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Chapter I

INTRODUCTION

Background of the Study

It has already been pointed out that mathematics is an essential discipline because

of its practical role to the individual and society. Without mathematics to describe

physical phenomena, we might be living in a world with beautiful art, literature, and

philosophy, but no technology. Even the medical advances of the last 50 years might not

have occurred.

Mathematics is truly the language of science. It deals with the way of describing

relationships between numbers and other measurable quantities and can express simple

equations as well as interactions among the smallest particles and the farthest objects in

the known universe and allows scientists to communicate ideas using universally

accepted terminology.

Encarta (2009) revealed the benefits of mathematical research every day. The

fiber-optic network carrying our telephone conversations was designed with the help of

mathematics. Our computers are the result of millions of hours of mathematical analysis.

Weather prediction, the design of fuel-efficient automobiles and airplanes, traffic control,

and medical imaging all depend upon mathematical analysis.

However, for the most part, mathematics remains behind the scenes. We use the

end results without really thinking about the complexity underlying the technology in our

lives. But the phenomenal advances in technology over the last 100 years parallel the rise

of mathematics as an independent scientific discipline.

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Sophian (2007) exposed that majority of the students nowadays are not interested

to learn mathematics because of its seemingly complex process. The analysis and

comprehension of the mathematical problems create in them a dislike for the subject.

Thus, the teaching of mathematics in the Philippines has been observed to be weak as

shown by the results of the survey tests given to the students recently.

Since most people around the world learn English as a second language, it is

taught more and more and has become the world’s language in science, mathematics,

business, and technology. Today it influences other languages because it is the medium

by which students learn the concept in any field of education.

Yap (2008) emphasized that English is a language of the world, a language of

Asia, a language of the Philippines. English is a language of the government, commerce,

industry and trade, science and technology, tourism, cinema, and other fields. It is a

prestige language, a language of progress and opportunities for a better life.

However, the Encyclopedia on Early Childhood Development as cited by Sophian

(2009) revealed that most students have problems understanding or expressing ideas

using the English language. These problems can slow down or even stop the learning of a

wide range of skills, including reading, spelling, writing and solving mathematical

problems. They include difficulty with the understanding and construction of sentences,

and confusion that occurs with lengthy or complex language such as solving algebraic

problems in mathematics.

The National Mathematics Advisory Panel (2008) added that in the Philippines,

particularly in some public schools, majority of the students have encountered complexity

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in mathematics in comprehending, constructing, analyzing mathematical text in word

problems and using correct mathematical operations.

Furthermore, it has been pointed out that students have poor performance if

mathematical concepts are associated into a problem solving in all mathematics subjects

because of the limited English vocabulary of the students.

The Philippines, a Southeast Asian country of some 7,100 islands and islets of the

southeast coast of mainland China, populated by about 70 million Filipinos is richly

blessed with over 170 languages and dialects spoken by about 90,000,000 population in

the archipelago. It is further said that there are as many as 300 languages and dialects in

these islands which belong to the Malayo-Polynesian family and languages.

All these languages and dialects contribute to the development and enrichment of

our evolving national language: Global Filipino. The growth, development and spread of

Global Filipino is unstoppable. It has been gaining acceptance and popularity, especially

among language organizations, linguistic circles, and in the academes here and abroad.

But this Global Filipino is still “in limbo” in the present educational system of our

country.

It is for this matter that in 2009, the Department of Education promulgated an

order institutionalizing a system of mother-tongue based multilingual education (MLE),

wherein instruction is conducted primarily in a student’s mother tongue with additional

languages such as Filipino and English being introduced as separate subjects. In

secondary school, Filipino and English become the primary languages of instruction, with

the learner’s first language taking on a secondary role.

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Yap (2008) emphasized that the mother tongues in the regions play an important

role in the Philippine educational system. She added that we Filipinos have strong ethnic

loyalty and pride in using our own native tongues in all occasions. We have the human

rights and language rights to use, develop and preserve our mother tongues, especially the

dialects in the brink of extinction.

In addition, the UNESCO commitment to Education for All in the multilingual

world is linguistic diversity and multilingualism. The Summer Institute of Linguistics

(SIL) Philippines has recommended “The ‘First Language’ Bridge to Filipino and

English Program” in all schools.

Relatedly, the study of the Department of Education Region IV-B (MIMAROPA)

entitled “Double Exposure in Mathematics: a Glimpse of Mother Tongue First” has

provided the local validation of the fundamental observation that top performing

countries in the Trends in International Mathematics and Science Study (TIMSS) are

those that teach and test students in science and math in their own languages.

Moreover, Article XIV, Section 7 of the 1987 Constitution of the Philippines

specifies, in part: that the regional languages are the auxiliary (secondary) official

languages in the regions and shall serve as auxiliary media of instruction therein.

It is along this premise that the researcher conducted this study to find out if the

use of Cebuano as a learning tool in solving algebraic problems improves the

mathematics’ performance of the students.

In general, the findings of this study could be of significance to the teachers by

comparing students’ performance using English vis-à-vis Cebuano (common language)

as a learning tool in solving algebraic problems.

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Objectives of the Study

This study simply aimed to compare English and Cebuano languages as learning

tool in solving algebraic problems.

Specifically, this study sought to achieve the following objectives:

1. describe the process of employing the English language vis-à-vis Cebuano as a

learning tool in solving algebraic problems;

2. find out the scores of the respondents in solving algebraic problems using the two

languages (Cebuano and English);

3. determine the incremental scores of the respondents between the two sets of tests

conducted using the English and Cebuano languages;

4. determine the significant relationship of the respondents’ scores using the English

language vis-à-vis Cebuano as a learning tool in solving algebraic problems;

5. determine the significant difference of the respondents’ scores in relation to their

incremental scores; and

6. elicit students’ feedback on their experiences and exposure with regards to the use

of English vis-à-vis Cebuano in solving algebraic problems.

Hypotheses

Ho1: There is no significant relationship between the respondents’ scores using

the English language and Cebuano as a learning tool in solving algebraic problems.

Ho2: There is no significant difference of the respondents’ scores in relation to

their incremental scores.

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Framework of the Study

Theoretical. The theories which provide the foundation for this study was geared

towards effective learning theories that have impact on the conduct of the study.

The study is anchored on the cognitive theory of Piaget, Multiple theory

intelligences of Gardner, Insight theory of Kohler and Reflective theory of John Dewey.

The researcher’s theory has evolved from the views and thinking of renowned

psychologists and philosophers; foremost of whom is St. Thomas Aquinas (1980), who

said that God is the primary and principal teacher and the primary cause of knowledge of

the students. The student is the secondary but principal cause of learning, for unless he

performs the necessary intellectual operations, nothing happens.

In the same light, Piaget (1980) stated that learning is based on students’ active

participation in the learning environment regarding a learning activity which they find

relevant and engaging such as problem-solving and critical thinking. They are

“constructing” their own knowledge by testing ideas and approaches based on their prior

knowledge and experience, applying these to a new situation, and integrating the new

knowledge gained with pre-existing intellectual constructs.

He further asserted that the skills in problem-solving couldn’t be taught. Instead,

the rules of experimentation and the rules of problem-solving must be invented by each

student. The rules of theories investigated on the area of any subject must be noticed by

individual. Different individuals have different problem-solving conceptions.

According to Lester (1994), the focus on teaching mathematics topics through

problem-solving contexts and enquiry-oriented environments are characterized by the

teacher, helping students construct a deep understanding of mathematical ideas and

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processes by engaging them in doing mathematics: creating, conjecturing, exploring,

testing, and verifying.

For learning to take place, Kohler said in his insight theory, gaining insight is a

gradual process of exploring, analyzing, and restructuring perceptions until a solution is

arrived. Learning can take place through the act of insight. In this theory, teacher should

give the students clues in puzzle format. From the clues, students will work together to

figure out the problem. Thus, they will develop the connection of the facts together to

reach thoughts and ideas which directs solution to the problem.

The researcher believes that when the amount of attention a student gives to a

lesson at hand is not complete, there is no understanding of the subject matter. There can

be no learning when the student is not interested to learn at all due to inability to

comprehend. The teacher on the other hand, is a secondary and merely instrumental

cause of learning, though he is also, in many situations, an indispensable one.

Moreover, Dewey’s reflective thinking considered the classic model for problem-

solving. He asserted that everyone learns from experience, either positive or negative. In

Mathematics, experience alone is not sufficient for lasting learning; rather it is the

analysis that leads to new meaning. Through reflection, students acquire meaning and

truth is an idea that has worked in practical experience.

As a philosopher, Dewey emphasized the practical, striving to show how

philosophical ideas can work in everyday life. His sense of logic and philosophy was

ever-changing, adaptive to need and circumstance. The process of thinking, in his

philosophy, is a means of planning action, of removing the obstacles between what is

given and what is wanted.

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On the other hand, Gardner’s (1985) modern definitions of intelligence, talk about

practical intelligence which enables 'the individual to resolve genuine problems or

difficulties that he or she encounters' and also encourages the individual to find or create

problems 'thereby laying the groundwork for the acquisition of new knowledge'. As was

pointed out earlier, standard mathematics, with the emphasis on the acquisition of

knowledge, does not necessarily cater for these needs.

Gardner is known for his theory in multiple intelligences. Logical/mathematical

as one of the eight (or more) intelligences identified by Gardner that people must have

inorder to accommodate students’ learning. It consists of the capacity to analyze

problems logically, carry out mathematical operations, and investigate issues

scientifically. He further asserted that it entails the ability to detect patterns, reason

deductively and think logically. This intelligence is most often associated with scientific

and mathematical thinking.

In the same manner, Thorndike is particularly known for his construction of

various intelligence and aptitude tests and for his repudiation of the belief that such

primarily intellectual subjects as languages and mathematics discipline the mind. Because

of his opposition to that belief, he greatly encouraged the inclusion of various

informational subjects, such as the physical and social sciences, in elementary and

secondary school curricula.

From these insights, the researcher all the more believed problem-solving

approach can be useful in resolving genuine problems or difficulties that a person

encounters and also encourages him to find or create problems, thereby; laying the

groundwork for the acquisition of new knowledge.

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Figure 1. The theoretical framework of the study

Problem Solvingin Algebra

Piaget(Cognitive Theory)

Gardner(Multiple Intelligences

Theory)

Thorndike(Various Intelligence

Theory)

St. Thomas Aquinas(God as the primary

teacher)

Dewey(Reflective Theory)

Kohler(Insight Theory)

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Conceptual. This study was conducted to compare the result of using the English

vis-à-vis Cebuano as a learning tool in solving algebraic problems.

The study utilized the researcher-made test to determine their level of

comprehension in solving algebraic problems using the two languages. In conducting,

the researcher constructed a ten-item problem-solving test using English and Cebuano

and administered it to the third year BEEd students who were the respondents of the

study.

Whereas, the respondents were given the English problems to be solved first

followed by Cebuano (common language) translation.

Furthermore, their scores in both presentations were taken into consideration and

the incremental scores were computed inorder to know whether the use of the English in

solving algebraic problems has significant relationship with their scores in the

subsequently conducted similar problems using Cebuano as a learning tool.

The illustration of the conceptual framework is presented in Figure 2.

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Figure 2. The conceptual framework of the study

[

English

Solving

Algebraic Problems

LEARNING

TOOL

Common Language(Cebuano)

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Importance of the Study

The researcher firmly believes that this study has significant value to the

following individuals:

School administrators. Results of this study may challenge the school

administrators to keep abreast of the new educational methods particularly in the use of

English and in relation to Cebuano as a learning tool in solving algebraic problems in

order to pave the way for a better system of education relevant to the needs of the

changing times.

Curriculum planners. Findings of this study is of great help to the curriculum

planners to include in the curricula some activities or lessons that call for the

development of higher order thinking skills through problem solving using Cebuano

aside from the usual English which is a pre-requisite to the successful implementation of

this study.

School personnel. Findings of this study will encourage the school personnel to

provide classroom activities and classroom environments that stress high academic

achievement while also preserving the native language and not be totally dependent on

the foreign languages.

Mathematics’ teachers. It is the hope of the proponent that teachers especially

those teaching Mathematics may employ the use of a language that could easily be

understood by the students and help them to start liking mathematics and eventually

improve their school’ performance. They should also be encouraged to utilize the

common language as a learning tool in solving algebraic expressions as well as in the

content of their textbooks and workbooks.

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Students. Results of this study shall eventually help improve students’

performance in solving mathematical formula using the language they understand most

particularly Cebuano.

Student teachers and novices. This study may persuade student teachers and

novices in profession that they should also be oriented with the basic concepts and skills

needed to successfully implement the study. This should be one of the major roles of

Teacher Education Institution in order to help the learners by employing an alternative

method for their absolute understanding of the lessons.

Parents. It is hoped that after this study, the parents will be able to help their

students understand and solve the mathematical problems not only through the use of

English as a learning tool but Cebuano as well.

Future researchers. A similar study should be undertaken to verify the results of

this investigation inorder to determine the effectiveness of the strategy both in high

school and college.

Scope and Delimitation of the Study

This study focused on determining the relationship of using English and Cebuano

as a learning tool in solving algebraic problems.

Respondents of this study were limited to ninety (90) students presently taking

mathematics handled by the researcher herself. They were randomly selected from the

four (4) sections among the one hundred sixty (160) BEED third year students of this

University.

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Definition of Terms

Several terms were used throughout this paper and have been conceptually and

operationally defined to establish a common understanding of their use in the reporting of

this study.

Algebraic problems. The term refers to the higher-order cognitive process that

requires the modulation and control of more routine or fundamental skills. In this study,

it refers to the solving problems constructed by the researcher and have been translated

from the English language to Cebuano.

Cebuano (Common Language). The term refers to the language used by a certain

group of people living in a particular locality and as used in this study, it refers to the use

of Cebuano dialect in presenting the algebraic problems to the students.

Dialect. The term refers to a variety of a language spoken by an identifiable sub-

group of people. In this study, it refers to the Cebuano dialect as spoken by some of the

students from the different municipalities of Biliran province.

English language. The term refers to the language used as one of the learning

tools in solving algebraic problems. It also refers to the primary language of the majority

of people in the United Kingdom, the United States, Canada, Australia, New Zealand,

other former colonies of Britain, and territories of the United States. English is spoken in

more parts of the world than any other language and by more people than any other

language except Chinese.

Language. The term refers to the principal means used by human beings to

communicate with one another which is primarily spoken, although it can be transferred

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to other media, such as writing. In this study, it refers to English and Cebuano as used in

presenting the algebraic problems to the students.

Learning tool. The term refers to the instrument being employed by the teacher in

providing knowledge to the learners. In this study, it refers to the medium of instruction

used by the teacher in presenting his lesson such as English and Cebuano.

Mother Tongue. The term refers to the first language learned at home in childhood

and still understood by the individual. It is quite possible that the first language learned

is no longer a speaker's dominant language. This includes young immigrant children,

whose families have moved to a new linguistic environment, as well as people who

learned their mother tongue as a young child at home (rather than the language of the

majority of the community), who may have lost, in part or in totality, the language they

first acquired (see language attrition).

Solving algebraic problems. The term refers to the mental process that includes

problem finding and problem shaping as well as finding ways to apply new solutions to

complex problem situations rather than relying on fixed rules or recipes. In this study, it

refers to the process of solving mathematical problems particularly algebra.

Respondents. The term refers to the individuals involved in any kind of research

or study. In this study, it refers to the BEEd third year COEd students at Naval State

University, Naval, Biliran.

Vis-à-vis. The term refers to the relationship of one thing from the other. In this

study, it refers to the comparison of the English language to Cebuano as a learning tool in

solving algebraic problems.

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Review of Literature

Statements of writers and recognized mathematicians as well as the findings from

previous studies were collected to provide a ground for the present study.

The lessons and findings of various local initiatives and international studies in

basic education have validated the superiority of the use of the learner’s mother tongue or

first language in improving learning outcomes and promoting Education for All (EFA).

Wikipedia (2008) defined the first language (also native language, mother tongue,

arterial language, or L1) as the language a person has learned from birth or within the

critical period, or that a person speaks the best and so is often the basis for sociolinguistic

identity. In some countries, the terms native language or mother tongue refer to the

language of one's ethnic group rather than one's first language. Sometimes, there can be

more than one mother tongue, when the child's parents speak different languages. Those

children are usually called bilingual. By contrast, a second language is any language that

one speaks other than one's first language.

Abadzi as cited by Padre (2010) stressed that for many children, education in

another language is more difficult than expected.  The deficits in native language

development common among the poor may inhibit the rapid acquisition of a second

language. Mother tongue instruction is a prerequisite if Education for All is to be

achieved, particularly when the official language has complex spelling rules. The official

language should be taught to children as early as possible. However, it should become the

platform for learning new information only after children know it sufficiently well to

process complex sentences and vocabulary. A gradually decreasing percentage of

mother-tongue instruction seems to be an effective way to introduce an official language.

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To catch up with native English speakers, minority language students must

receive effective bilingual instruction (that is, studying parts of subjects in both

languages). Otherwise they continue to score lower on basic skills tests throughout their

12 years of school. The performance difference between students receiving bilingual

education and those receiving only English or English-as-a-second language instruction

may be dramatic.

Nation and Waring (1997) emphasized that the positive results of literacy in

mother tongues are evident in a program piloted in 800 schools in Zambia. The children

learned to read just in local languages in grade 1 while learning English orally at the same

time. Efforts were made to use instructional time well and employ interactive, “student-

centered” methods. English writing was introduced in grade 2. The results were

astounding. In 1999, students read on average two grade levels below their grade level in

English and three grades below their grade level in Zambian languages; but in 2002,

students reading and writing scores were 575 percent above baseline for grade 2, 417

percent for grade 3, 300 percent for grade 4, and 165 percent for grade 5. Scores in

Zambian languages ranged from 780 percent above baseline from grade 1 to 218 percent

in grade 5. Subsequently, the program was introduced to all schools of the country.

They added that children must learn 2,000-3,000 words through interactive speech

before they can understand the content of the lessons sufficiently. To keep up with the

increased complexity of school, they learn about 1,000-2,500 words per year.

In second-language acquisition, a college student taking immersion class in a

foreign language for three hours a week would require about four years or about 600

hours of interactive instruction and reading to attain relative mastery in one of the

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common languages. Given the limited instructional time and competence of many

teachers, it is unknown how long it takes to provide sufficient levels of instruction.

Thomas and Collier (1997) suggest that a very effective model of language

introduction is 10 percent of foreign language in grade 1, gradually increasing to 20

percent, 30 percent, 40 percent, and 50 percent by grade 5. Students who start school

performing at grade level and receive such gradual bilingual education will catch up with

English-language students by grade 5.

Moreover, Philippine Daily Inquirer (2010) as written by Tarra Quismundo

published that the 170 + Talaytayan MLE Inc. – a group of professors and education

reform advocates urged the Aquino administration to institutionalize the use of mother

tongue multilingual education (MTBMLE) in the country's public schools as it expressed

alarm over declining functional literacy among Filipinos.

“Counting and comprehension skills among Filipinos remain dismally and

alarmingly low,” said Ricardo Ma. Nolasco, head of the Talaytayan group and associate

linguistics professor at the University of the Philippines-Diliman.

She further said that the government needs to “vigorously implement its ten-point

agenda for education including changing the exclusively English and Filipino-based

curriculum into one in which Filipino children start learning through their mother

tongue.”

Veering away from traditional bilingual teaching, the method is proven to

improve comprehension and retention among young students and builds a strong

foundation for learning other languages and Philippine waterloo subjects like math and

science.

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The 2008 Functional Literacy and Mass Media Survey (FLEMMS) released by

the National Statistics Office last month showed that one of every 10 Filipinos aged 10 to

64 were functionally illiterate, or had a time reading, writing, computing and

understanding. The survey was administered on a sample of some 70,000 Filipinos

nationwide.

Based on FLEMMS results, Nolasco noted that the number of Filipinos who can

read but cannot understand rose from 19.6 million from 2003 to 20.1 million in 2008

given the rise in population; while the number of Filipinos who could not compute

remained at 9.1 million.

In addition, the Department of Education (DepEd) Undersecretary Yolanda

Quijano said that these results could be traced to the use of a foreign language in official

instruction.

DepEd continues to test mother tongue instruction in some 100 public elementary

schools around the country with initial results showing significant improvement in

learning and understanding among students.

Many scholars have given definitions of 'mother tongue' through the years based

on common usage, the emotional relation of the speaker towards the language, and even

its dominance in relation to the environment. However, all of these criteria lack precision.

DepED Order No. 74 s. 2009 on Basic Education policy issued by the Department

of Education thru Secretary Jesli A. Lapus institutionalizing mother tongue-based

multilingual education (MLE).

It further stressed that the first language of a child is part of their personal, social

and cultural identity. Another impact of the first language is that it brings about the

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reflection and learning of successful social patterns of acting and speaking. It is basically

responsible for differentiating the linguistic competence of acting.

In addition to this, UNESCO proclaimed February 21 as the International Mother

Language Day by on November 17, 1999.

Reactions against national languages in Africa have been widespread and have

resulted in reversal of programs in Guinea and Madagascar. However, the success of

programs in Zambia, Mali, and Burkina Faso are encouraging.

In the most remote schools it may be ultimately impossible to teach sufficient

language and make a transition to higher grades possible to many students. If that is the

case, then fluent reading and math skills in a native language as well as basic concepts

may be all that most may acquire.

Mother Tongue-Based Multilingual Education, hereinafter referred to as MLE, is

the effective use of more than two languages for literacy and instruction. Henceforth, it

shall be institutionalized as a fundamental education policy and program in this

Department in the whole stretch of formal education including preschool and in the

Alternative Learning System (ALS).

The use of the learner’s First Language (L1) as the primary medium of instruction

(MOI) from pre-school until, at least, grade three. During such period, L1 shall be the

main vehicle to teach understanding and mastery of all subjects areas like Math, Science,

Makabayan, and language subjects like Filipino and English;

Mother Tongue as a subject and as a language of teaching and learning will be

introduced in grade one for conceptual understanding; The language of instruction shall

also be the primary language for testing in all regular school-based and system-wide

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examinations and in all international benchmarking and assessment exercises. It shall be

maintained that the focus of educational assessment shall be specifically on the learner’s

understanding of the subject content and not be muddled by the language of testing;

There must be a continuing in-service training (INSET) in partnership with MLE

specialists on the effective use of L1 as language of instruction – to facilitate reading,

Cognitive Academic Language Proficiency, and the development of cognitive and higher

order thinking skills (HOTS) of the learner. INSET shall likewise equip educators to

develop cultural sensitivity and enhance appreciation for cultural and linguistic diversity;

and An MLE technical working group at the regional and division levels shall be

established to facilitate MLE planning, monitoring and evaluation.

In world Englishes today, Philippine English as the English language used in the

Philippines, is recognized, respected and accepted as a variety or “nativized” English. It

is a powerful vehicle of communication and information. We acquire the wisdom and

knowledge of the world through English. We read and learn more scientific researches

and advanced knowledge about Filipino and other Philippine languages through English.

English can enrich our national language and other languages, and cultures, and even

strengthen rather than “engulf” our national identity as a people. And Philippine English

is here and here to stay in education and other important domains of language.

SWS September 2009 findings (PDI, 07 November 2009). Revealed that amidst

national economic downturn in our super typhoon-battered nation, with 53 percent of

Filipinos call themselves mahirap (poor), and poverty is the same after 26 years.

Moreover, experts (PDI, 16 November 2009) said that 35percent now live below

poverty line, considering that there are more than 150 languages and dialects as shown in

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the presented Linguistic Map of the Philippines – can the Philippine educational system

successfully implement the DepEd Order No. 74, s. 2009: Mother Tongue-based

Multilingual Education (MT MLE), beginning school year 2010-2011?

In Congress, several bills have been introduced and pending for deliberation and

enactment into law. The House and Senate Bills aim to change or modify the current

Bilingual Education Policy (BEP) into a Trilingual Education Policy (TEP). That is, the

use of the Mother Tongue (L1), Filipino (L2), English (L3), and optional use of foreign

languages (L4) in all levels of the Philippine Education System.

In the DepEd Mother Tongue-based Multilingual Education (MT MLE) Policy,

English is given importance in the policy implementation, and in the functional and basic

literacy programs and projects. In the Bilingual Education Policy (BEP) and in the MT

MLE, English plays an important role.

One of the factors that complicate the language situation in the Philippines is

diversity. Linguists say there are 75 to 150 native languages spoken by Filipinos. The

latest estimate is 109 languages, or 110 if Chavacano is included (McFarland 1994:83).

Although these languages are in some ways grammatically and lexically similar, they are

mutually unintelligible.

Furthermore, each of the major languages has several dialects that differ,

especially at the phonological and lexical levels. Depending on their region of origin,

Filipino immigrants will speak at least one dialect of one of these mutually unintelligible

languages.

On a basis of a probable 75 mother tongue according to Weber (1989), six are

classified as major languages: (Tagalog-25%; Cebuano-24%; Ilocano-9%;

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Hiligaynon;9%; Bicol-6%; Waray-5%; and other 22%. Because of immigration, these

major languages as well as Pampagno and Pangasinan are represented in America. The

Chinese and the non-Tagalog communities in the Philippines also frequently code-switch

their language, be it Cebuano or Min Nan Chinese, with Taglish.

On the other hand, the National Council of Teachers of Mathematics (NCTM,

1989) recommended that problem-solving be the focus of mathematics teaching, because

it encompasses skills and functions which is an important part of everyday life.

Unfortunately, students have struggled and encountered difficulty in solving word

problems in the subject, maybe because they do not know how to choose the correct

principle, concept and operation to apply or they could not fully comprehend the problem

especially those students who are not well-versed in the English language.

For this reason, mathematics teachers should therefore be dynamic and creative so

that students could learn and enjoy the subject. With their unique expertise, they should

weave a web of magic so that it would emerge as the ideal subject to stimulate creativity,

enhance thinking skills, and sharpen problem solving abilities of the students.

Stanic and Kilpatrick (1995) asserted that in the past decade, problem-solving

techniques can be made available most effectively through making problem solving the

focus of the mathematics curriculum. Although mathematical problems have traditionally

been a part of the mathematics curriculum, it has been only comparatively recent that

problem solving has come to be regarded as an important medium for teaching and

learning mathematics.

Olkin and Schoenfeld (1994) gave further reason why a problem-solving

approach is valuable is an aesthetic form. According to him, it allows the student to

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experience a range of emotions associated with various stages in the solution process.

Mathematicians who successfully solve problems say that the experience of having done

contributes to an appreciation for the 'power and beauty of mathematics' which is like the

“joy of banging your head against a mathematical wall and then discovering that there

might be ways of either going around or over that wall.

However, although it is this engagement which initially motivates the solver to

pursue a problem, it is still necessary for certain techniques to be available for the

involvement to continue successfully. Hence, more needs to be understood about what

these techniques are and how they can best be made available.

An influential but controversial claim in current research literature on early

numerical abilities holds that the brain is “hard wired.” This idea is often supported by

evidence of numerical discrimination by human infants and by animals. Further,

accumulating evidence indicates that language and other cultural products and practices

make enormous contributions to young children’s acquisition of numerical knowledge.

In the past, problem solving had a place in the mathematics classroom, but it was

usually used in a token way as a starting point to obtain a single correct answer, usually

by following a single 'correct' procedure.

More recently, however, professional organizations such as the National Council

of Teachers of Mathematics (2000) have recommended that the mathematics curriculum

should be organized around problem solving, focusing on: developing skills and the

ability to apply these skills to unfamiliar situations; gathering, organizing, interpreting

and communicating information; formulating key questions, analyzing and

conceptualizing problems, defining problems and goals, discovering patterns and

25

similarities, seeking out appropriate data, experimenting, transferring skills and strategies to

new situations; and developing curiosity, confidence and open-mindedness.

Cobb et al. (1991) suggested that the purpose for engaging in problem solving is not

just to solve specific problems, but to encourage the exteriorization and reorganization of the

involved schemes as a result of the activity.

The Object File Model better accounts for these abilities, as well as the discovery of a

recent effect in certain tasks, which may be due to the process of updating numerical

information. These data also address the general issues of the independence of mathematical

abilities from language as well as their evolutionary origins.

In addition, Schoenfeld (1994) described the way in which the use of problem solving

in his teaching has changed since the 1970s.

The preponderance of local and international research, consistent with the Basic

Education Sector Reform Agenda (BESRA) recommends and affirms the benefits and

relevance of MLE.

Notable empirical studies like the Lingua Franca Project and Lubuagan First

Language Component show that: First, learners learn to read more quickly when in their first

language (L1); Second, pupils who have learned to read and write in their first language learn

to speak, read, and write in a second language (L2) and third language (L3) more quickly

than those who are taught in a second or third language first; and Third, in terms of cognitive

development and its effects in other academic areas, pupils taught to read and write in their

first language acquire such competencies more quickly.

In conclusion, it is very clear that these related literature and studies cited are in one

way or another related to the present study because they dealt with the significance of

26

utilizing the mother tongue (common language) as the first language in the classroom

instruction.

Chapter II

METHODOLOGY

This chapter shows the research design, research subjects, research locale,

research instruments, the data gathering procedure, data scoring, and the statistical tools

for the analysis of data gathered.

Research Design

The design of the present study followed the descriptive-survey method. The

main purpose in conducting this study was to compare and relate the respondents’ score

after taking the test using the English language and its Cebuano translation. This design

was suitable because it determined the relationship of the English and Cebuano as a

learning tool in solving algebraic problems.

Research Respondents

A total of ninety (90) randomly selected students from the four sections of the

third year BEEd students of Naval State University were chosen as respondents for the

study. The researcher selected thirty (30) students from Section A, another thirty (30)

from section B, twenty (20) from section C and the remaining ten (10) from Section D as

the respondents, constituting about 60% of the total BEEd population.

Research Locale

27

The venue of this study was the College of Education of Naval State University-

Main Campus located at P.I. Garcia, Naval, Biliran.

Research Instrument

This study originally utilized a 15-item teacher-made algebraic problem tests

using English language classified into easy, average, and difficult with five (5) questions

each.

In order to test the instrument’s validity, the researcher conducted a dry-run to the

third year BS Marine Engineering students of the university in which the original 15-item

test was reduced to 10-item, after analyzing each item based on the level of difficulty of

the students.

After the conduct of the dry-run, the researcher submitted the remaining algebraic

problems to some mathematics’ teachers for their Cebuano translation of the problems.

Having prepared the instrument, the researcher identified the respondents and

administered the two sets of algebraic problems to assess if there is significant difference

in their scores using the two languages (English and Cebuano).

Aside from the teacher-made tests, the researcher also distributed survey

questionnaire to the respondents in order to elicit feedback on their experiences and

exposure throughout the duration of the study.

Data Gathering Procedure

Before the full implementation of the study, the researcher secured an

endorsement letter or permission from the Dean of Maritime Education for the conduct of

the dry-run and eventually asked the NSU Graduate School and College of Education

28

deans for their approval to distribute survey questionnaire to the respondents to elicit the

data needed for the study. Answered questionnaires were collected and tabulated.

Data Scoring

The results of this study were tabulated to satisfy the level of performance of the

respondents and were described and categorized later after the conduct of the

investigation.

There were 10 items presented in English and another 10 items using the Cebuano

language. To categorize the results of the data, the following were tabulated with the

following description.

The scores of the respondents were categorized as follows:

Score Weight Description

10 5 Outstanding

8 – 9 4 Very Satisfactory

6 – 7 3 Satisfactory

5 – 6 2 Fair

0 – 4 1 Poor

The incremental scores were categorized based on the mean score of the learners.

They are classified as follows:

Incremental Point Description

4-5 High

1-3 Average

-2-0 Low

29

On the extent of the respondents’ responses about the highlights of their

experiences and exposure during the implementation of the study, the categorization

below was used.

Range Weighted Points Qualitative Description

4.3 – 5.0 5 Strongly Agree

3.5 – 4.2 4 Agree

2.7 – 3.4 3 Undecided

1.9 – 2.6 2 Disagree

1.0 – 1.8 1 Strongly Disagree

Statistical Treatment of Data

The analysis of data consisted of the comparisons between the scores of the

respondents in English and Cebuano (common language) tests, their incremental scores,

as well as the analysis of questionnaire answers. Tests comparisons were obtained by

determining means and standard deviations. The differences between their scores in the

two sets of tests were analyzed with the following:

To determine the level of performance of the respondents through problem

solving, the frequency distribution with underlying percentage were applied using the

following formula:

% = f/n x 100

where:

% = is the percentage

f = is the frequency

30

n = is the total number of cases

Weighted Mean. The weighted mean were computed in determining the

highlights of the respondents’ experiences and exposure during the implementation of the

study.

f x wp

WM = E -----------------------

∑

WM - weighted mean

∑ - summation of

wp - weighted points

Descriptive Statistics categorized as mean percentage and frequency counts were

used to describe the respondents’ scores in the tests.

The t-test was used to find out significant differences in their scores in both

English and Cebuano presentations.

31

Chapter III

RESULTS AND DISCUSSION

This chapter presents the results of the study conducted among the third year BEEd

students of Naval State University. Results are presented according to the objectives such as

the process of employing English and Cebuano as learning tools in solving algebraic

expressions; the scores of the respondents in the tests using the two languages; their

incremental scores in the two sets of tests conducted; significant difference of their scores in

English and Cebuano as well as the significant difference of their scores in relation to the

incremental scores; and finally, the highlights of their experiences and exposure during the

implementation of the study.

Common Language Vis-à-vis English as a learning tool in solving algebraic problems

This study utilized two languages (English and Cebuano) as the tools in presenting

and solving algebraic problems.

In this study, the respondents were given algebraic problems in which the usual

English mathematical problems were translated into Cebuano and were consecutively

administered to the respondents.

32

Throughout the conduct of the experiment, the students gained knowledge on the

common language translation of some mathematical expressions; thus, they were able to

understand it better and get accurate answers compared to presenting it in English language

only. Most of them had pleasant experiences as evidenced by the results presented in table 6.

Furthermore, this process allows students to think and analyze the problems in both

English and Cebuano, thereby enhancing their creative thinking skill.

Students’ Score in Algebraic Problems

In this study, the students’ scores using the English and Cebuano languages in

solving algebraic problems were determined. In included 10-item using the frequency,

summation of frequency and the means of the scores in English and Cebuano.

Table 1 presents the scores of the respondents.

Table 1

Scores of the Respondents

ScoresEnglish Cebuano

f fx f fx10 0 0 0 09 0 0 3 278 0 0 21 1687 2 14 13 916 17 102 5 305 19 95 5 254 7 28 9 363 21 63 17 512 15 30 9 181 5 5 6 60 4 0 2 0

∑ x = 90 ∑fx = 337 ∑ x = 90 ∑ fx = 452 ∑ fx __ ------- = x2 = 3.74 ∑ x

∑ fx __------- = x1 = 5.02 ∑ x

33

As shown in the table, the scores of the respondents in algebraic problems ranged

from 0 to 10 both in English and Cebuano. It further shows that out of 90 respondents,

only 21 got the score of 8 (highest frequency) using the Cebuano language while nobody

(0) obtained the same score using the English language. Meanwhile, 21 out of 90 got the

score of 3 (highest frequency) in the English translation while only 17 in Cebuano.

The lowest score obtained by the respondents was 0 with a frequency of 2 for

Cebuano and 4 for English. Furthermore, the table shows that there is a difference in the

scores of the respondents using English and Cebuano languages as evidenced by their

mean score of 3.74 in English and 5.02 in Cebuano.

With the scores presented, majority of the respondents who answered the

Cebuano test got scores above 5 with a total frequency of 47 while only 43 in English.

Moreover, majority of the respondents got scores below 5 in the English translation with

a total frequency of 71 and only 19 in the Cebuano.

Mean and Percentage Distribution of the Respondents’ Scores. The mean and

percentage distribution of the scores of the respondents are presented in Figure 3.

Figure 3

Mean and Percentage Distribution of the Respondents’ Scores

34

As reflected on the figure above, the English algebraic problems obtained a

slightly higher percentage (%) score that falls under the ‘low’ category and slightly lower

under the ‘average’ category compared to its Cebuano translation. Moreover, only 3

percent belongs to ‘high’ category in Cebuano while zero (0) in English. The mean

scores of the two groups were; (x1 =3.74; x2=5.02), English and Cebuano respectively.

Frequency and Percentage Distribution of the Respondents’ Scores. The

frequency and percentage distribution of the respondents’ scores in English and Cebuano

algebraic tests are presented in table 2.

The succeeding table and figure above clearly shows that out of the ten questions,

only one got higher frequency using the English language with 64 or 71.11 percent

compared to Cebuano with 52 or 57.77 percent.

35

It further shows that eight or 80 percent of the common language translation were

answered correctly by most of the respondents than in its English counterpart.

Among the algebraic problems, item 10 is the most difficult and it can be seen

that nobody (0) answered correctly using the English language, while six or 6.66 percent

were able to get the answer in the Cebuano translation.

Furthermore, the result shows that item 7 got the same results with 8 or 8.88

percent in both English and Cebuano.

It further shows that majority of the respondents got correct answers using

Cebuano compared to its English counterpart.

Table 2

Frequency and Percentage Distribution of the Respondents’ Scores

English F %Cebuano

(Common Language) f %1. One number is 19 less than the other,

their sum is 65. Find the numbers. 57 63.331. Ang usa ka numero mubo ug 19 kaysa lain nga

numero, unya 65 ang ilang total. Unsa man ning mga numeroha?

73 81.11

2. The sum of two consecutive even integers is 62. What are the numbers? 79 87.77

2. Kung 62 ang total sa duha ka magkasunod nga pares nga numero, unsa man ni nga mga numero? 85 94.44

3. Separate 98 into two parts so that, when the greater is divided by the smaller, the quotient is 3 and the remainder is 6.

52 57.773. Bahina ang 98 sa duha ka parte nga kung ang daku

nga parte bahinon sa gamay nga parte, ang resulta 3 unya may sobra nga 6.

63 70.00

4. James can paint a certain house in 10 days and Allan can paint the same house in 12 days. How long will it take to paint the house if both men work?

41 45.55

4. Mapintorahan ni James ang usa ka balay sulod sa 10 ka adlaw samtang si Allan makahuman ug pintora niini sulod sa 12 ka adlaw. Kung magtinabangay silang duha pagpintora sa maong balay, unsa kadugay mahuman nila ang pagpintora niini?

46 51.11

5. Half of Henry’s age added to 1/3 of Frank’s age is 11. Six years from now, the sum of their ages will be 40. How old is each now?

30 33.33

5. Katunga sa edad ni Henry gidugang sa ikatulo ka parte sa edad ni Frank, ang resulta 11. Unom ka tuig gikan karon, ang total sa ilang edad mahimong 40. Pila man ang edad ni Frank ug ni Henry karon?

44 48.89

6. The denominator of a certain fraction is four less than thrice its numerator. If seven is added to both its numerator and denominator, the fraction becomes 2/3.

4 4.44

6. Ang denominator sa usa ka fraction menos ug upat sa katulog pilo sa iyang numerator. Kung dugangan ug matag 7 ang numerator ug denominator, ang fraction mahimo nga 2/3. Unsa

34 37.77

36

What is the original fraction? man ang orihinal nga fraction?7. A certain number of two digits is four

times the sum of its digits, and if 36 be added to it, the digits will be reversed. Find the number.

8 8.88

7. Ang usa ka numero nga duha ka digits, upat ka pilo sa total sa mao nga mga digits; pero kung dugangan ang resulta ng 36, mabaliktad ang digits. Unsa man ni nga numero?

8 8.88

8. The sum of the squares of the two digits of a positive integer number is 13. If the number itself is 2 more than 6 times the sum of its digits, find the number.

2 2.22

8. Trese ang total sa squares sa duha ka digits nga positibo nga numero. Kung ang mao nga numero sobra ug duha sa kaunom nga pilo sa total sa iyang digits, unsa man ni numero?

36 40.00

9. The length of a rectangular building lot is twice its width. If the perimeter is 240 meters, what are the dimensions of this building lot?

64 71.11

9. Ang katas-on sa usa sa eskinado (rectangular) nga lote sa building, kadoblehon sa iyang gilapdon. Kung 240 metros ang iyang sukod palibot, unsa man ang katas-on ug kalapdon niini nga lote?

52 57.77

10. A parking lot is in the form of a square. The lot is enlarged by adding strips of 16 meters wide on one side and 12 meters wide on the adjacent side. If the rectangular area formed contains 1,440 square meters, find the original area of the lo

0 0

10. Eskinado (square) ang porma sa usa ka parking-nganan. Gipadako lamang kini pinaagi sa pagdugang ug mga strips (floor covering) nga 16 metros ang gilapdon sa usa ka parte ug 12 metros ang gilapdon sa lain nga parte. Kung ang naporma nga eskinado (rectangular) adunay area nga 1,440 metros kwadrados, unsa man ang orihinal nga area sa mao nga lote?

6 6.66

Graph presentation of the frequency and percentage distribution of the

respondents’ scores in both English and Cebuano

The graph presentation on the frequency and percentage distribution of both

English and Cebuano in the respondents’ scores in items 1-10 are presented in figure 4.

Figure 4

Consolidated Data on the Frequency and Percentage Distribution of English and Cebuano Scores

37

Incremental scores of the respondents

After the administration of the test both in English and Cebuano, the difference of

the respondents’ scores were computed and as referred as the incremental scores. Table 3

shows the incremental scores of the respondents.

As reflected in the succeeding table, the incremental scores of the respondents

ranged from -2 to 5; where most of them got 2 increment points or 23 percent and the

least was 5-point increment or 2 percent.

38

Zero increment means that the respondents obtained the same score in both

English and Cebuano in solving algebraic problems and there is no difference at all in

their scores; while the negative increment points show that their score in English is

comparatively higher than the common language translation.

Table 3

Incremental Scores of the Respondents

Incremental PointFrequency Percentage Frequency x

incremental pointF % fx

5 2 2.0 104 8 9.0 323 11 12.0 332 21 23.0 421 18 20.0 180 15 17.0 10-1 10 11.0 -10-2 5 6.0 -10

∑ x = 90 100.0 ∑ fx = 125

Mean and Percentage Distribution of the Respondents’ Incremental Scores

The mean and percentage distribution of the respondents’ incremental scores are

presented in Figure 5.

Figure 5

Mean and Percentage Distribution of the Respondents’ Incremental Scores

39

The figure shows that out of 90 respondents, 30 or 33.33 percent falls under ‘low’

level (-2-0 increment points); 50 or 55.56 percent under ‘average’ level (1-3 increment

points); and 10 or 11.11 percent under ‘high’ level (4-5 increment points)

Furthermore, the mean incremental score of the respondents is statistically low

which is only 1.39.

Significant Difference of the Respondents’ Scores inEnglish and Cebuano

To determine the relationship between English and Cebuano based on the scores

of the respondents in the test conducted, the t-test was used to ascertain if there was a

significant difference in the main gain of the respondents’ scores. The results are

presented in table 4.

40

Table 4

Significant Difference of the Respondents’ Scores

Test Scores Decision

_x SD tc tv

Ho1

Rejected Significant

English3.74 1.79

3.92 1.98Cebuano 5.02 2.58

Alpha level of significance (a) = 0.05 degree of freedom (df) =89Level of significance = two-tailed or non-directional

Based on the data presented in table 4, there is a significant difference in the

respondents’ scores in solving algebraic problems using English and Cebuano as a

learning tool; hence the hypothesis that “there is no significant relationship between the

respondents’ scores using English and Cebuano as a learning tool in solving algebraic

problems is rejected.

Both English and Cebuano have higher computed absolute t-value, 3.92 compared

to the tabular value of 1.98 at .05 level of significance. The result explains that there is a

significant relationship between the respondents’ scores using the two languages (English

and Cebuano) as a learning tool in solving algebraic problems.

Meanwhile, the mean score of the English language was 3.74, significantly lower

than the Cebuano mean sore of 5.02; showing an increase of the respondents’ scores from

English to Cebuano.

Significant Difference of the Respondents’ Scores and Incremental Points

41

To determine the relationship between English and Cebuano based on their scores

in the test conducted as well as their incremental scores, the t-test was used to ascertain if

there was a significant difference in the mean gain of the respondents’ scores. The results

are presented in table 5.

Table 5

Significant Difference of the Variables

Variable Groups t SDSig. (2-tailed)

Decisiontc tv

Test ScoresEnglish 3.74

2.31 3.921.98 Ho2

RejectedSignificantCebuano 5.02

Incremental Score

English (-) Cebuano 1.39 1.71 32.58 1.96 Ho3

RejectedSignificant

Alpha level of significance (a) = 0.05

The incremental scores were found to be of significant difference as compared to

the test results. As gleaned from the results, there is a significant difference in the

incremental scores and the test scores of the two languages as further evidenced by the

computed t-value of 32. 58 lower than the tabled value of 1.96.

Cebuano got a higher mean gain of 5.02; while English’ mean was only 3.74. The

computed t- value is 3.92, higher than its tabled value of 1.98, thus, the hypothesis that

there is no significant difference in the variables is rejected.

Moreover, statistical analysis revealed that there is a significant difference

favoring the students who were exposed to Cebuano (common language translation)

42

which further means that it contributed in the increase of the respondents’ incremental

scores.

In general, the hypothesis that “there is no significant relationship between the

respondents’ scores and their incremental scores” is rejected and that there is indeed a

significant difference in the two variables.

Highlights of the respondents’ experiences in English vis-à-vis Cebuano (common language) in solving algebraic problems

To give highlights of the employed teaching strategy, different views or feedbacks

from the respondents on the benefits gained in translating the English questions into the

Cebuano were taken and presented in table 6.

Special considerations of this study are the reactions of the respondents exposed

to Cebuano as a new method in teaching Mathematics. Arranged from highest to lowest

in terms of weight (score), their opinions are expressed and interpreted according to the

degree of agreement relative to the use of English and Cebuano as shown in table 6.

Respondents’ feedback on the benefits gained using Cebuano as a Learning Tool in Solving Algebraic Problems

The respondents’ feedback on the benefits gained using Cebuano as a learning

tool in solving algebraic problems is presented in table 6.

Table 6

Feedback of the Respondents on the Benefits Gained Using Cebuano Language

FEEDBACKSSA5

A4

UN3

D2

SD1 WM

Interpre-tation

1. We gave importance to our mother tongue. 48 40 1 1 0 4.5Strongly

Agree2. It can be used in non-formal setting and provides a good relationship 42 43 5 0 0 4.4 Strongly

43

for the teacher and students. Agree3. I could understand fully the problems when the common language is

used. 35 48 6 1 0 4.3Strongly

Agree4. Some terms were fully understood using the common language than in

English. 40 43 5 2 0 4.3Strongly

Agree5. Students are comfortable in answering the test.

43 33 12 2 0 4.3Strongly

Agree6. It helps to promote our common language among the Filipinos and

even to other citizens. 33 52 4 1 0 4.3Strongly

Agree7. I find it easier to answer problem solving questions using the common

language than the English language. 28 51 10 0 1 4.2 Agree8. It is easy to read because it is written in our dialect.

35 45 7 3 0 4.2 Agree9. Some students can understand but it only depends on the level of

comprehension and the structure of the sentence. 28 50 10 2 0 4.2Agree

10. My understanding of the problems has improved because my native language was used. 31 48 9 2 0 4.2 Agree

11. It promotes understanding between the teacher and students. 26 55 6 3 0 4.2 Agree

12. Cebuano people who have wide vocabulary in Mathematics will have the great capacity in understanding Cebuano translation. 33 46 8 3 0 4.2

Agree

13. Students can easily understand the simple terms in the problem. 32 47 10 1 0 4.2 Agree14. It is one way of- preserving the Cebuano language which is getting

obsolete nowadays. 33 46 9 2 0 4.2 Agree15. Utilizing the common language gives us the privilege to convey our

message to other people. 32 47 10 1 0 4.2 Agree

16. We could better understand the problems and analyze it word for word. 27 45 15 3 0 4.1 Agree17. It is easier to interpret and analyze the problems using the common

language. 25 49 12 4 0 4.1 Agree18. Using the common language in Mathematics would result a good result

because it is our mother tongue. 26 45 15 4 0 4.0 Agree19. It is easy for the teachers to formulate questions and for the students to

understand its meaning. 23 46 13 6 2 3.9 Agree20. The common language is easier to understand but it depends largely on

the given problem. 18 48 17 7 0 3.9 Agree

Total Weighted Mean 4.2 Agree

The preceding table explains that the respondents strongly agree on the benefits

gained of employing the common language (Cebuano) in solving algebraic problems. It

is evident in the following statements: “We gave importance to our mother tongue;” “It

can be used in non-formal setting and provides a good relationship for the teacher and

students;” “I could understand fully the problems when the common language is

44

used;””Some terms were fully understood using the common language than in English;”

and “Students are comfortable in answering the test.”

With the mean score of 4.2, the students “strongly agree” that the teachers use

Cebuano as a learning tool in teaching Mathematics because of the positive results

derived from it.

Chapter IV

SUMMARY OF FINDINGS, CONCLUSION AND RECOMMENDATIONS

This chapter presents the general summary of findings, conclusion and

recommendations based on the data and other valuable information gathered.

45

Summary of Findings

The main purpose of this study was to determine the relationship of English and

Cebuano as a learning tool in solving algebraic problems. Employing the descriptive-

survey design, 90 students of BEEd third year students of Naval State University were

involved as subjects based on the following objectives: describe the process of employing

the English and Cebuano as a learning tool in solving algebraic expressions; the scores of

the respondents in the tests using the two languages (English and Cebuano); their

incremental scores in the two sets of tests conducted; significant relationship of their

scores in both English and Cebuano as well as the significant difference of their scores in

relation to the incremental scores; and finally, the highlights of their experiences and

exposure during the implementation of the study.

The Common Language vis-à-vis English as a learning tool in solving algebraic

problems. The learning tool involved in this study were English and Cebuano in which

the students were first made to answer a 10-item algebraic problems presented in the

usual English language followed by the same algebraic problems translated into Cebuano

(common language). Assessments were administered to them individually to examine

whether the expected outcomes of the objectives were met.

Students’ Score in Mathematics. The scores of the students in English ranged

from 0-7 while in Cebuano test ranged from 0-9. The highest score obtained by the

students in such tests were 7 for English while 9 for Cebuano and the lowest was 0,

although it did not fall on the same test items.

46

Majority of the respondents got scores above 5 with a total frequency of 43 using

English, while 47 in Cebuano. Majority of the respondents got scores below 5 in English

with a total frequency of 71 and only 19 in Cebuano.

Mean and Percentage Distribution of the Respondents’ Scores. The English

algebraic problems obtained a slightly higher mean (x) score than its common language

counterpart the (x1 = 5.02; x2 = 3.74).

Frequency and Percentage Distribution of the Respondents’ Scores. Majority of

the respondents correctly answered using Cebuano compared to its English counterpart.

Incremental scores of the respondents. The incremental scores of the respondents

ranged from -2 to 5; where most of them got 2 increment points or 23 percent and the

least was 5-point increment or 2 percent.

Mean and Percentage Distribution of the Respondents’ Incremental Scores. The

mean incremental score of the respondents is statistically low (1.39.)

Significant Difference of the Respondents’ Scores in English and Cebuano. There

is a significant difference in the respondents’ scores in solving algebraic problems using

English and Cebuano as a learning tool; hence the hypothesis that “there is no significant

relationship between the respondents’ scores using English and Cebuano as a learning

tool in solving algebraic problems is rejected.

47

Significant Difference of the Respondents’ Scores and Incremental Points. There

is a significant difference in the incremental scores and the test scores of the two

languages as further evidenced by the computed t-value of 32. 58 lower than the tabled

value of 1.96. In general, the hypothesis that “there is no significant relationship between

the respondents’ scores and their incremental scores” is rejected.

Highlights of the respondents’ experiences and exposure during the

implementation of the study. With the mean score of 4.2, the students strongly agree that

the teachers will use Cebuano as a learning tool in teaching Mathematics because of the

positive results derived from it.

Conclusions

After thorough analysis of the results based on the findings gathered from the

study, the following conclusions were drawn:

The learning tools involved in this study are English and Cebuano in which the

scores of the students in English is lower than in Cebuano.

Majority of the respondents got scores above 5 with 43 using English, while 47

using Cebuano. Majority of the respondents got scores below 5 in English 71 and only

19 in Cebuano. The English algebraic problems obtained a slightly higher mean (x) score

than its common language counterpart.

Majority of the respondents correctly answered using Cebuano compared to its

English counterpart.

48

Most of the incremental points from English to Cebuano are in negative integers,

from Cebuano to English, the incremental points are in positive integers. The mean

incremental score of the respondents is statistically low (1.39.)

There is a significant difference in the respondents’ scores in solving algebraic

problems using English and Cebuano as a learning tool.

There is a significant difference in the incremental scores and the test scores of

the two languages.

The students strongly agree that the teachers will use Cebuano as a learning tool

in teaching Mathematics because of the positive results derived from it.

Recommendations

Based on the findings and conclusions of the study, the following

recommendations are hereby offered for consideration:

1. The school administrators should provide opportunities for teachers’ seminars and

trainings to update them with the new trends and strategies in teaching.

2. Teachers should find alternative ways to make the teaching-learning more

meaningful and plan for various ways in presenting the lessons.

3. Students should continue to receive common language intervention in solving

algebraic problems to maintain and improve their performance in the class.

4. Mathematics’ teacher who implements this teaching method must be flexible and

extremely organized because it is very time consuming to translate the algebraic

problems on a daily basis.

49

5. The intervention utilized in this study should be used continuously with newly

identified students, especially those found to have low comprehension level in the

English language.

6. Students who are academically at risk could also benefit from this program

because it introduces a new method in learning.

7. Other researchers might explore whether this teaching method could be

implemented to other year levels especially those taking mathematics as their

field of specialization. Perhaps, with earlier renovations on the teaching method,

there could be more successful learners.

8. Capability building activities that would enhance teachers’ skills and ability in

order to provide their students with the best knowledge must be conducted.

9. Since the study was only limited to the third year NSU-COEd students and the

duration of the experiment was relatively short, it is highly recommended that a

follow-up study employing a larger scope of topics and duration of the experiment

be conducted.

50

LITERATURE CITED

51

LITERATURE CITED

Abadzi, Helen. Efficient Learning for the Poor: Insights from the Frontiers of Neuroscience. 2010

Butterworth B. The mathematical brain. New York, NY: Macmillan; 1999.

Canobi KH, Bethune NE. Number words in young children’s conceptual and procedural knowledge of addition, subtraction and inversion. Cognition 2008; 108(3)

Catherine Sophian, Ph.D.; Numerical Knowledge in Early Childhood; University of Hawaii, USA; June 11, 2009

Clements DH, Sarama J, DiBiase AM, eds. Engaging Young Children in Mathematics:

Dehaene S. The number sense: How the mind creates mathematics. Oxford, UK: Oxford University Press; 1997

DepED Order #74 s. 2009. Education policy, language policy, medium of instruction, mother tongue as language of instruction, pedagogy, Teaching profession | Tags: bilingual education, medium of instruction (MOI), mother tongue as MOI, Posted in bilingualism. Spanish profs train Pinoy teachers on language   teaching . MLE Strategic Plan Approved by National Learning   Strategies .

Duncan GJ, Dowsett CJ, Claessens A, Magnuson K, Huston AC, Klebanov P, Pagani LS, Feinstein L, Engel M, Brooks-Gunn J, Sexton H, Duckworth K, Japel C. School readiness and later achievement. Developmental Psychology. 2007.

Encyclopedia on Early Childhood Development 1 ©2009 Centre of Excellence for Early Childhood Development Sophian C.

Griffin S, Case R.; Re-thinking the primary school math curriculum: An approach based on cognitive science. Issues in Education 1997.

H. Shibata; Problem Solving: Definition, terminology, and patterns; Hidetoshi Shibata Copy rights © all reserved, 1997, 1998  

Klibanoff RS, Levine SC, Huttenlocher J, Vasilyeva M, Hedges LV. Preschool children's mathematical knowledge: The effect of teacher "math talk." Developmental Psychology 2006.

Kretzschmar, William A. "American English." Microsoft® Student 2009 [DVD]. Redmond, WA: Microsoft Corporation, 2008.

52

Lamont L.A.; Chaar L; Toms C.: Using interactive problem-solving techniques to enhance control systems education for non English-speakers, 2001.

Levine, Melvin D. "Education of Students with Learning Disorders." Microsoft® Student 2009 [DVD]. Redmond, WA: Microsoft Corporation, 2008.

Mahwah, N.J.: Lawrence Erlbaum Associates Standards for early childhood mathematics education; 2004.

Margaret Taplin; Mathematics through Problem Solving; Institute of Sathya Sai Education, Hong Kong

Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.

Mix KS, Sandhofer CM, Baroody AJ. Number words and number concepts: The interplay of verbal and nonverbal quantification in early childhood. In: RV Kail, ed. Advances in child development and behavior. vol. 33. New York, NY: Academic Press; 2005.

National Mathematics Advisory Panel. Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC.: U. S. Department of Education; 2008.

Piaget J. The child's conception of number. Gattegno C, Hodgson FM, trans. New York, NY: Norton; 1952. and "Microsoft® Student 2009 [DVD]. Redmond, WA: Microsoft Corporation, 2008.

Quismundo, Tarra “Use of mother tongue instruction in schools pushed,” Philippine Daily Inquirer, First Posted 23:24:00 10/02/2010. Filed Under: Education, Language

Schliemann AD, Carraher DW. The evolution of mathematical reasoning: Everyday versus idealized understandings. Developmental Review 2002.

Schafersman, Steven D.; An Introduction to Critical Thinking; January 1991.

Sophian C. The origins of mathematical knowledge in childhood. New York, NY: Lawrence Erlbaum Associates; 2007.

Sophian C, Garyantes D, Chang C. When three is less than two: Early developments in children's understanding of fractional quantities. Developmental Psychology 1997.

Starkey P., Klein A., and Wakeley A. Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly 2004.

53

Starkey P., and Klein A. Sociocultural influences on young children’s mathematical knowledge. In: Saracho ON, Spodek B, eds. Contemporary perspectives on mathematics in early childhood education. Charlotte, NC: IAP/Information Age Publication.; 2008.

VA Mental Illness Research, Education, and Clinical Centers (MIRECC); Positive Coping Skills Toolbox; December 29, 2009.

Wikipedia, the free encyclopedia, August 2008

www.GlobalVillageSchool.org. Online School Curriculum. Online private school curriculum program for K-12 students. Adds by Goggle

Yap, Fe A. Commission on the Filipino Language. The 10th Philippine Linguistics Congress , 10-12 December 2008 – UP-Diliman, Quezon City

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APPENDICES

55

APPENDIX A

LETTER OF REQUEST

Republic of the PhilippinesNaval State University

Naval, Biliran

January 4, 2011The University PresidentNaval State University Naval, Biliran

Madam:

I have the honor to request permission to conduct my research entitled, “COMMON LANGUAGE VIS-À-VIS ENGLISH AS A LEARNING TOOL IN SOLVING ALGEBRAIC PROBLEMS” from the first to the last week of January 2011.

This request is in connection with my desire to improve teaching strategies in Mathematics as well as to comply the requirements for my thesis, as I will soon be graduating from a degree of Master of Arts in Teaching Mathematics in this University.

I am hoping for the kind consideration and support extended towards this matter.

Respectfully yours,

(SGD) JOAN J. SINAGPULO

Researcher

Noted:

(SGD) SUSAN S. BENTOR, Ph. D. Dean, College of Education

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APPROVED:(SGD) EDITA S. GENSON, Ed. D.

University President IIIAPPENDIX B

LETTER OF REQUEST

Republic of the PhilippinesNaval State University

Naval, Biliran

January 4, 2011

The Dean Graduate SchoolNaval State University Naval, Biliran

Madam:

I have the honor to request permission to conduct a dry-run of my survey questionnaire for my research entitled, “COMMON LANGUAGE VIS-À-VIS ENGLISH AS A LEARNING TOOL IN SOLVING ALGEBRAIC PROBLEMS” from January 4-7, 2011.

This request is in connection with my desire to improve teaching strategies in Mathematics as well as to comply the requirements for my thesis, as I will soon be graduating from a degree of Master of Arts in Teaching Mathematics in this university.

I am hoping for the kind consideration and support extended towards this matter.

Respectfully yours,

(SGD) JOAN J. SINAGPULO Researcher

57

APPROVED:

(SGD) LORETA E. GONZALES, Ed. D. Dean, Graduate School

APPENDIX C

LETTER OF REQUEST

Republic of the PhilippinesNaval State University

Naval, Biliran

January 4, 2011

The Dean College of EducationNaval State University Naval, Biliran

Madam:

I have the honor to request permission to conduct my survey questionnaire in your college for my research entitled, “COMMON LANGUAGE VIS-À-VIS ENGLISH AS A LEARNING TOOL IN SOLVING ALGEBRAIC PROBLEMS” from January 4-7, 2011.

This request is in connection with my desire to improve teaching strategies in Mathematics as well as to comply the requirements for my thesis, as I will soon be graduating from a degree of Master of Arts in Teaching Mathematics in this university.

I am hoping for the kind consideration and support extended towards this matter.

Respectfully yours,

(SGD) JOAN J. SINAGPULO Researcher

58

APPROVED:

(SGD) SUSAN S. BENTOR, Ph.D. Dean, College of Education

APPENDIX D

LETTER OF REQUEST

Republic of the PhilippinesNaval State University

Naval, Biliran

January 4, 2011

The Dean College of Maritime EducationNaval State University Naval, Biliran

Sir:

I have the honor to request permission to conduct a dry-run of my survey questionnaire in your college in relation to my research entitled, “COMMON LANGUAGE VIS-À-VIS ENGLISH AS A LEARNING TOOL IN SOLVING ALGEBRAIC PROBLEMS” from January 4-7, 2011.

This request is in connection with my desire to improve teaching strategies in Mathematics as well as to comply the requirements for my thesis, as I will soon be graduating from a degree of Master of Arts in Teaching Mathematics in this university.

I am hoping for the kind consideration and support extended towards this matter.

Respectfully yours,

(SGD) JOAN J. SINAGPULO Researcher

59

APPROVED:

(SGD) CAPT. FEDERICO JAMIN Dean, College of Maritime Education

APPENDIX E

SURVEY QUESTIONNAIRE

(English)

Directions: Solve the following and show your solution.

1. One number is 19 less than the other, their sum is 65. Find the numbers.

2. The sum of two consecutive even integers is 62. What are the numbers?

3. Separate 98 into two parts so that, when the greater is divided by the smaller, the quotient is 3 and the remainder is 6.

4. James can paint a certain house in 10 days and Allan can paint the same house in 12 days. How long will it take to paint the house if both men work?

5. Half of Henry’s age added to 1/3 of Frank’s age is 11. Six years from now, the sum of their ages will be 40. How old is each now?

6. The denominator of a certain fraction is four less than thrice its numerator. If seven is added to both its numerator and denominator, the fraction becomes 2/3. What is the original fraction?

7. A certain number of two digits is four times the sum of its digits, and if 36 be added to it, the digits will be reversed. Find the number.

8. The sum of the squares of the two digits of a positive integer number is 13. If the number itself is 2 more than 6 times the sum of its digits, find the number.

9. The length of a rectangular building lot is twice its width. If the perimeter is 240 meters, what are the dimensions of this building lot?

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10. A parking lot is in the form of a square. The lot is enlarged by adding strips of 16 meters wide on one side and 12 meters wide on the adjacent side. If the rectangular area formed contains 1,440 square meters, find the original area of the lot.

APPENDIX F

SURVEY QUESTIONNAIRE

(Common Language)

Panuto: Basaha ug sabta pagmaayo ang mga problema.

1. Ang usa ka numero mubo ug 19 kaysa lain nga numero, unya 65 ang ilang total. Unsa man ning mga numeroha?

2. Kung 62 ang total sa duha ka magka-sunod nga pares nga numero, unsa man ning mga numeroha?

3. Bahina ang 98 sa duha ka parte nga kung ang daku nga parte bahinon sa gamay nga parte, ang resulta 3 unya may sobra nga 6.

4. Mapintorahan ni James ang usa ka balay sulod sa 10 ka adlaw samtang si Allan makahuman ug pintora niini sulod sa 12 ka adlaw. Kung magtinabangay silang duha pagpintora sa maong balay, unsa kadugay nila mahuman ang pagpintora niini?

5. Katunga sa edad ni Henry gidugang sa ikatulo ka parte sa edad ni Frank, ang resulta 11. Unom ka tuig gikan karon, ang total sa ilang edad mahimong 40. Pila man ang edad ni Frank ug ni Henry karon?

6. Ang denominator sa usa ka fraction menos ug upat sa katulog pilo sa numerator. Kung dugangan ug matag 7 ang numerator ug denominator, ang fraction mahimo nga 2/3. Unsa man ang orihinal nga fraction?

7. Ang usa ka numero nga duha ka digits, upat ka pilo sa total sa mao nga mga digits; pero kung dugangan ang resulta ug 36, mabaliktad ang digits. Unsa man ni nga numero?

8. Trese ang total sa squares sa duha ka digits nga positibo nga numero. Kung ang mao nga numero sobra ug duha sa kaunom nga pilo sa total sa iyang digits, unsa man ni nga numero?

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9. Ang katas-on sa usa sa eskinado (rectangular) nga lote sa building, kadoblehon sa iyang gilapdon. Kung 240 metros ang iyang sukod palibot, unsa man ang katas-on ug kalapdon niini nga lote?

10. Eskinado (square) ang porma sa usa ka parking-nganan. Gipadako lamang kini pinaagi sa pagdugang ug mga strips (floor covering) nga 16 metros ang gilapdon sa usa ka parte ug 12 metros gilapdon sa lain nga parte. Kung ang naporma nga eskinado (rectangular) adunay area nga 1,440 metros kwadrados, unsa man ang orihinal nga area sa mao nga lote?

APPENDIX G

Request of Consent

This sign of consent is to certify my willingness to participate in the thesis entitled: “COMMON LANGUAGE VIS-À-VIS ENGLISH AS A LEARNING TOOL IN SOLVING ALGEBRAIC PROBLEMS.”

1. That I understand the general purpose/objective of the study which is to find out the effects of problem-solving in enhancing the comprehension skills and numerical abilities of the third year Bachelor in Elementary Education students of Naval State University.

2. That my participation as a subject of this research was done with my personal consent and voluntary participation with the researcher in the conduct of this study. I further acknowledge that my participation will not hamper or derail my daily work and activities as well as my personal responsibilities and obligations.

3. That the information about myself obtained from this study will be strictly kept confidential by the researcher, and none of my personal information be identified/revealed in any report of publication without my prior consent or permission.

4. That it was agreed that if there are some questions which are offensive, discriminating, or derogatory on my part, I am free to refuse, withdraw or terminate my participation anytime in the course of the interview without prejudice, penalty, or loss of credibility to the subject matter being studied.

5. That I also acknowledge that my participation in this study involves no monetary compensation on my part, except that whatever appropriate, I may be provided with additional pertinent information after the result of my participation.

62

With all those terms and conditions, I do hereby affix my signature blow to prove that I will freely agree to participate in the conduct of this study.

Participant’s assent:

________________________ _____________ Name and signature Date

APPENDIX H

FEEDBACK EVALUATION SHEET

Dear Respondent,

The items appearing in this sheet pertain to the use of multisensory structured language techniques in teaching English. Being exposed to this teaching method, please rate the following items by checking the score corresponding each item using the following rating scale.

5-Strongly Agree 4- Agree 3- Undecided 2- Disagree 1-Strongly Disagree

FEEDBACKSSA5

A4

UN3

D2

SD1

1. We gave importance to our mother tongue.2. It can be used in non-formal setting and provides a good relationship for the teacher

and students.3. I could understand fully the problems when the common language is used.

4. Some terms were fully understood using the common language than in English. 5. Students are comfortable in answering the test.

6. It helps to promote our common language among the Filipinos and even to other citizens.

7. I find it easier to answer problem solving questions using the common language than the English language.

8. It is easy to read because it is written in our dialect.9. Some students can understand but it only depends on the level of comprehension and

the structure of the sentence.10. My understanding of the problems has improved because my native language was

used.11. It promotes understanding between the teacher and students.12. Cebuano people who have wide vocabulary in Mathematics will have the great

capacity in understanding Cebuano translation.13. Students can easily understand the simple terms in the problem.14. It is one way of- preserving the Cebuano language which is getting obsolete

nowadays.15. Utilizing Cebuano gives us the privilege to convey our message to other people.

63

16. We could better understand the problems and analyze it word for word.17. It is easier to interpret and analyze the problems using the common language.18. Using Cebuano in Mathematics would result good because it is our mother tongue. 19. It is easy for the teachers to formulate questions and for the students to understand its

meaning. 20. The common language is easier to understand but it depends largely on the given

problem.

APPENDIX I

COMPUTED T-VALUE AND TABULAR T-VALUE

Test Scores Decision

_x SD tc tv Ho1

Rejected Significant

Common Language(Cebuano) 5.02 2.58

3.92 1.98English 3.74 1.79

VariableGroups t df

Sig. (2-tailed)Decision

tc tv

Test Scores

Common Language(Cebuano) 5.02

89 3.921.98

Ho2

RejectedSignificantEnglish 3.74

Incremental Score

English (-) Cebuano 1.39 89 32.58 1.98Ho3

RejectedSignificant

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APPENDIX J

TALAYTAYAN MLE CONSORTIUM

65

APPENDIX I

APPENDIX K

LINGUISTIC MAP OF THE PHILIPPINES

66

67

CURRICULUM VITAE

JOAN JAMIN SINAGPULO

Borac, Naval, Biliran joansinagpulo@yahoo.com Mobile No. 09289029577

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CURRICULUM VITAE

Name : JOAN JAMIN SINAGPULO

Date of Birth : December 23, 1984

Place of Birth : Bagong Silang, Babatngon, Leyte

Sex : Female

Civil Status : Single

Height : 5 feet & 4 inches

Weight : 110 pounds

Father : Tito P. Sinagpulo

Mother : Ester J. Sinagpulo

Religion : Roman Catholic

Educational Background

Graduate Studies : Master of Arts in Teaching-Mathematics (MAT-Mathematics)Naval State UniversityNaval, BiliranMarch 2011

Collegiate : Bachelor of Secondary Education major in Mathematics (BSEd-Math)Naval State UniversityNaval, Biliran 2003-2007

Secondary : The Sisters of Mary SchoolTalisay, Cebu City1998-1999Naval School of Fisheries

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Naval, Biliran2000-2003

Elementary : Naval Central SchoolNaval, Biliran1992-1998

Work Experience:

Instructor I : Naval State UniversityNaval, Biliran 2008 – Present

Eligibility: Date Taken Rating

Civil Service Eligibility to Cum Laude Graduates

Professional Board Examination for Teachers 2007 77%