EFFECTS OF GUIDED-DISCOVERY LEARNING STRATEGY AND COGNITIVE STYLES ON SENIOR SCHOOL STUDENTS’...

EFFECTS OF GUIDED-DISCOVERY LEARNING STRATEGY AND COGNITIVE STYLES ON SENIOR SCHOOL STUDENTS’

PERFORMANCE IN MATHEMATICS IN OSUN, NIGERIA

An Oral Ph.D. Thesis Defence

ByAKANMU, Morenikeji Alex

98/25OC030

DEPARTMENT OF SCIENCE EDUCATION, UNIVERSITY OF ILORIN,

ILORIN, NIGERIA

SUPERVISOR: PROF. M. O FAJEMIDAGBA

• Mathematics is the science of patterns and relationships.

• Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its intrinsic interest.

• As a vital tool for the understanding and application of science and technology, the discipline plays the vital role of a precursor and harbinger to the much needed technological and of course national development, which has become imperative in the developing nations of the world.

Background to the Problem

• Mathematics difficulties are persistent, and students who have difficulties may never catch up to their normally achieving peers (Jordan, 2010).

• These difficulties, consequences of which are serious for everyday functioning and educational attainment, have been linked to learners’ self perceptions of mathematics ability and Poor teaching methods

• It is against this background that the present researcher is interested in using guided discovery method of teaching mathematics compared with expository method in relation to cognitive styles - field-dependence field-independence construct, which has become a sort of general theory of perception, intellect, and personality (personal trait which reflect both differences in ability and personalities) and find out its effect on secondary school students mathematics achievement.

Statement of the Problem

Specifically, this study investigated the:

i difference in mean gain scores of senior school students in mathematics when taught using guided-discovery strategy and non-guided discovery learning strategy.

ii. influence of cognitive styles on the performance of students in mathematics when taught using guided-discovery learning strategy.

iii. influence of gender on the performance of students in mathematics when they are taught using guided-discovery learning strategy.

iv. influence of scoring levels on the performance of students in mathematics when they are taught using guided-discovery learning strategy on the performance of students in mathematics.

Purpose of the Study

v. the interaction effect between the treatment and cognitive style on the performance of students in mathematics.

vi. the interaction effect between the treatment and gender on the performance of students in mathematics.

vii. the interaction effect between the treatment and the students’ scoring levels on the performance of students in mathematics.

viii. the interaction effect among the treatment, cognitive style, gender and students’ scoring levels on the performance of students in mathematics.

Purpose of the Study

The following research questions were raised in the study:

1. What is the difference between the mean gain scores of students in mathematics taught using guided–discovery learning strategy and non guided-discovery learning strategy?

2. Does cognitive style (Field-dependent and Field-independent) have influence on the performance of senior school students in mathematics when taught using guided-discovery learning strategy?

3. What is the influence of gender on senior school students performance in mathematics when taught using guided-discovery learning strategy?

4. Is there any difference in the senior school students performance in mathematics on the basis of their scoring levels when taught using guided –discovery learning strategy?

Research Questions

The following research questions were raised in the study:

5. Is there any interaction effect between the treatment and cognitive

style on the performance of students in mathematics?

6. Is there any interaction effect between the treatment and gender on the performance of students in mathematics?

7. Is there any interaction effect between the treatment and the students’ scoring levels on the performance of students in mathematics?

8. Is there any interaction effect among the treatment, cognitive style, gender and students’ scoring levels on the performance of students in mathematics?

Research Questions

The following null hypotheses were tested in this study:

• HO1: There would be no significant difference in post-test mean scores of the senior school students taught using guided discovery method in mathematics and those taught using conventional method.

• HO2: There would be no significant difference in the mean post-test scores of field-dependent and field-independent students when taught using guided discovery.

Research Hypotheses


• HO3: There would be no significant difference in the post-test mean scores of male and female students in mathematics when they are taught using guided discovery method.

• HO4: There would be no significant difference in post-test mean scores of students with high, medium and low scoring level when they are taught using guided discovery method.

Research Hypotheses


HO5: There would be no significant interaction effect between the treatment the treatment and the cognitive style on the performance of students in mathematics.

HO6: There would be no significant interaction between the treatment and gender on the performance of students in mathematics.

Research Hypotheses


HO7: There would be no significant interaction effect between the treatment and students’ scoring levels on the performance of students in mathematics.

HO8: There would be no significant interaction effect among the treatment, cognitive style, gender and scoring levels of students on the performance of students in mathematics.

Research Hypotheses

• This study was limited to Mathematics students in Senior Secondary Class I (SSI) and their Mathematics teachers. The choice of SSI students was considered appropriate because these students would not have been taught the topic. Two schools from Ejigbo Local Government Area of Osun State, Nigeria participated in the study. The schools were government-owned institutions operating co-educational system. The mathematics teachers in the selected schools were trained mathematics teachers with at least five years of teaching experience at the Senior Secondary Level.

• The content Area for treatment were drawn from West African Examinations Council (WAEC) recommended syllabuses for mathematics on Set Theory because it was observed that there are always questions every year on this topic in WAEC SSCE (Ale, 1989).

Scope of the Study

In this study, the following terms were operationally defined: • Teacher-Student Ratio

• Mathematics Performance

• Guided discovery method

• Cognitive styles • Control Method

• Field-dependent and Field-independent

• Scoring Level: Low Scorer students, Medium Scorer students and High Scorer students

Clarification of Major terms and Variables

It is expected that, school administrators, curriculum planners, teachers, students,

parents and the public would find useful the results of this study:

Create students with learning challenges that would enable them develop, understand

and or find out to their effective learning through mental process.

Teachers would be more sensitive to the goals of mathematics teaching. Hence, the

appropriate choice of methods of teaching for improved performance or achievement in

mathematics.

Study might provide useful information to curriculum designers and the school

administrators on appropriate curriculum materials, teaching strategies and instructional

aids for schools.

The findings of this study would acquaint federal and state ministries of education

(Mathematics division) and educational agencies such as Mathematical Association of

Nigeria (MAN) with the current structure in the mathematics classrooms in Nigeria.

Significance of the Study

The review of the related literatures covers the following areas

1. nature and objectives of the Senior Secondary General Mathematics Curriculum in Nigeria

2. theoretical framework of the study;

3. factors influencing Students’ Performance in General Mathematics;

4. influence of Teaching Strategies on Students’ academic performance in Mathematics;

5. influence of Gender on Students’ Performance in General Mathematics; 6. influence of Scoring Levels on Students’ Performance in General Mathematics; and

7. appraisal of the Literature Reviewed

Chapter Two: REVIEW OF RELATED LITERATURE

Research design

This study was a quasi-experimental research designed to determine the effects of

cognitive styles and guided-discovery learning strategy as predictor of learners’

achievement in mathematics. The research design represents the major

methodological thrust of the study, being a distinctive and specific approach which is

best suited to answer the research questions.

Therefore the pre-test and post-test control group design was considered appropriate

for this study. The pre-test, post-test of 2 x 2 x 3 experimental design was employed.

The experimental levels are as follows: Methods of teaching at 2 levels (guided-

discovery and conventional), Gender occurring at 2 levels (male and female) with

Performance (scoring ability) at 3 levels (high, medium and low scorers)

CHAPTER THREE: RESEARCH METHODOLOGY

TREATED (EXPERIMENTAL) GROUP EXPOSED TO GUIDED DISCOVERY

NON-TREATED (CONTROL) GROUP NOT EXPOSED TO GUIDED

DISCOVERY

Field Dependent

L M H L M H L M H L M H

Field Independent

M F M F

Field Dependent

L M H L M H L M H L M H

Field Independent

M F M F

Diagrammatic Representation of the Experimental Design

Diagrammatic Representation of the Experimental Design

Sampling frame for the students that participated in the Experimental group

label No M F LS-M MS-M HS-M LS-F MS-F HS-F

Field-dependent 29 16 13 0 1 15 0 1 12

Field-independent 61 30 31 3 24 3 3 25 3

label No M F LS-M MS-M HS-M LS-F MS-F HS-F

Sampling frame for the students that participated in the control group

Field Dependent 17 8 9 0 4 4 0 3 6

Field Independent 95 65 30 3 59 3 2 27 1

• The target population consisted of all students in Senior Secondary School I in Ejigbo, Osun State offering Mathematics. The choice of SSI students was considered appropriate because these students had not been taught the topic. The sample consisted of 202 students from the two purposively selected Schools. The schools were labelled A and B with school A used as experimental and B as the control group respectively. The students in the schools selected were randomized into the two treatment groups’ with the use of standardized (adopted from past questions of the West African Examinations- 1988-2011) Group Embedded Figures Test (GEFT).

• The students in each of the school selected were later stratified into the three scoring groups (Low, Medium and High) using the students’ post test scores in the Mathematics Achievement Test of Group Embedded Figures Test type into the high, medium and low scorers groups.

Sample and Sampling Technique

Group Embedded Figures Test (GEFT) type which had been applied

most commonly was adopted for this study. There were two reasons for

choosing GEFT in this study. The Mathematics Achievement Test

contained twenty multiple choice questions also drawn from the West

Africa Senior School Certificate Examinations Mathematics questions.

Validation and Reliability of the

Instruments

Apart from the content validation being ensured, the test items were

given to the researcher’s supervisor , internal-external examiner and

two experienced senior secondary school mathematics teachers in two

secondary schools in Ilorin.

Research Instrument

Procedure for Data CollectionAfter obtaining permission from the selected schools for the study and

interaction established with mathematics teachers in the chosen

schools, the first week was devoted to training the research assistant

and educate the teachers of the schools on the task.

Data Analysis TechniqueHypotheses one, two and three were tested with independent

(uncorrelated) sample t-test statistics while hypothesis four was tested

using Analysis of Covariance (ANCOVA). Statistical Package for the

Social Sciences (IBM SPSS 20.0 version) was used to analyzed the data

while Duncan post hoc test was used to ascertain the homogeneous

nature of the groups (where the significance level lied)

Research Instrument ...contd.

HO1: There would be no significant difference in post-test mean scores of students taught using guided discovery and those taught without the use of guided discovery.

Table 4. The t-Test Analysis showing difference in post-test mean scores of students taught using guided discovery and those taught without the use of guided discovery.

Hypothesis one

Variables No Mean Std df t-value sig.

Guided 90

14.0667 2.49404

200 9.389 .000

Conventional 112 10.7143 2.54484

Table 4 reveals that the calculated t-value =9.389 with p-value of .000

˂ 0.05 alpha level. Since the p-value is lesser than the alpha level of

0.05, the null hypothesis one was rejected and the alternative

hypothesis that, there would be a significant difference in post-test

mean scores of students taught using guided discovery and those

taught without the use of guided discovery was upheld. To ascertain

where the significant difference lies, the mean scores of the two

groups were compared. The mean scores of the guided discovery

(14.0667) is greater than the mean scores (10.7143) of the

conventional method. Thus, it is favour of guided discovery learning.

HO2: There would be no significant difference in the mean post-test scores of field dependent and field independent students when taught using guided discovery method.

Table 5:

The t-Test Analysis showing difference in the mean post-test scores of field

dependent (FD) and field independent(FID) students when taught using

guided discovery method

Hypothesis Two


FD 61

13.4918 2.71798

88 3.348 .001

FID 29 15.2759 1.30648

Table 5 shows that the calculated t-value = 3.348 with p-value of

.001 ˂ 0.05 alpha level. It implies that the null hypothesis two was rejected

and the alternative hypothesis that, there would be a significant difference

in the mean post-test scores of field dependent and field independent

students when taught using guided discovery method is accepted. To further

ascertain where lies the significant difference, the mean scores of the field

dependent and field independent students were compared and it was found

that it was in favour of the field independent students. The mean scores

obtained for the field dependent is (15.2759) which is greater than the mean

scores (13.4918) obtained in respect of the field dependent learners.

Ho3: There would be no significant difference in post-test mean scores of male and female students in mathematics when they are taught using guided discovery method

Table 6:

The t-Test Analysis showing difference in post-test mean scores of male and

female students in mathematics when they are taught using guided

discovery method

Hypothesis Three


Male 46

14.0652 2.58545

88 .168 .867

Female 44 13.9767 2.37535

From Table 6, analysis reveals that the calculated t-value = .168 with p-value

of .867 ˃ 0.05 alpha level. It implies that the null hypothesis three which

state that there would be no significant difference in post-test mean scores of

male and female students in mathematics when they are taught using guided

discovery method was accepted . In other words, the performance of male

and female students taught using guided discovery method shows no

difference. Hence, the hypothesis is upheld. The mean scores obtained for

male and female in field-dependent were 5.5667 and 5.0968 respectively. For

the field-independent, 11.6250 and 12.3846 was obtained as mean scores for

male and female in the group.

HO4: There would be no significant difference in post-test mean scores of students with high, medium and low scoring level when they are taught using guided discovery method

Table 7:

ANCOVA Analysis showing difference in the post-test mean scores of

students with high, medium and low scoring level when they are taught

using guided discovery method

Hypothesis Four

Source Type III Sum of Squares

df Mean Square

f Sig.

Corrected Model97.785a 3 32.595 6.150 .001

Intercept2517.655 1 2517.655 475.013 .000

Pretest4.006 1 4.006 .756 .387

Scoring Level89.186 2 44.593 8.413 .000

Error455.815 86 5.300

Total18362.000 90

Corrected Total553.600 89

Table 7 indicates the Analysis of Covariance containing the scoring level

ability, mean squares, f-test value and the corresponding p-values. From the

table, the calculated f-value is 8.413 with p-value equals .000 which is less

than the alpha level of 0.05. this implies that the null hypothesis four is

rejected and the alternative hypothesis which states that there would be a

Significant difference in post-test mean scores of students with high,

medium

and low scoring level when they are taught using guided discovery method.

Hypothesis Five

HO5: There would be no significant interaction effect between the treatment and thecognitive style on the performance of students in mathematics.

Table 11: ANCOVA Computation on Post-test Mean Scores of Students in the TreatmentGroup and Cognitive style Source


df Mean Square F Sig.

Corrected Model 876.820a 4 219.205 44.702 .000

Intercept 1685.064 1 1685.064 343.630 .000

Pretest 49.284 1 49.284 10.050 .002

Treatment 161.788 1 161.788 32.993 .000

Cognitive style 24.452 1 24.452 4.986 .027

Treatment * Cognitive style 32.041 1 32.041 6.534 .011

Error 966.031 197 4.904

Total 31850.000 202

Corrected Total 1842.851 201

a. R Squared = .476 (Adjusted R Squared = .465)

Table 11 showed that at F(1, 197) = 6.534, p <

0.005, the null hypothesis was rejected. Hence,

there was significant interaction effect between

the treatment and the cognitive style of the

students. The profile plot is shown in figure 10.

Figure 10: Graph on the interaction effect between the treatment andthe students’ Cognitive Style

Hypothesis 6

HO6: There would be no significant interaction between the treatment and gender on the performance of students in mathematics. Table 12: ANCOVA Computation on Post-test Mean Scores of Students in the Treatment Group and Gender




Intercept 4535.492 1 4535.492 877.569 .000

Pretest 251.631 1 251.631 48.688 .000

Treatment 372.906 1 372.906 72.153 .000

Gender .142 1 .142 .027 .869

Treatment * Gender .011 1 .011 .002 .963

Error 1018.144 197 5.168

Total 31850.000 202



From table 12, there was no significant interactioneffect between the treatment and students’ gender.

This was because at F(1, 197) = .002, p > 0.05.therefore, the null hypothesis was not rejected.This is further corroborated in the profile plot as shownin figure 11 where the two lines appeared too closeindicating that, there was no major difference even inthe treatment condition.

Figure 11:Graph on the interaction effect between the treatment and the students’ Gender

Hypothesis 7

HO7: There would be no significant interaction effect between the treatment andstudents’ scoring levels on the performance of students in mathematics. Table 13:ANCOVA Computation on Post-test Mean Scores of Students in the Treatment Group and Scoring levels


Df Mean Square F Sig.


Intercept 3290.016 1 3290.016 1342.647 .000

Pretest 30.681 1 30.681 12.521 .001

Treatment 59.919 1 59.919 24.453 .000

Scoringlevel 453.486 2 226.743 92.533 .000

Treatment * Scoringlevel .420 1 .420 .171 .679

Error 480.278 196 2.450

Total 31850.000 202



Table 13 showed that the computed value of F(1,196)

= .171, p < 0.05, the null hypothesis was rejected.

Therefore, there was a significant interaction

between the scoring levels of the students and the

treatment. Figure 12 also revealed the difference that

existed in the treatment condition.

Figure 12: Graph on the interaction effect between the treatment and the students’ Scoring levels

Hypothesis 8

HO8: There would be no significant interaction effect among the treatment, cognitive style, gender and scoring levels of students on the performance of students in mathematics.

From table 14, F(1, 183) = .221, p < 0.05, the was

significant interaction effect among the treatment,

cognitive style, gender and scorings of the students.

No profile plot is shown as SPSS 20.00 can only plot

graph for variables not exceeding three.

Table 14:

ANCOVA Computation on Post-test Mean Scores of Students in theTreatment Group, Cognitive style, Gender and Scoring levels




Intercept 1053.398 1 1053.398 510.348 .000

Pretest 80.838 1 80.838 39.164 .000

Treatment 24.297 1 24.297 11.772 .001

Scoringlevel 170.115 2 85.058 41.209 .000

Gender .411 1 .411 .199 .656

Cognitivestyle 10.510 1 10.510 5.092 .025

Treatment * Scoringlevel 4.124 1 4.124 1.998 .159

Treatment * Gender .038 1 .038 .018 .892

Treatment * Cognitivestyle 7.130 1 7.130 3.454 .065

Scoringlevel * Gender .773 2 .387 .187 .829

Table 14 contd.

Scoringlevel * Cognitivestyle 22.893 1 22.893 11.091 .001

Gender * Cognitivestyle .795 1 .795 .385 .536

Treatment * Scoringlevel * Gender .050 1 .050 .024 .876

Treatment * Scoringlevel * Cognitivestyle

2.491 1 2.491 1.207 .273

Treatment * Gender * Cognitivestyle

4.380 1 4.380 2.122 .147

Scoringlevel * Gender * Cognitivestyle

1.823 1 1.823 .883 .349

Treatment * Scoringlevel * Gender * Cognitivestyle

.455 1 .455 .221 .639

Error 377.726 183 2.064

Total 31850.000 202



The following are the summary of major findings in this study:

1. the experimental group taught using guided-discovery learning strategy had a

significantly higher score than the control group taught using the non guided-

discovery;

2. the post test mean scores of the field-independent students were significantly higher

than the post test mean scores of the field-dependent students when taught using

Guided-discovery learning strategy;

3. post test mean scores of male students was not significantly higher than that

of the female students when taught using guided-discovery learning strategy;

4. higher scorers benefited most, followed by medium scorers and the low scorers

benefitted least when taught using guided-discovery learning strategy. To further

ascertain this with respect to where the difference lied, Duncan post-hoc test was

carried out and the output of 15.1818 in table 8 subset 3 reveals that students with high

scoring ability is most significant of all the groups. •

Summary of Major Findings

5. there was significant interaction effect between the treatment and the cognitive style of the students, F(1, 197) = 6.534, p < 0.05.

6. there was no significant interaction effect between the treatment and students’ gender. This was because at F(1, 197) = .002, p > 0.05.

7.there was a significant interaction between the scoring levels of the students and the treatment, F(1,196) = .171, p < 0.05.

8. the was significant interaction effect among the treatment, cognitive style, gender and scorings of the students, F(1, 183) = .221, p < 0.05.

Summary of Major Findings...contd

Discussion

The findings of this study agreed and also varied with the findings existing

studies

Conclusion

Results from this study have shown that there was a significant difference in

the performance of Mathematics students taught using guided discovery

method over the students taught using conventional method. The study has

shown the potency of guided discovery method of teaching in improving

student’s performance. Equally, the outcome of the study with respect to

cognitive styles was in favour of the field independent students. Findings from

the present study have also shown that gender has no role to play in the

performance of the students. The findings of this study has also revealed that

all scoring ability groups benefited from the method of teaching with high

scoring ability as most significant of all the groups.

Chapter Five: Discussion, Conclusion and Recommendations

n line with the findings of this study, the following are recommended: • Guided Discovery Learning was found helpful in learners’ ability to

extract a simple figure from a complex one since it was more interactive. It is recommended that the teachers should make the teaching-learning of mathematics an interactive and activity – based one for the students. Teachers should use many methods while teaching mathematics, for instance set theory, so that all students could gain from the teaching irrespective of the ability levels of the students.

• Mathematics teachers should be taught different methods of teaching. This can be made possible by organising seminars and workshops on pedagogy for the teachers.

• Students could be rewarded for their performance in mathematics test with little gifts which are not expensive. This will ginger the low scorers to improve on their performance

Recommendations

• Male and females should have roles to play in mathematics class since males are not superior to female in mathematics class as found out in this study.

• Ministries of Education at both Federal and State levels should periodically asides regular workshops for teachers develop a mean of reviewing / assessing the impact of teaching methods.

Recommendations

Further study be carried out to involve other methods for

teaching mathematics.

Other variables like attitude, school type and teachers

qualification can be included alongside either with guided

discovery or other identified methods of teaching.

Further study be conducted in other States of the Federation or geo-

political zone.

A replication of a similar study be carried out to either

corroborate or refute the findings of this study since knowledge

and human behaviour are dynamic.

Suggestions for Further Studies

Thank you

EFFECTS OF GUIDED-DISCOVERY LEARNING STRATEGY AND COGNITIVE STYLES ON SENIOR SCHOOL STUDENTS’...

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