantitative problems related to

1. Revise the

previous work

on ratios

2. Solve

problems on

ratios

3. Appreciate

the application

of ratios in

every day life.

4. Solve

quantitative

reasoning

problems related

to ratios.

Charts of

solved

problems on

ratios

Pupils to:

1. solve

given

problems on

ratios

2. solve

some

quantitative

reasoning

problems on

ratios.

181

ratios.

4. solve

problems in

direct

proportion.

5. appreciate

applications of

direct

proportions in

daily life

activities.

ii. Direct

proportion

1. Guides pupils to solve direct

proportion problems e.g.

A man saves money everyday.

If he saves N30 each day, how

much can be saved in 4 days?

Saving (N) day

30 1

80 2

90 3

120 4

He saves N120 in 4 days.

2. Leads pupils to notice that his

saving is in direct proportion to

the number of days.

3. Leads pupils to appreciate the

application of direct proportion

in everyday life.

1. Solve

examples on

direct

proportion.

2. Notice that

the saving is in

direct proportion

to the number of

days.

3. Appreciate

the application

of direct

proportion in

everyday life

Charts of

solved

examples on

Direct

proportions.

3. solve

given

problems on

direct

proportions.

6. solve

problems on

quantitative

reasoning

involving direct

proportion

iii.

Quantitative

reasoning

Leads pupils to solve problems

on quantitative reasoning

involving direct proportion.

Solve

quantitative

aptitude

problems

involving direct

proportion

4. solve

problem on

quantitative

aptitude

involving

direct

proportion.

182


THEME: MEASUREMENT



LEARNING MATERIALS

EVALUATION GUIDE

TEACHER PUPILS

7. Weight Pupils should be

able to:

1. work word

problems on

weights.

2. express the

same weight in

different unit

gram, kilogram

tonne

3. appreciate the

relationship of

different unit of

measurement.

World

problems

on weights

1. Guides pupils obtaining

measurements of their

weight, rock sample etc

using weighing scales.

2. Explains that weight of

small objects expressed in

kilograms while heavy

objects are expressed in

tones.

1 tonne = 1000kg

1000g = 1kg

3. Leads pupils to appreciate

the relationship between

different units of

measurement.

1. Practice

converting weights

in tones to kilogram

and vice versa.

2. Identify objects

whose weights

could be expressed

in tones, in

kilograms and in

grams.

3. Practice solving

word problems on

weights.

4. Pupils appreciate

the relationship

between different

units of

Samples of

minerals

different

types of

weighting

scales and

spring

balance.

Pupils to;

1. convert

weights

expressed in

tones to

kilograms

and vice

versa.

2. solve

word

problems on

weights.

183

measurement e.g.

grams, kilograms,

tones.

8. Time Pupils should be

able to:

1. tell time in

seconds and

minute.

2. solve

quantitative

aptitude

problem on

time.

i. Timing

in minutes

and

second.

1. Guides pupils to find the

time it will take the class

captain or class monitor to

trek the width of the class in

seconds or minutes, using

the seconds-pendulum and

also stop watch and compare

the result.

2. Leads pupils to solve

quantitative aptitude

problems on time.

3. Gives further assignments

on timing.

1. Work in groups

to time in seconds

and minutes.

2. Time them selves

on how long it will

take them to

complete various

activities. Solve

quantitative

aptitude problem on

time.

3. solve assigned

exercises

Second

pendulum,

stop-watch

Pupils to:

1. time

certain

events in

seconds and

minutes.

184


THEME: MEASUREMENT



LEARNING MATERIALS

EVALUATION GUIDE

TEACHER PUPILS

3. read timetable

of journeys

especially by

trains and

aeroplanes.

4. value the need

for time in real

life.

ii. Reading

time-table

of journeys

1. Brings time table of

journey by train or by

aeroplane.

2. Guides the pupils to

use these time tale to

estimate the time-

interval it will take a

train or aeroplane to get

to a specific

destination.

3. Leads the pupils to

value time in real life.

1. Use time table of

train to estimate the

time it will take a train

to get to a designated

destination.

2. Use time-table to

estimate the time it

takes an aeroplane to

get to a specific

destination.

3. Value the need for

time in real life.

Time-table

of train,

aeroplane

from

different

airlines

Pupils to:

1. obtain time

table or schedule

of flights from

any airlines to

estimate the

time it takes an

aeroplane to get

to specific

destination.

2. obtain time

table of train

and estimate the

time it will take

the train to get

to specific

destination.

185

8. Time

athletics

Pupils should be

able to estimate

time to complete

races.

Pupils value the

use of

mathematic in

every day living.

Standard

time for

races

1. Given record times

for 100m, 400m, 800m

by men and women

from different

competitions for

different years.

2. Lead pupils to value

the use of maths in

every day life.

1. Make the table for

races and time value

the use of maths in

every day life.

2. Value the use of

mathematics in every

day life

Charts

showing

races and

time for

100m,

440m and

800m

Pupils to:

1. estimate time

a boy will take

to run 100m.

2. Estimate time

a girl will take

to run 100m

9. Speed Pupils should be

able to work

more problems

on speed

Solve more

quantitative

aptitude

problem on time

and speed.

Average

speed.

1. Guides the pupils

using the idea of steady

speed to explain

average speed.

2. Further explains that

the ratio of distance

covered and time taken

is called speed. Speed

is expressed in km/hr,

etc.

3. Lead pupils to solve

more quantitative

aptitude exercises

1. Mention the distance

of their homes from the

school and the time it

takes them to cover it.

2. Give the distance

covered by the train,

bus or aeroplane to

travel from one town to

another and the time

taken.

3. Compute the speed

for the train, bus or air

journeys from one

Clock face

stop watch

railway

time-table,

bus time-

table, air

time-table

Pupils to:

1. determine

how long it

takes to travel

by bus, train

aeroplane from

one town to the

other.

2. solve more

problems on the

topic to obtain

time taken for a

journey distance

186

related time and speed town to the other.

4. Solve more

quantitative aptitude

exercises relate to time

and speed.

covered and

average speed.

187


THEME: ALGEBRAIC PROCESSES



LEARNING MATERIALS

Evaluation Guide

TEACHER PUPILS

Open

sentences

People should

be able to

1. solve

problems

expressed as

open sentence.

2. interpreter

words into open

sentences and

solve them.

3. solve related

problems on

quantitative

aptitude.

Open

sentences

1. Prepares teaching materials

and brings them to class.

2. Leads the pupils on revision

of open sentence.

3. Gives open sentence words to

be interpreted and solved e.g.

equal number is 60 oranges are

in three baskets, if the total

number of oranges is 60, how

many are in one basket?

4. Leads the student to solve as

follows. Let the number of

oranges in each basket be M so

that M + M + M = 60

3m = 60

M = 60/3 = 20.

5. Leads the pupils to solve

quantitative aptitude related

1. prepare their

own flash cards

are bring to

class.

2. Carry out

revision on open

sentences as

guided by the

teacher.

3. Interpret word

problems into

open sentence

and solve them.

4. solve the

problems on

pupils flash

cards.

1. Charts of

worked

examples,

flash cards

on open

sentences.

2. Charts and

flash cards

on worked

example of

quantitative

aptitude test.

Pupils to:

1. solve

problems on

open

sentence.

2. to

interpret

words into

open

sentence and

solve them.

3. solve

quantitative

aptitudes

involving at

least three

arithmetic

OPERATIO

188

problems involving three or

more arithmetic operations in a

sample

5. solve

quantitative

aptitude

problems

involving three

or more

arithmetic

operations in a

sample.

NS in a

sample.

189





LEARNING MATERIALS

Evaluation Guide

TEACHER PUPILS

Angles Pupils should be

able to:

1. Measure

angles in

degrees

1.

Measureme

nt of angles

1. Brings teaching

materials to the class.

2. Uses board and

protractor, to guide the

pupils in the correct

placement of the

protractor and leading of

the value of a given

angle by using various

angles drawn on the

chalkboard.

3. Emphasizes that

angles are measured in

degree and indicate the

symbol) e.g. 600

1. Bring protractor

ruler and writing

materials to the class.

2. Draw and measure

angles in the

chalkboard and in their

workbooks.

3. Verify the teaching

of angle measurement

by their colleagues

Mathematica

l set an

chalkboard

protractor

Pupils to:

1. measure

identified

angles from

diagram in

their text

books, work

books etc.

2. draw

various plane

shapes and

measure

resulting

angles to the

nearest

degree.

2. Measure

angles in a plane

1. Asks pupils to indicate

the edges, vertices and

1. Identify the number

of edges vertices and

Protractors,

net of

Pupils to:

1. identify

190

surfaces of given three

dimensional shapes.

2. Leads pupils to

measure the size of

angle, indicate lines that

are parallel and

perpendicular in each of

the given shape.

3. Leads the pupils to

appreciate the relevance

of angle to daily life.

surfaces for different

shapes.

2. Use protractors to

determine the sizes of

angles in a given shape

and confirm the result

of these measurements.

3. Identify lines that are

parallel and

perpendicular in three

dimensional shapes.

4. Use graph sheets to

produce models of

given shapes.

5. Appreciate the

relevance of angles to

daily life.

polygons,

adhesive

tapes, graph

sheets and

clinometers.

the edges,

vertices and

faces of

given three

dimensional

shapes.

2. measure

the sizes of

angle in a

two

dimensional

shapes

3. prepare

nets and

models of

identified

three

dimensional

shapes.

191


THEME: GEOMETRY AND MENSTRUATION



LEARNING MATERIALS

Evaluation Guide

TEACHER PUPILS

3. review basic

properties of

a. Isosceles

b. Equilateral

c. Right angle

d. Scalene

triangles.

ii. Review

of basic

properties

of

a. Isosceles

b.

Equilateral

c. Right

angle

d. Scalene

triangles


the class.

2. Leads pupils to identify

isosceles, equilateral, right

angle and scalene triangular

shapes

3. Guides pupils to draw the

different triangular shapes.

4. Guides pupils to review the

properties of triangular shapes

such as equal sides, equal base

angles right angle, unequal

sides of triangles.

1. Observe the

materials

brought by the

teacher.

2. Identify

isosceles,

equilateral, right

angle and

scalene

triangular

shapes.

3. Draw the

different

triangular

shapes.

4. Review the

properties of

triangular

shapes such as

Isosceles,

equilateral,

right angle

and scalene

triangular

shapes,

metre rule

tape,

protractor

3. draw the

different

triangular

shapes.

4. state the

properties of

different

types of

triangular

shapes.

192

equal sides,

equal base

angles, right

angle, unequal

sides of

triangles.

4. review the

basic properties

of a circle

iii.

Properties

of a circle

(review)

iv.

Quantitativ

e reasoning


the class

2. Leads pupils to identify the

circle

3. Guides pupils to draw a circle

4. Leads pupils to review the

properties of a circle.

5. Leads the pupils to solve

quantitative aptitude problems

such as

Where the pupils is expected to

match the shapes to its

properties.

1. Observe the

materials

brought by the

teacher.

2. Identify the

circle

3. Draw the

circle

4. Review the

properties of a

circle.

5. Solve

quantitative

aptitude

problems as

directed by the

teacher

Circular

shapes pi-

demonstratio

n board,

pencil

5. draw

given

circular

shapes

6. state the

properties of

a circle.

7. solve

some

quantitative

aptitude

problems.

Isosceles

triangle

square

rectangle

Four sides

Equal three

sides equal

Base angles

equal

193

Department of Science Education,

University of Nigeria,

Nsukka.

2/02/2014

Sir/Madam,

Request to Validate a Research Instrument

I am a post graduate student of the University of Nigeria Nsukka, currently

undertaking a research project aimed at finding out the effect of achievement

motivational instructional approach on primary six pupils’ numerical aptitude,

achievement and retention in mathematics.

I therefore wish to use your school(s) for the exercise which wish involve

action participation of pupils and teachers of primary six (6). This exercise will last

for about three (3) weeks.

Thanks for your cooperation

Mrs. Pauline Akor

PG/Ph.D/07/48424.

194

APPENDIX H

Computation of the Reliability of MAT S/N R W p q pq

1 15 15 0.50 0.50 0.25 2 12 18 0.40 0.60 0.24 3 17 13 0.57 0.43 0.25 4 13 17 0.43 0.57 0.25 5 11 19 0.37 0.63 0.23 6 12 18 0.40 0.60 0.24 7 17 13 0.57 0.43 0.25 8 17 13 0.57 0.43 0.25 9 14 16 0.47 0.53 0.25

10 14 16 0.47 0.53 0.25 11 12 18 0.40 0.60 0.24 12 8 22 0.27 0.73 0.20 13 13 17 0.43 0.57 0.25 14 13 17 0.43 0.57 0.25 15 17 13 0.57 0.43 0.25 16 16 14 0.53 0.47 0.25 17 19 11 0.63 0.37 0.23 18 12 18 0.40 0.60 0.24 19 14 16 0.47 0.53 0.25 20 15 15 0.50 0.50 0.25 21 15 15 0.50 0.50 0.25 22 19 11 0.63 0.37 0.23 23 16 14 0.53 0.47 0.25 24 15 15 0.50 0.50 0.25 25 14 16 0.47 0.53 0.25 26 13 17 0.43 0.57 0.25 27 16 14 0.53 0.47 0.25 28 15 15 0.50 0.50 0.25 29 12 18 0.40 0.60 0.24 30 17 13 0.57 0.43 0.25 31 13 17 0.43 0.57 0.25 32 11 19 0.37 0.63 0.23 33 12 18 0.40 0.60 0.24 34 17 13 0.57 0.43 0.25 35 17 13 0.57 0.43 0.25 36 14 16 0.47 0.53 0.25 37 14 16 0.47 0.53 0.25 38 12 18 0.40 0.60 0.24 39 8 22 0.27 0.73 0.20 40 8 22 0.27 0.73 0.20 41 24 6 0.80 0.20 0.16 42 23 7 0.77 0.23 0.18 43 21 9 0.70 0.30 0.21 44 17 13 0.57 0.43 0.25

195

45 21 9 0.70 0.30 0.21 46 17 13 0.57 0.43 0.25 47 13 17 0.43 0.57 0.25 48 19 11 0.63 0.37 0.23 49 24 6 0.80 0.20 0.16 50 15 15 0.50 0.50 0.25

Total 11.85 R = Number of Examinees that choose correct option W = Number of examinees that choose wrong options p = Proportion of examinees that choose correct option q = Proportion of examinees that choose wrong options pq = Product of proportion of those that choose correct option and those that choose wrong options S2 = Variance of the total score on the test n = Number of items in the test K-R(20) = Kuder-Richardson formula 20

Σ−−

=−21

11

)20(b

S

pq

n

nRK

=

−

− 16.74

85.111

150

50

= )16.01(49

50 −

= 1.02(0.84) = 0.86

196

APPENDIX I

Computation of the Reliability of NAT using K-R(20) S/N R W p q pq

1 17 13 0.57 0.43 0.25 2 16 14 0.53 0.47 0.25 3 19 11 0.63 0.37 0.23 4 12 18 0.40 0.60 0.24 5 14 16 0.47 0.53 0.25 6 15 15 0.50 0.50 0.25 7 15 15 0.50 0.50 0.25 8 19 11 0.63 0.37 0.23 9 16 14 0.53 0.47 0.25

10 15 15 0.50 0.50 0.25 11 24 6 0.80 0.20 0.16 12 15 15 0.50 0.50 0.25 13 16 14 0.53 0.47 0.25 14 13 17 0.43 0.57 0.25 15 13 17 0.43 0.57 0.25 16 17 13 0.57 0.43 0.25 17 16 14 0.53 0.47 0.25 18 19 11 0.63 0.37 0.23 19 12 18 0.40 0.60 0.24 20 14 16 0.47 0.53 0.25 21 15 15 0.50 0.50 0.25 22 15 15 0.50 0.50 0.25 23 19 11 0.63 0.37 0.23 24 16 14 0.53 0.47 0.25 25 15 15 0.50 0.50 0.25 26 14 16 0.47 0.53 0.25 27 13 17 0.43 0.57 0.25 28 16 14 0.53 0.47 0.25 29 15 15 0.50 0.50 0.25 30 12 18 0.40 0.60 0.24 31 17 13 0.57 0.43 0.25 32 13 17 0.43 0.57 0.25 33 11 19 0.37 0.63 0.23 34 12 18 0.40 0.60 0.24 35 17 13 0.57 0.43 0.25 36 17 13 0.57 0.43 0.25 37 14 16 0.47 0.53 0.25 38 14 16 0.47 0.53 0.25 39 12 18 0.40 0.60 0.24 40 8 22 0.27 0.73 0.20 41 8 22 0.27 0.73 0.20 42 14 16 0.47 0.53 0.25 43 23 7 0.77 0.23 0.18 44 21 9 0.70 0.30 0.21

197

45 17 13 0.57 0.43 0.25 46 21 9 0.70 0.30 0.21 47 17 13 0.57 0.43 0.25 48 17 13 0.57 0.43 0.25 49 19 11 0.63 0.37 0.23 50 24 6 0.80 0.20 0.16

Total 11.95 R = Number of Examinees that choose correct option W = Number of examinees that choose wrong options p = Proportion of examinees that choose correct option q = Proportion of examinees that choose wrong options pq = Product of proportion of those that choose correct option and those that choose wrong options S2 = Variance of the total score on the test n = Number of items in the test K-R(20) = Kuder-Richardson formula 20

Σ−−

=−21

11

)20(b

S

pq

n

nRK

=

−

− 84.63

90.111

140

40

= )19.01(39

40 −

= 1.02(0.81) = 0.83

DEPARTMENT OF SCIENCE EDUCATION...Akor, A.E Pauline Prof. K.O. Usman (Student) (Supervisor) 7...

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