The Strengths and Weaknesses of First Year Students in Learning Elementary Algebra_LGM_JDN_JVO

ANGELES UNIVERSITY FOUNDATION-COLLEGE OF EDUCATION PAGE 1

THE STRENGTHS AND WEAKNESSES OF FIRST YEAR HIGH SCHOOL

STUDENTS IN LEARNING ELEMENTARY ALGEBRA: BASIS FOR

ENRICHMENT ACTIVITIES

An Undergraduate Thesis

Presented to

The Faculty of the College of Education

ANGELES UNIVERSITY FOUNDATION

in Partial Fulfillment

of the Requirements for the Degree

BACHELOR OF SECONDARY EDUCATION

Major in Mathematics

Lovely G. Mercado

Jemima D. Nicasio

Josel V. Ocampo

April , 2011


APPROVAL SHEET

This undergraduate thesis entitled “THE STRENGTHS AND WEAKNESSES OF

FIRST YEAR HIGH SCHOOL STUDENTS IN LEARNING ELEMENTARY

ALGEBRA: BASIS FOR ENRICHMENT ACTIVITIES” prepared and submitted by

LOVELY G. MERCADO, JEMIMA D. NICASIO AND JOSEL V. OCAMPO in partial

fulfillment of the requirements for the degree BACHELOR IN SECONDARY

EDUCATION major in MATHEMATICS, has been examined and is recommended for

acceptance for ORAL EXAMINATION.

PANEL OF EXAMINERS

Approved by the Committee on Oral Examination with a grade of

_____________ on April 6, 2011.

LEONORA L. YAMBAO, Ph.D. Chairman

VILMA L. TACBAD, Ph.D. ELIZABETH M. ACAMPADO, Pd.D. Member Member

FILIPINAS L. BOGNOT, Ph. D. Professor, Research

Accepted and approved in partial fulfillment of the requirements for the

degree BACHELOR IN SECONDARY EDUCATION major in MATHEMATICS.

ANGELITA D. ROMERO, Ph.D.

Dean

Date: _____________________


ACKNOWLEDGEMENT

“There is no oil without squeezing the olives; no wine without pressing the

grapes; no fragrance without crushing the flowers; and no success without

handwork.” Indeed, the quotation above is very true. With deepest gratitude,

the researchers would like to thank the following persons who have helped

them pursue this academic endeavor.

Dr. Filipinas Bognot, their professor in Action Research in Mathematics

(Math20), for providing them sufficient guidance throughout the process;

Mr. Carlos Gozun, Mrs. Rosemarie Quito, Engr. Bernadette Sanchez, Engr.

Editha Flores, Mrs. Pinky Lumba and Ms. Jimelo Silvestre-Tipay, their

consultants, for helping them select the proper statistical tools to be used and

validating the test;

Mr. Cristian David and Ms. Leilanie Soriano, their cooperating teacher at

Angeles City Science High School, for allowing them to administer the test;

I-Joule of Angeles City Science High School, our dear respondents, for

being cooperative during the administration of the test.

The Blazing Etherons, their friends, for creating memories and

opportunities for each other; Lastly, to God, the Almighty Creator for showering

us with magnificent skills, talents and resources, during the conduct of the

study.

L.G.M.

J.D.N

J.V.O.


DEDICATION

The researchers dedicate this product of labor and great effort to the

following key persons:

Their parents, whom they owe their existence, for providing them the

essentials of life and the lifelong legacy of education;

Their teachers (AUF-CED, ACSCI Faculty, and AUF-MPD), who

continuously inspire them to strive for excellence and be passionate and

grateful for being in the teaching profession;

Their colleagues, who morally supported them and with whom they shared

momentous memories in spite of all the nerve-wrecking obstacles throughout

the study;

To the Almighty God, the divine providence, who guided us in every step

of the way;

To God be the glory.

L.G.M.

J.D.N

J.V.O.


TABLE OF CONTENTS

Title Page………………………………………………………….……….. 1

Approval Sheet……………………………………………………………. 2

Acknowledgement………………………………………………………… 3

Dedication……………………………………………………………...….. 4

Table of Contents…………………………………………………………. 5

Chapter 1: THE PROBLEM AND ITS SETTING

Introduction…………………………………………………….…… 8

Theoretical and Conceptual framework…………………….....… 11

Statement of the Problem…………………………………………. 16

Significance of the Study…………………………………………... 17

Scope and Delimitation…………………………………………….. 19

Definition of Terms………………………………………………… 19

Chapter 2: REVIEW OF RELATED LITERATURE AND STUDIES

Related Literature….……………………………………………….. 22

Related Studies...…………………………………………………… 46

Chapter 3: RESEARCH METHODS AND PROCEDURES


Research Design…………………………………………………. 59

Research Locale……………………………………………………. 59

Respondents of the Study…………………………………………. 59

Research Instruments………………………………………………. 60

Statistical Tool and Analysis of Data……………………………… 60

Research Procedures……………………………………………… 61

Chapter 4: PRESENTATION, ANALYSIS, AND INTERPRETATION OF

DATA

Classification of Students according to their Grades in Elementary

Algebra in the Second Grading

Period……………………………………….…………………….… 63

Table of Specifications in Elementary Algebra …………………… 64

Item Analysis of the Test Administered To I-Joule Students… .. 68

Strengths and Weaknesses of the Students in Learning

Elementary Algebra ………………………………………………… 71

Implications of the Result of the Study …………………………… 74

Proposed Enrichment Activities…………………………………… 77

Chapter 5: SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS

Summary……………………………………………………………… 92

Conclusions…………………………………………………………… 93

Recommendations…………………………………………………… 94


Bibliography………………………………………………………………… 95

Curriculum Vitae…………………………………………………………… 102

Appendices…………………………………………………………..…….. 112


CHAPTER 1

THE PROBLEM AND ITS BACKGROUND

INTRODUCTION

“Mathematics should be visualized as the vehicle to train a child to think,

reason, analyze, articulate, logically. Apart from being specific subject it

should be treated as a concomitant to any subject involving analysis and

meaning.”

-National Policy on Education (1986)

In the practice of the teaching profession, according to Torralba (1998),

delivery of instruction must be done in a “professional, formal and structured”

manner through following a certain curriculum. This curriculum basically

constitutes of what he termed as knowledge subjects, enabling subjects and

skills subjects. Under the knowledge subjects, students are taught about the

reality. These subjects include Science (that furnishes students the

understanding of their nature and its application for humanity);Social Studies

(that allow them to focus on man and his society); and, Values Education (that

teaches them the universal criteria in the proper conduct of themselves).On the

other hand, he identified Arts and Literatures (that teaches them to appreciate

artistry and aesthetics), Technology and Home Economics (that helps them

produce materials beneficial to mankind), and Physical Education (that aids

them in keeping a sound mind and body) as the enabling subjects. These

subjects condition our mind and body for learning other subjects. Lastly,


English, Filipino (that enables students learn the four macro skills across both

languages) and Mathematics are categorized under the skills subjects because

they accentuate on acquiring learning tools. In addition, Mathematics allows the

students to state and understand the reality in the abstract, using symbols and

its coverage include Arithmetic, Algebra, Geometry, Trigonometry, Statistics,

Consumer Mathematics and Business Mathematics. Since the researchers are

BSEd students having Mathematics as their area of specialization and

cognizant about the contributions of the field to all walks of life, they decided to

focus on Mathematics, specifically Elementary Algebra, in the conduct of their

action research.

In the Philippine Basic Education Curriculum for the Secondary Level

(2002), Elementary Algebra equally highlights that students, on their first year,

must acquire a set of competencies to cope up with the demands of the ever-

changing world. This roster of skills includes solving real-world problems

concerning the following areas: measurement, real number system, algebraic

expressions, first degree equations and inequalities in one variable, linear

equations in two variables, and special products and factoring. With Algebra

being the science of using symbols, Malaborbor et al. (2002) and Nivera (2003)

contend that generalizing operations and relationships will be of help to

students while they master the aforementioned math skills.


Even in learning Mathematics, specifically, the seemingly unending

string of enjoying yet complicated steps in Algebra, there are always two sides

of a coin. At one side, Torralba (1998) maintained with marvel that there are

noble students who “prefer Algebra for their salad” since they love Mathematics

and its other branches more than any other luxury in the world. With this

realization, Esteban (2010) claimed that these people would also consider

mathematics as their “code of life” since its beauty and worth within unravels

their clouds of unawareness and apathy. Hence, being the code of life, Algebra

has proven its significance as it also structures the foundation of problem-

solving concepts and techniques highly applicable in real-life situations (Chu,

2009).

In spite of this, Esteban (2010) introduced the perspective of those who

see the other side of the coin – the persistent dilemma of the nearly 90 % of the

entire human population (not only students) in learning mathematics. In a

narrower context, Nivera (2003) asserted that researches on students’

misconceptions about algebra and the difficulty that comes while learning it,

proved that students account such dilemma on the manner Algebra is taught;

thus, bearing a different notion that it is an inexplicable hodgepodge of symbols

that can only be comprehended by the noble few. Aside from the way of

presentation, the “letter-focused” sequence of textbooks also leads to the

vague understanding of the concept and utility of these letters. Indeed, it is just


commonplace for students to regard Algebra as very fearful, awfully

complicated, highly intangible and incredibly pointless.

In this regard, the researchers decided to determine the strengths and

weaknesses of high school students in learning Elementary Algebra. The

researchers hope that this study will generate results stating the areas of power

and difficulty of students in learning established proficiencies in Elementary

Algebra across Benjamin Bloom’s levels of the cognitive domain. Furthermore,

as another output of the study, it is also expected that a set of enrichment

activities be designed and implemented to enhance the weak points and to

reinforce the strong points of students in learning Elementary Algebra. In this

light, the researchers are certain that these activities will result to a more

effective and quality curriculum and instruction since it will make the teachers

and the students cognizant of the areas for improvement and eventually, such

awareness will call for an action to counteract mediocre teaching.

THEORETICAL AND CONCEPTUAL FRAMEWORK

According to Gibson (2010), Algebra is the gateway to exploring the

world around us. It is a steppingstone in learning all the things about the

universe that people lives in. However, despite of the advantages it offers,

students still find learning it difficult. This also leads the reason why teachers

find it difficult to teach it to students who perceive it as “not learnable”. To

decrease this problem, theories in teaching mathematics, specifically algebra,


were formulated. Here are some of the learning theories for mathematics

education (Wong KhoonYoong, 2006):

The teacher explains and demonstrates the lesson while the students

just listen and pay attention to the lesson. This technique is called Traditional

Rule-Based Teaching. This is presented in a pattern “explain, → practice, →

feedback” which consists of changes in observable or measurable behaviors

based on stimulus (S) and response (R). This S-R Bond helps the teaching of

mathematics become easier. To reinforce the S-R Bond Thorndike formulated

several laws such as Law of Exercise, Law of Effect, and Law of Recency;

however, behaviorism may out be suitable theory for use if the objectives are to

develop higher order thinking skills.

Teacher and pupils hold different views about what learning

mathematics is all about. Skemp (1979) proposed three types of understanding

namely: instrumental, relational, and logical. According to him the examples

and non-examples pattern must be used in discussing a concept.

Jerome Bruner proposed that a student acquire mathematical concepts

through three modes: enactive, iconic and symbolic. According to him, each

mode is dependent on the previous mode. For instance, the teacher can ask

the student to cut a circle into two sectors and make two cones from the sectors

(enactive); draw diagrams of the sectors and the cones (iconic); derive the

formula form the picture (symbolic). From this theory of Bruner, multi-modal


thinkboard was made, consisting: a.) Word; b.) Number; c.) Real Thing; d.)

Diagram; e.) Story and; f.) Symbol.

This multi- modal thinkboard accommodates different learners inside the

classroom that results to effective teaching and learning.

Another theory, the “Information Processing Theory”, states the

comparison of a computer to a human brain. They compare human thinking to

computer in regards with these elements: input, processing, output, and

memory storage. As cited in this theory, students have short attention span, so

teachers need to vary learning activities every 10-15 minutes to preserve their

attention. This indicates that there’s a need for the teacher to use different

instructional materials such as graphic organizers, models, manipulatives etc.

Another theory that helps to master learning effectively is the

Cooperative Learning and Social Constructivism. To strengthen

Cooperative Learning, Lev Vygotsky advocated Social Constructivism where he

mentioned the term Zone of Proximal Development (ZPD). According to him,

providing hints, clues, asking questions, and breaking problems into smaller

types will strengthen ZPD. For this theory to be effective, the following factors

should be preset: a.) Mutual Dependence; b.) Individual Accountability; c.)

Face-to-face interaction and; d.) Interpersonal and group skills.

The aforementioned theories stressed that students are not empty

vessels (tabula rasa) for teachers to fill their minds with all sorts of facts,

concepts, rules, etc. but an active learner inside the classroom.


Other articles also state that teaching strategies affect the performance

of students in learning Algebra. Therefore, failure in the proper implementation

and execution of these strategies may be one reason of the low performance of

the students in class, resulting to weaknesses in some algebraic competencies.

Otherwise, the result will be reinforcements of the strengths in these

competencies.

In this light, the researches formulated a paradigm (Figure 1) that will

assist them in the conduct of the study. The study considered the second

grading period academic performance of the students in the target school as a

basis for classifying the respondents. Review of literatures, theses, articles,

books, journals and other publications as a support to the inputs of the

researchers was also done. These literatures and studies included information

about the characteristics of students in learning mathematics and the guidelines

of the Department of Education in teaching Elementary Algebra.

To achieve its objectives, the researchers developed a teacher-made

test in Algebra following its psychometric properties. Upon approval and

validation, administration of the validated test proceeded. Based from the

results, the researchers identified the strengths and weaknesses of the

students in learning Algebra. This became the basis of the output of the study,

that is, the formulation and implementation of enrichment activities in teaching

Algebra.


Figure 1. The Paradigm of the Study “The Strengths and Weaknesses of First Year High School Students in Learning

Elementary Algebra: Basis for Enrichment Activities”

Reviews on the theories on teaching Algebra Characteristics of students in leaning mathematics DepEd Guidelines in the teaching of Elementary

Algebra (literatures, theses, articles, books, journals and other publications)

Second grading period rating of students

Preparing a teacher-made test in algebra (Table of Specifications, Item Analysis, Validity Test)

Validating the teacher-made test Administering the teacher-made test to the first year

high school students Organizing, interpreting and analyzing the results

Formulating enrichment activities in teaching

Elementary Algebra

Identifying the strengths and weaknesses of the students in Elementary Algebra


STATEMENT OF THE PROBLEM

This study determined the strengths and weaknesses of high school

students in Angeles City Science High School in learning Elementary Algebra

as a basis for enrichment activities. Specifically, it sought to answer the

following questions:

1. How may the students be classified according to their grades for the

Second Grading Period, S.Y. 2010-2011?

2. How may the test be constructed according to its psychometric properties?

3. How may the strengths and weaknesses of high school students be

classified according to the following level of the Revised Bloom’s

Taxonomy of the Cognitive Domain?

a. Remembering

b. Understanding

c. Applying

d. Analyzing

e. Evaluating

f. Creating

4. What are the implications of determining the strengths and weaknesses of

students in learning Elementary Algebra to Mathematics Education?

5. What enrichment activities can be designed and implemented to enrich the

present status of the students?


SIGNIFICANCE OF THE STUDY

Dating to approximately 4,000 years ago, Algebra is one of the

eldest of the divisions of Mathematics. Currently, with its unchanging rules, it

does not only offer the language and reasoning employed in other limbs of

mathematics. Moreover, it does permit the discovery of patterns and

establishment of relationships; thus enabling students of critical thinking and

reasoning, of communication of ideas and of practical problem solving (Nivera,

2003). Christiansen (2009) also added that no enchanted event can just occur

so we all go through the trial and error process when solving problems. In this

light, Algebra better furnishes a very conducive environment for learning and

developing the aforementioned skills.

Determining the strengths and weaknesses of high school students in

learning algebra as basis for enrichment activities is highly significant for the

following:

Department of Education. This paper can supply information regarding

the areas for support, revision and enrichment on Philippines’ Basic Education

Curriculum. This is so since it will reflect the competencies with which the

students are experiencing ease and difficulty.

Department Chairs in Mathematics. This study can provide

information, on a more focused context, during curriculum development and

adjustment. They may initiate the amendments on the shifts of methodologies

or strategies and changes of instructional materials.


Mathematics Teachers. This research can help teachers teaching

Mathematics in maintaining focus on competencies where students are strong

and weak at. Through this, their concentration will lead them to adopting,

modifying or designing their own learning activities, implementing instructional

and motivational strategies, and carrying out proper assessment methods. This

can all lead to a better facility of learning.

Elementary Algebra Students. Not only will this paper provide the

students self-cognizance of the areas where they excel and where they fail,

students, this can also help them in setting the goal to excel more and fail no

more. In doings so, schemes on monitoring and improving their own progress

and achievement can be done. They can also suggest ways and activities to

their teachers on how to make the instruction more meaningful and successful.

Future Researchers. This study can serve as benchmarks for

succeeding similar theses. Researchers can refer to the findings and outputs of

this paper as a baseline for new studies.

SCOPE AND DELIMITATION OF THE STUDY

This study aimed to identify the strengths and weaknesses of first year

high school students in learning Elementary Algebra. To do this, the

researchers constructed a test with respect to validity and item analysis. The

said test will be administered to the first year high school students of Angeles

City Science High School who are currently enrolled in the school year 2010-


2011.Results of which were used to classify them according to the Revised

Bloom’s Taxonomy and as an output of this study, the findings will be employed

as bases for modifying and designing enrichment activities to better enhance

the educative process.

For practical purposes, the researchers decided to cover and focus only

on the lessons from the first up to the second grading period. In lieu of this, the

students were classified according to their grades in Elementary Algebra for the

second grading period as a basis of their performance as well. The research

was conducted from January to April 2011.

DEFINITION OF TERMS

The following terms are defined for better understanding of the study at

hand:

Algebra. It is a system where general patterns, relationships, and

procedures are represented in a concise manner symbols, usually letters of

alphabet (Lee Peng Yee, 2006).

Basic Education Curriculum. An order that sets the standards for what

your students should learn in the basic education, which in the Philippines is

from grade 1- 6 and from first year to 4th year high school. Available at

http://www.slideshare.net/methusael_cebrian/the-philippine-bec



Bloom’s Taxonomy. It refers to a classification of the different objectives

that educators set for students (learning objectives). Available at

http://en.wikipedia.org/wiki/Bloom%27s_Taxonomy

Elementary Algebra. It is the most basic form of algebra taught to

students who are presumed to have no knowledge of mathematics beyond the

basic principles of arithmetic. Available at

http://www.wordiq.com/definition/Elementary_algebra

Enrichment Activities. These are activities that give students

opportunities for accelerated progress and access to new, more challenging

concepts or content of the lesson. In this study, it is the suggested activities for

improving the weaknesses of the first year high school students in Elementary

Algebra. Available at

http://www.brookes.ac.uk/schools/education/rescon/cpdgifted/docs/secondaryla

unchpads/8enrichment.pd

Grade. It is a mark given in an exam or for a piece of schoolwork (Oxford,

2005).

High school (Philippines). This refers to 4 years of education after 6–7

years of grade school usually of from age thirteen or fourteen and complete it

when they reach age sixteen or seventeen. Available at

http://www.answers.com/topic/high-school



http://www.brookes.ac.uk/schools/education/rescon/cpdgifted/docs/secondarylaunchpads/8enrichment.pd

http://www.brookes.ac.uk/schools/education/rescon/cpdgifted/docs/secondarylaunchpads/8enrichment.pd

http://www.answers.com/topic/philippines



Item analysis. It is the process of evaluating test items by any of several

methods; this involves the determination of how well an individual item

separates examinees, its relative difficulty value, and its correlation with some

criterion of measurement (Clark, 2010).

Validity. It is the degree to which a test or measuring instrument

measures what it intends to measure (Calmorin, 2007).

Mathematics. A branch of science that deals with numbers, and their

operations, interrelations, combinations, generalizations, and abstractions and

of space configurations and their structure, measurement, transformations, and

generalizations. Available at http://www.merriam-

webster.com/dictionary/mathematics?show=0&t=1294120510

Strength. It is a quality or an ability that a person or thing has that gives

them an advantage (Oxford, 2005).

Table of Specifications. It is a plan prepared by a classroom teacher as

a basis for test construction especially a periodic test (Asaad, 2004).

Test. It is a tool or a device used to gather data or evidences needed for

evaluation (Reganit, et.al, 2004).

Weakness. It means lack of strength, power, or determination (Oxford,

2005).

http://www.merriam-webster.com/dictionary/mathematics?show=0&t=1294120510

http://www.merriam-webster.com/dictionary/mathematics?show=0&t=1294120510


CHAPTER 2

REVIEW OF RELATED LITERATURE AND STUDIES

This chapter presents a variety of literature and studies reviewed by the

researchers, which are of significance to the study. These resources are

presented in order to provide readers a broader scrutiny of the problem being

analyzed.

RELATED LITERATURE

The Teaching of Mathematics

Recognizing that Mathematics is highly applicable and related to every

field, the teaching of Mathematics must then be given importance. Thus,

according to the Kothari Commission, to include Mathematics as one of the

subjects to be offered in the basic education should be a must. Sharan et al.

(2006) delves into recognizing the contributions of the queen of all sciences to

the development of various endeavors, which is tantamount to saying that it is

has been the moral fiber of our civilization. Famous authorities in education and

humanities described Mathematics as follows: a) Mathematics is an abstract

system founded on abstract elements (Marshall Stone); b) Mathematics

habituates the reasoning of children (John Locke); c) Mathematics may be the

subject in which we never know what we are talking about, not whether what

we are saying is true (Bertrand Russell); and, d) Mathematics is the language

God used to write the Universe (Galileo Galilee).These descriptions only prove


that Mathematics is a complex system; however, its essence does not lie in

complicating things, but in simplifying them. It will take a lot of effort, though, on

the teacher’s part to arouse the interest of his/her students and keep them

believing that essence. Therefore, the teacher must make provisions on

maintaining such interests.

The Teaching of Algebra

Aside from the mastery of the subject matter, propriety of the methods to

be used is also a major concern. Yee (2006) in his book The Teaching of

Secondary Mathematics enumerated major approaches in teaching algebra.

First, he claims that arithmetic must be used to as an association to algebra

because this allows them to explore before generalizing. Finding patterns is

one skill developed in Algebra; thus, emphasizing on making generalizations

through observing specific situations is another teaching approach. Moreover,

he also argues that we should not jeopardize students’ conceptual

understanding by focusing on procedural manipulation; instead, we should

promote for its emphasis. The use of instructional materials, such as algebra

tiles, is also a necessary aid to instruction. He also highly recommends the

stress on links to the model methods during problem solving. Lastly, variations

during drill and practice, in the form of games and open-ended tasks, should be

a must.


How to Teach Algebra

Moreover, when coupled with the abovementioned approaches, Gibson

(2010) mentions that students will earn confidence and the likelihood to

continue learning geometry, trigonometry and the other branches, if they

succeed in Algebra. Therefore, he enumerates four tips to teaching Algebra to

aid teachers, parents, significant others and tutors, and to benefit the students.

These tips include 1) being aware if the students are “with you” during the

instruction, which stresses mastery and review of pre-requisite skills before

advancing to more complicated lessons; 2) setting the minds of the students

that Algebra is not an enemy but a friend in order to boost their confidence in

learning Algebra; 3) teaching hierarchically, beginning from simple to complex

to assure students’ understanding of the lesson and to maintain confidence-

build up; and, 4) avoiding shortcuts by showing detailed solutions. He ended

that among the techniques of teaching Algebra, no single method is the only

correct way. In conclusion, he perceived that easing Algebra anxiety and

powering up confidence coupled with sufficient examples point the students to

the pinnacle of learning the challenging Algebra.

Calculating the Best Way for Teaching Algebra

In contradiction to Gibson’s conclusion and in search for the best formula

in teaching Algebra, the Researchers from the Center for Social Organization of


Schools at Johns Hopkins University launched a study which seeks to evaluate

two ways in teaching Algebra to ninth-graders, identifying if one approach is

more effective in increasing mathematics skills and performance or whether the

two approaches are equally effectual. The two strategies constitute the Stretch

Algebra, a yearlong course in Algebra 1 with extended class hours and the

other is sequence of two courses. Stretch Algebra provides students a “double

dose” of algebra, giving time for mathematics skills to be practiced as the need

arises. For the second strategy, the first course is described as “Transition to

Advanced Mathematics” and is developed by the researchers, followed by

Algebra 1. Findings are likely to be released this year (Maushard, 2009).

Why Study Algebra

Since teaching is twice learning, teachers must possess mastery of the

content of what they are teaching; thus, teachers also study Algebra to enrich

their knowledge of the subject and it is not impossible that they also do

experience difficulties in learning it. Because of this scenario, they are not

bewildered upon hearing the same comments from students. As a matter of

fact, in reality, the statement “Why will I study Algebra? I won’t use it anyway!”

is almost trite; however, Christiansen (2009) mentions some valid reasons why

we must take and be serious at it. Algebra, according to him, forms the solid

foundation for learning and improving our problem-solving skills because its

rules are firm. Therefore, we do not have to fear failures since we can always


try and explore other possibilities. Furthermore, there is no secret to anything

magical; problem-solving follows a path of trial and error. The valuable lessons

that we can derive from learning Algebra is, in itself, a struggle; nevertheless,

these become indispensable as they are applied in other aspects of our lives

such as being mindful that your banker cheats on your credit card account

because you are equipped with how interests are computed. In conclusion, we

must not be afraid of Algebra for it helps us be careful of developing our

problem-solving skills.

The previous article is supportive about the idea that Algebra is worth

learning. Moreover, according to a top state education official in an interview

done to K-12 teachers in Ohio, it is important that all students know how to do

math. “Doing math” is an accumulative skill just like the instruction of Algebra.

Algebra involves analysis towards developing problem-solving skills that goes

beyond the algebra problems since such skills are applicable to any problem

once done analytically and systematically; thus, Algebra is highly significant. On

the other hand, though considered to be a foundation for further learning,

students are being confined to mimicking problem-solving methods from rote

memory instead of developing the skill to solve any problem. In this light, the

reason why some authorities in education and the stakeholders themselves

(parents, teachers and students) fail to recognize the importance of Algebra in

the curriculum can be insufficiency of learning the subject as well (Chu, 2009).


Suggested Strategies and Materials in Teaching Mathematics

Aside from the tips reflected above, the 2002 Basic Education Curriculum

of the Republic of the Philippines (PSLC, 2002) recommended the following

strategies and materials for mathematics teaching: 1.) Discussion – is a

teacher-student or student-student exchange of ideas during exposition; 2.)

Practical Work – includes students-centered activities allowing students to

boost self-confidence in discovering solutions and while concretizing

abstractions; 3.) Practice and Consolidation – promote mastery of concepts

necessary for problem-solving and investigation; 4.) Problem Solving – is the

application of mathematics in the real world by exploring the solution to a given

situation; 5.) Mathematical Investigation – is a open-ended problem solving

through exploring mathematics situations, conjecturing, and reasoning logically;

6.) Cooperative Learning – encourage teaching and collaborations while

exchanging ideas.

DepEd recommends the use of approved textbooks and lesson plans that

target higher-order thinking skills, values integration, multiple intelligences and

cooperative leaning. Sample plans are provided on the latter part of the

handbook. Indeed, teaching math must not always conform to the

conventionality of the traditional method; rather, it must be taught where

students will find their leaning fun and meaningful yet equally substantial.


Difficulties in Learning Algebra

Since common notions about Algebra being a confusing subject continue

to persist, difficulties also arise despite the presented advantages it provides

and despite the various ways to teach it in the easiest manner. Since Algebra

comprises the use symbols/letters in representing numbers and expressions,

this is considered the first difficulty of students with Algebra. Wagner& Parker,

(1999) mentioned that Algebra is also a language. Likewise with any language,

the features of the language may bear linguistic difficulties and difficulties

during translation. As with Algebra, linguistic difficulties lie on variables and

expressions whereas translation difficulties lie on representing word problems

into equations. To improve instruction, efforts to enhance the teaching of

Algebra are recommended. In doing so, teachers must be careful in linking prior

knowledge to the new ones to establish connection and sense of progress

Common Errors

In conformity with the article above, students often commit mistakes in

Algebra tasks. The understanding of which can guide teachers during

instructional planning in order to eradicate them. These are categorized into

three: 1.) Procedural knowledge that is not backed up by conceptual

understanding because of lack of opportunities to engage in the enactive or

iconic representations of the concepts. This can be counteracted by using the


familiarity of students with arithmetic, by employing enactive and iconic

symbols, and by avoiding the use of procedural phrases such as “cancelling”

and “bringing over” during the preliminaries of the teaching-learning process.

2.) Long-held beliefs due to engagement with arithmetic. Arithmetic beliefs do

cause error and error patters, such as 5c-7c+2c=0c. 3.) Many algebraic

equations where alphabet letters are used. Students assign varied meanings

for letters used in algebraic expressions and equations. These interpretations

include letters being evaluated, letters as an object, letters as specific unknown

and letters as variable (Yee, 2006).

Children’s Difficulties in Beginning Algebra (Why is Algebra Difficult to

Learn)

As mentioned on the previous articles, students really find learning algebra

as a challenging dilemma. Due to these difficulties, they usually commit

mistakes learning algebraic tasks and computations that all the more strengthen

their notion that algebra is a dreaded subject. In addition to the aforementioned

usual errors, Booth identifies other aspects of the subject, which appears to be

difficult for students despite of their varied demographic profiles. These findings

are derived from one research project conducted by the math department of the

Strategies and Errors in Secondary Mathematics (SESM) project from 1980-

1983, these difficulty is to excavate common errors students commit and the

wherefores of those errors.


The following includes the various aspects from which errors are rooted: 1.)

The focus of algebraic activity and the nature of “answers”; 2.) The use of

notation and convention in algebra; 3.) The meaning of letters and variables; 4.)

The kinds of relationships and methods used in arithmetic.

Mathematics Enrichment Activities

Another supporting article reflects about the errors students commonly

make during algebraic activities. In this light, teachers must keep moving in

improving classroom instructions to lessen and hopefully, eradicate these

difficulties that will facilitate better leaning. In view of this, the Virginia State

Department of Education (1986) mentions that teachers must provide the

learners with enrichment activities to stimulate their interests. Such enrichment

activities promote a different leaning atmosphere since they are distinct from

regular classroom activities, enrichment activities are therefore, designed to

enrich mathematics at various grade levels. Basically, an enrichment activity has

the following components: introduction, objectives, a list of materials needed

and a description of the task, as well as some students’ worksheets and

solutions to problem for teachers.

As stated above, enrichment activities are necessary to further the

teaching of mathematics. Enrichment activities, according to Learning Point

Associates are interactive and project-focused tasks that expand on students’

learning in ways that vary from the methods used during the regular instruction.


They bring new concepts to light or by using old concepts in new ways. While

having fun and gaining knowledge at the same time. They let the participants to

apply knowledge and skills emphasized in school to real-life experiences.

(Available at http://www.learningpt.org/promisingpractices/whatis.htm.

Accessed on December 15, 2010). We use four primary criteria to evaluate

whether or not a particular activity is “high quality.” High-quality activities have

the following characteristics: 1.) They display well-integrated academic content;

2.) They improve resilient relationships between the participants and caring

adults, older students, or peers; 3.) They offer opportunities for genuine

decision-making by the participants; and, 4.) They allow the possibility for

student leadership in the activity.

Test Construction

To come up with the expected results, the researchers used testing as its

main research instrument in gathering data. In lieu of this, the researchers

referred on the following steps and principles for test construction.

Planning the Test

During the planning, determining the purpose of the Test is a primordial

concern. Test can be used in an instructional program to assess entry

behavior (placement test), monitor learning progress (formative test),

http://www.learningpt.org/promisingpractices/whatis.htm


diagnose learning difficulties (diagnostic test) and measure performance at

the end of instruction (summative test). Afterwards, Identifying and defining

the intended learning outcomes proceed. The learning outcomes measured

by a test should be faithfully reflecting the objectives of instruction.

Therefore, the first thing to do is to identify the instructional objectives that

are to be measured by the test an then make certain that they are stated in

a manner that is useful for testing. One useful guide for approaching this

task is the Taxonomy of Educational Objectives. After preparing the

content and objective outline, the construction of the table of specifications

follows. The function of the specifications is to describe the achievement

domain being measured and to provide guidelines for obtaining a

representative sample of test tasks. Moreover, the learning outcomes for a

particular course will depend on the specific nature of the course, the

objectives attained in previous courses, the philosophy of the school, the

special needs of the students, and a host of other local factors that have a

bearing on the instructional program. Clarifying the specific types of

performance to be called forth by the test will aid in constructing test terms

that re most relevant to the intended learning outcomes. More so, particular

types of student performance can overlap a variety of subject matter areas,

and vice versa, it is more convenient to list each aspect of performance

and subject matter separately and then to relate them in the table of

specifications. The content of a course may be outlined in detail for


teaching purposes, but for test planning only the major categories need be

listed. (Grondlun, 1993)

Constructing Relevant Test Items

The quality of test depends on how closely the test maker can match the

specifications. Some considerations in constructing items include selecting

the type of test item that measures the intended learning outcome most

directly, writing the test item so that the performance it elicits matches the

performance in the learning task; writing the test item so that the test task

is clear and definite; writing the test item so that it is free from nonfunctional

material; Write the test item so that irrelevant factors do not prevent an

informed student from responding correctly; writing the test item so that

irrelevant clues do not enable the uninformed student to respond correctly;

writing the test item so that the difficulty level matches the intent learning

outcome, the age group to be tested, and the use to be made of the

results; writing the test items so that there is no disagreement concerning

the answer; writing the test item far enough in advance that they can be

later reviewed and modified as needed; and, writing more test items than

called for by the test plan (Grondlun, 1993).

Assembling, Administering, and Evaluating the test

In reviewing and editing the items, the group of items for a particular test,

after being set aside for a time, can be reviewed by the individual who

constructed them or by a colleague. In either case it is helpful for the


reviewer to read and answer each item as if taking the test. Afterwards, in

arranging the items in the test, it is usually desirable to group together

items that measure the same learning outcome. Where possible, the items

should be arranged so that all items of the same type are grouped

together. Furthermore, the item should be arranged in order of increasing

difficulty. In terms of writing directions, directions should be simple and

concise and yet contain information concerning to each of the following: (1)

purpose of the test, (2) time allowed completing the test, (3) how to record

the answers, and (4) whether to guess when doubt about the answer.

If items are to be marked on the test itself, provision should be made for

recording the answers on the left side of the page. This simplifies the

scoring. If the separate items are to be used and the test is to be

administered to more than one group of students, it is usually necessary to

warn the students not to make any marks on the test booklets. It is also

wise to make more copies of the test than are needed because some

students will ignore the warning. The mimeograph, ditto, photocopy, or

photo-offset processes commonly reproduce achievement tests for

classroom use. Regardless of the method of reproduction used, the

master copy should be checked carefully for item arrangement, legibility,

accuracy of detail in drawings, and freedom from typographical errors.

After the reproduction of the test, the administering of a prepared informal

achievement test is largely a matter of proving proper working conditions,

keeping interruptions to a minimum, and arranging enough space between


students to prevent cheating. Scoring is facilitated if all answers are

recorded on the left side of each test page. Under this arrangement,

scoring is simply a matter of marking the correct answers on a copy of the

test and placing it next to the column of answers on each student’s

paper.(Grondlun, 1993)

Interpreting the Test Results

Test results can be interpreted in terms of the specific tasks performed

(criterion- referenced interpretation) or how the test performance compares

to that of others (norm- referenced interpretation). In many cases, both

types of interpretation can be used. A set of scores can be described by

computing the average score (e.g. median or mean) and the variability, or

spread of scores (e.g. range or standard deviation). A simple ranking of

scores from high to low with a frequency column showing the number of

individuals earning each score is satisfactory for presenting test results to

small classroom groups (Grondlun, 1993).

Designing Test Items (Teaching Secondary Mathematics)

As an output of this study, the researchers will formulate enrichment

activities to enhance the weak competencies of students. Prior to designing

them, they must first know the competencies where they are strong and weak at.


Therefore, testing is the major instrument to be used to obtain such results.

Wong (2006) mentioned that a “repertoire of interesting and meaningful

problems” must be developed, to challenge all students, including those who are

weak, who could have just lost their interest, thus exerting less effort because of

routine exercises. To meet this need, he enumerated five main themes to make

them more challenging.

These themes include a.) Changing the givens; b.) Using more open-ended

tasks (Open-ended tasks probe deeper understanding of concepts to promote

creative thinking by providing many possible solutions); c.) Including interesting

or meaningful contexts (Contextualizing problems will widen students’

perspectives of their local environments and the wider world, and provide links

to other subjects. Contexts include day-to-day situations that are meaningful,

current affairs, historical events and cultural practices. Students will feel the

challenge because methods may be concealed); d.) Using creative imagination

(Einstein believed that “imagination is more important than knowledge. It is the

supreme art of the teacher to awaken joy in creative expression and knowledge”.

Making math fun and enchanting may involve fantasy and imagination. This is

possible by asking students mentally assemble figures and then write about it.

Mary Boole, the wife the famous algebraist George Boole, used mental pictures

to teach mathematics); and e.) Using Different Formats. To help low performing

students master problem solving, it is encouraged that problems be presented in

a “diagram + explanation” form prior to moving to a verbal format.


RELATED STUDIES (FOREIGN)

In Hong Kong, Poon & Leung (2010) conducted a pilot study on Algebra

Learning among the Junior Secondary Students. Their research primarily aimed

to determine common mistakes made by 815 student- respondent in leaning

algebra. Moreover, it also sought to compare whether the perception of the

teachers vis-à-vis the ability of the students has a relationship. To achieve these

targets, the researches constructed and administered an examination to the

participating students. Based from the result of the examination, they found out

that, students from high-performing schools obtained better ratings in the said

algebra test, in contradiction with the low test results of students from low-

performing leaning institutions. Furthermore, they proved that the perception of

the teacher is correlated with the level of achievement of the students. From

these major findings, the researchers discussed an assessment instrument

measuring one’s effectiveness in teaching. Moreover, they also determined the

typical errors of students in algebra, and as an output of the study, they

recommended some ideas for an instructional design to further the teaching of

Algebra.

Similarly, this study also aimed to identify common errors during algebraic

tasks and activities to determine the weaknesses of student; however, the

researchers included in the parameter the strengths of the learners in learning

algebra to find out which competencies they do excel. To reach the objectives,


test construction, validation and administration were employed also, but the

respondents belonged to the second sections in the first year of a single school.

The ratings of the students in Elementary Algebra for second grading period

were also used, but not to be correlated with any factor; rather to be used to

classify only the respondents. As an output, the researchers used their findings

regarding the levels of the cognitive domain at which students excel and fail as

basis for designing enrichment activities.

Related literatures indicated that the fear of students in Algebra fail their

performances in leaning it. Nevertheless, Matthews & Farmer (2008)

determined, through another study, other factors that affect students’ Algebra I

performance. In their research, however, secondary data were used to evaluate

the relationship between chosen factors and the Algebra I performance of

academically able and gifted learners. To further find this out, results from a

standardized examination measuring Algebra I achievement, including the

selected variables were examined using structural equation modeling. These

variables are the following: prior mathematics activity, parental education level,

giftedness of a student, participation in school activities, time spent on

assignments, and the amount of class sessions. The major findings involved:

mathematics reasoning and Algebra I achievement are strongly related;

giftedness is not strongly related to Algebra achievement; and the amount of

class time spent on discussions is significant to the amount of time spent for

weekly homework. Relying on these findings, the researchers recommended the


integration of more classroom discussion on mathematical topics for gifted

learners is not related to giftedness that strongly predicts mathematics

reasoning.

The present study could use the variables employed by the researchers

above during the interview part of our procedure. This was in support of the

identified strength and weaknesses of the students in learning Elementary

Algebra. A noted difference of the previous study with ours was the choice of

respondents. Theirs were the academically talented learners while ours were

the resource or the regular students. Nonetheless, both studies used testing as

one of their research instruments; however, theirs was standardized and ours

was self-constructed and teacher-validated.

Another parallel study noted reasons why students fail in Algebra. Islip

(1987) used qualitative approaches in making eight 12th-graders, who all flanked

the subject and have enrolled in independent study programs and voluntarily

analyzed their previous failure in their Algebra classes to determine the reasons

of the failure of the students in the said subject. To collect data, Interviews

through questionnaires were done and the respondents were also exposed to

an intervention program while their behavior was being observed. Moreover,

students completed some surveys regarding perceptions, histories and personal

needs in learning Mathematics. The researcher reached the following


conclusions and recommendation at the culmination of the study: a.) intelligence

is not related to the students’ failure; b.) social skills, attendance, attention span,

personal attention needs, and family divorce are the determined reasons for

such disappointments; c.) the respondents are distinctly unique from one

another; d.) differentiated instruction must be considered as an intervention;

and, e.) counseling programs and communication tools must be used to help

these students reach the optimum level of performance.

Like the previous thesis presented, the study at hand also sought to

support the findings about the strengths and weaknesses of students in learning

Algebra by discovering the reasons behind their difficulty, and worse, their

failure. The results found, however, were highly social and personal. The

researcher of the paper above was also commendable because she was able to

examine the profile of her subjects in a in-depth manner.

A teacher’s effectiveness in teaching the subject may also be significant on

the performance of the students in an Algebra class. This may be due to the

some frustration they acquire when searching for solutions. In this light, Sergio &

Robert (2008), reported the results of their action research that are sought to

raise proficiency levels in mathematics in their own schools with the researchers

being high school principals. In raising their mathematics proficiency level, they

centered their study on raising Students Achievements in Algebra by proposing

productive strategies. Among these strategies were leadership empowerment of


department chairs of specific instructional pedagogies of the teachers and

coaches.

The similarities of the research above with the current study lied on the

objective to raise proficiency levels of students in leaning algebra. However,

ours focused on designing enrichment activities. Teachers can implement this to

enhance more the competencies of the students, unlike theirs, whose

significance is for teachers, coaches, and chairs. Students, therefore, can take

part in raising their own achievement in Algebra since it is not the sole

responsibility of the teacher to make his students achieve. After all, the students

must be more concerned about his academic progress.

LOCAL STUDIES

Locally, a study similar to Poon and Leung’s (2010) was also conducted

by Mesina (2004); however, the latter’s purpose was not solely confined to

identifying mistake, but, rather, it was more concerned with assessing the

difficulties of students in learning College Algebra, specifically in terms of the

following concepts: a) polynomials; b) factoring an d special products; c)

fractions; d) exponents and radicals; e) linear and quadratic equations, and f)

related worded problems. The researcher also sought to find the significant


difference of these difficulties as to the mentioned contents, across academic

degrees or courses.

333 college students participated in this descriptive research that revealed

the following findings: a.) the difficulties of students across the selected

contents: Polynomials- applying the four fundamental operations (addition,

subtraction, multiplication and division) on monomials, binomials and

polynomials; Factoring and Special Products- involving the four fundamental

operations in factoring, finding the square and difference of even powers and

finding special products; Fractions- applying the four fundamental operations,

reducing values and expressions to lowest terms, canceling in division, finding

the factors, determining the least common denominator, and reciprocating the

divisor; Exponents and Radical- applying the four fundamental operations on

exponents and radicals; Linear and Quadratic Equations- applying the four

fundamental operations, solving for the unknowns, extracting roots, solving

equations with the quadratic formula, and transposing; and worded Problems

– applying algebraic representation, solving for the unknowns, transposing

and substituting; b.) there is no significant difference among the difficulties

students are experiencing across academic degrees or courses; and, c.) the

following are the implications of the study to instruction: students must

intensify their awareness of College Algebra being a baccalaureate

requirement through diligence and assistance from peer tutors; teachers must

continuously improve pedagogically and professionally through seminars and

class advising; college Deans must enrich the learning environment for


College Algebra through intervention programs and regular publications; and,

curriculum planners must consider enriching and revising some parts of the

College Algebra curriculum.

In lieu of the abovementioned findings, Mesina (2004) suggested that the

divulged weaknesses across the six areas be strengthened with the assistance

of the professors; that the concerned colleges could hire competent and

effective teachers; and, that similar studies be conducted.

Relative to this paper, the present research also aimed to determine the

strengths and weaknesses of students in Algebra for the betterment of learning

and instruction; however, our target respondents were high school students

taking up Elementary Algebra. Therefore, our focus was on the high school

algebra. The results of the former study were then utilized to cite some

implications to classroom instruction unlike ours, since our results were used

as basis for developing enrichment activities. Both studies employed testing as

their main research instrument in collecting data.

Cognizant of the abovementioned difficulties, teachers should not remain

apathetic without counteracting the downfalls they might cause to the future of

the learners. With this perception, Dimal (2007) conducted a study regarding

making selected topics in high school algebra more appealing with the

knowledge that students still consider the subject important to their lives. It was


directed towards identifying selected topics in Mathematics II that will make

their learning of high school algebra of more appeal and interest. It sought to

carefully design, apply and integrate simulation and games to make learning

interesting as compared to the conventional way. This descriptive study was of

significance to teachers in considering the proposed games to heap on the

teaching-learning process. The researcher identified ways of improving

students’ interest in Mathematics through discussions/recitations,

games/contests, lectures and experiments. As a result of the study, the

integration of the designed games improved the performance of the students.

Based on the findings, the teachers, with collaboration, must provide their

students with discussions of interest to motivate them learn Algebra and they

also must present fascinating activities to keep their interests.

In relation to the previous study, the current study hoped to determine the

areas of strengths and weaknesses in terms of the competencies in

Elementary Algebra. To complete the paradigm of this study, an output in the

form of enrichment activities was to be formulated. With the mentioned ways of

improving Mathematics, games and simulations were considered. With the

proven effectivity of the proposed games as evidenced by improvements on

the students’ rating, the current researchers considered formulating enrichment

activities in the form of games.

A local study authored by Calara, et al. (2003) discussed the factors

affecting the mathematical comprehension of senior students on Algebra. This


is a descriptive research which pointed to determine the relationship between

selected factors such as study habits, teaching strategies, school facilities, peer

influence and parental support vis-à-vis the students’ mathematical

comprehension on Algebra by floating a questionnaire, administrating test,

interviewing and analyzing ratings. This yielded the following results: a) there is

no significant relationship between ratings in Algebra and all the selected

factors. Based from this major finding, the researchers recommended

employing teaching strategies that will make students develop critical thinking;

b) implementing proper motivational strategies as well as the pee tutoring

technique to improve grades; and, c) asking for parents’ cooperation to assist

their children in the development of effective study habits.

Similar with the study conducted by Matthews & Farmer (2008) the

questionnaire used in this paper can be used as a basis in formulating their

own questionnaire as a support on the findings about the strengths and

weaknesses of the students in learning Algebra. The researchers were

recognizing the possibility that these factors can be some of the reasons why

behind their performance in the said subject.

The previous study used teaching strategies as one of the variables to

arrive at their point. On a narrower context, Canlapan (2009) designed

proposed activities in teaching the addition and subtraction of polynomials with

the use of Algebra tiles. This experimental study compared students’


achievement in learning the said topic while taught conventionally and while

taught with the use of manipulatives (Algebra tiles). They found out that both

the methods are effective; conversely, the teaching of the content is even

effective through the use of the latter. From this finding, they suggested the use

of Algebra tiles to increase comprehension, the use of the proposed activities

and lesson plans as guide, and the use of manipulatives.

Relating it to the study at hand, the use of Algebra tiles, with its proven

effectivity in teaching, can be a used as a material on a proposed enrichment

activity in teaching topics about polynomials. As a result, the use of the

manipulatives can reinforce and enrich the algebraic competencies of the

students.

One of the conclusions of the study conducted by Calara, et al. (2008)

was to use strategies that develop critical thinking to increase their

comprehension, which, in turn, alleviates some weaknesses and reinforce

some strong points. This connoted that critical thinking is needed to learn the

competencies. Cunan, et al. (2007), in their study, proposed mathematical

games in enhancing the critical thinking skills of students. Their research

intended to motivate and improve the competencies of students and for

teachers to employ more creativity in making Mathematics a fascinating subject

beyond any problem-solving methods. They employed the experimental

method through floating evaluation questionnaires. They discovered that there

is a variety of strategies and techniques in teaching Mathematics and among


them are mathematical games. Furthermore, mathematical games motivate the

students because they provide a competitive atmosphere; they develop critical

thinking skills; they develop the physical aspects; and, they develop the

interpersonal skills of the students. In addition, students highly favored card

games since they are enjoyable. Based from these conclusions, the

researchers recommended the formulation of more games, the use of

improvised materials, clear statement of instructions, a good facility of the game

by the teacher, the use of a scoreboard and the provision of some explanations

regarding the learning acquired by the winning group.

The study at hand was one with the objectives of the preceding thesis in

enhancing the competencies of the students through games that can be

considered as one form of an enrichment activity since both require completion

of the tasks. Both studies also hoped to make teachers creative in making their

instruction interesting through such activities. Differences lied on the choice of

respondents because the prior study targeted elementary pupils, thus,

improving achievement in Elementary Mathematics. Unlike the previous study,

the focal point of our study is in the field of Elementary Algebra only (not the

entire secondary mathematics). They also differed in the process of obtaining

results because our study still employed testing to know which competencies to

strengthen and to reinforce.


CHAPTER 3

RESEARCH DESIGN AND PROCEDURE

This chapter exhibits the method and procedures used by the

researchers in the conduct of this study.

RESEARCH METHOD

The researchers used the descriptive method to identify the strengths and

weaknesses of the high school students of Angeles City Science High School in

Elementary Algebra. This research method is employed to acquire information

concerning the current category of the phenomena to describe “what exists”

with respect to variables or conditions in a situation (Best & Kahn, 2003).

Likewise, this study aims to modify and/or design enrichment activities to

reinforce and enhance the identified strengths and weaknesses, respectively.

RESEARCH LOCALE

This study was performed at Angeles City Science High School, Angeles

City.

RESPONDENTS OF THE STUDY

The respondents of the study were the First Year students, specifically I-

Joule, of Angeles City Science High School who were taking up Elementary

Algebra in the S.Y. 2010-2011.


RESEARCH INSTRUMENTS

Generally, the researchers employed testing as the main research tool.

The test was prepared by the researchers following the basic principles in test

construction and considering the psychometric properties of a good test such

as validity and item analysis. Questions covered include the lessons from First

Grading to Second Grading. The initial draft was subjected for improvement

depending upon the comments of selected Math teachers in the university.

After the revision, the final draft of the examination was administered to the

target respondents.

STATISTICAL TOOL AND ANALYSIS OF DATA

The following statistical tools were employed for the analysis of the

research data:

1. Item Analysis

This process is done to evaluate the test items by computing for the

difficulty/facility index and the discrimination Index. The facility index describes

the difficulty level of the test items in terms of the number of students who

correctly answered an item. On the other hand, the discrimination index

indicates the characteristic of a specific item to discriminate between the

achievers and the non-achievers. In this study, the standard used to obtain the

upper and the lower group is 33% since the respondents are only 40.

2. Descriptive Statistics


The following tools are used to organize and analyze the strengths and

weaknesses of the students in learning Elementary Algebra:

a. Mean- is a measure of central tendency, which is often referred to as

the arithmetic average of a given set of numbers. This is computed by getting

the ratio of the sum of all the elements and the number of elements in the set.

b. Median- is another measure of central tendency, which is considered

to be the midpoint of the array of a set of numbers.

c. Minimum- is the smallest value/observation in a given set.

d. Maximum- is the largest value/observation in a given set.

e. Standard Deviation- is a measure of variability that shows how much

variation or dispersion there is from the mean.

RESEARCH PROCEDURES

Primarily, the researchers drafted the test (covering only the lessons in the

first two grading periods) with respect to the basic principles in test construction

and considering the psychometric properties of a good test such as validity and

item analysis. Teachers then validated the test for suggestions and

improvement of test items. After the validation, the examination was

administered to the respondents. Prior to the administration, the researchers

sent letters seeking for permission and endorsement to administer the validated

test. Afterwards, the data underwent proper organization and presentation and


eventually, analysis and interpretation. The results of the study were the point

of reference in modifying and/or designing enrichment activities.


CHAPTER 4

PRESENTATION, ANALYSIS, AND INTERPRETATION OF DATA

I. Classification of Students According to their Grades in Elementary

Algebra in the Second Grading Period

Twelve point five percent of the students obtained an above average

rating in their Elementary Algebra class during the second grading period,

while 42.5% obtained an average performance rating and 45% of them

obtained poor ratings. The descriptive ratings are based from the curriculum of

the research locale where standards are set a higher level, being a considered

as a science high school. This suggests that majority of the students are below

the average performance which implies that they are having difficulty in

learning Elementary Algebra.

Table 1

Second Grading Period Ratings of First Year High School Students in

Elementary Algebra

Student # Grade

Descriptive Ratings

Student # Grade

Descriptive Ratings

1 82 Below Average 21 84 Below Average

2 94 Above Average 22 88 Average

3 80 Below Average 23 86 Average


5 89 Average 25 86 Average

6 84 Below Average 26 90 AboveAverage

7 88 Average 27 82 Below Average




11 92 Above Average 31 83 Below Average






16 91 Above Average 36 84 Below Average





II. Preparation and Development of the Elementary Algebra Test for First

Year

A. Validity

To ensure content validity, the researchers constructed the following table

of specifications prior to developing the test.

As can be reflected from the table below (Table 2), the researchers

decided to equally distribute ten (10) items in each level. Based from these

specifications, the researchers drafted a 60-item test composing of four types of

tests, namely multiple choice (45 items), problem solving (5 items), table

completion (5 items) and Mohr’s type (5 items). They agreed to employ a

variety of test types to satisfy the congruence of the set objectives and their

levels with the items to be constructed.

Furthermore, they largely depended on the content areas and objectives

stipulated on the Philippine Secondary Learning Competencies (2002). As

delimitation, they included only the topics covering the first two grading periods

that encompass the following: sets and its operation, the number of elements in


a set, measurements and its history and development, measures and

measuring devices, problem solving and application involving measurements,

real number system, absolute values, integers and their operations, properties

of equality, properties of real numbers, problem solving involving integers,

common fractions and their operations, decimal fractions and their operations,

problem solving and applications involving decimals and fractions, square

roots, algebraic expressions, simplifying numerical expressions, algebraic

expressions, laws of exponents, scientific notation, polynomial, operations on

polynomials, problem solving involving polynomials, linear equations and

inequalities, solving first degree equations and inequalities, properties of

inequalities, and, mathematical equations and verbal sentences. These were

also the same topics that the research locale considered in their curriculum.

To further prove the validity of the test, the researchers requested

teachers from the Mathematics and Physics Department of the Angeles

University Foundation to conduct a face validation on the items. The revisions

mostly include clarifications on the stems and the choices and proper phrasing

of the items. No items were largely revised nor deleted from the test.


Table 2

Table of Specifications in Elementary Algebra (1st and 2nd Grading Period)

Topic

Rem

em

beri

ng

Un

ders

tan

din

g

Ap

ply

ing

An

aly

zin

g

Evalu

ati

ng

Cre

ati

ng

No

. o

f It

em

s

Item

Pla

cem

en

t

Sets and Its

Operation 1 1 4

The Number of

Elements in a Set 1 1 7

Measurements and

Its History and

Development

2 1 3 1,3, 57

Measures and

Measuring Devices 1 1 2 2, 16

Problem Solving and

Application Involving

Measurements

2 2 11, 12

Real Number

System 1 1 2 8, 56

Absolute Values 1 1 2 14, 19

Integers and Their

Operations 1 1 1 1 4

15, 17,

21, 58

Properties of

Equality 1 1 2 5, 59

Properties of Real

Numbers 2 2 6, 10

Problem Solving 1 1 20


Involving Integers

Common Fractions

and Their

Operations

1 1 1 3 13, 23,

60

Decimal Fractions

and Their

Operations

1 1 25

Problem Solving and

Applications

Involving Decimals

and Fractions

2 2 22, 24

Square Roots 1 1 2 9, 18

Algebraic

Expressions 1 1 26

Simplifying

Numerical

Expressions

1 1 36

Algebraic

Expressions 2 1 3

31, 33,

42

Laws of Exponents 1 1 2 30, 37

Scientific Notation 1 1 45

Polynomial 1 5 6

27, 51,

52, 53,

54, 55

Operations on

Polynomials 2 2 4

38, 39,

47, 50

Problem Solving

Involving

Polynomials

1 1 46

Linear Equations

and Inequalities 1 2 3

28, 34,

35, 43


Solving First Degree

Equations and

Inequalities

1 1

Properties of

Inequalities 1 1 1 3

29, 32,

44

Mathematical

Equations and

Verbal Sentences

1 1 2 4 40, 41,

48, 49

TOTAL: 10 10 10 10 10 10 60

B. Item Analysis

Table 3 encapsulates the item analysis of the test administered to the

respondents. Based from the administration, there are 38 items with average

difficulty, 6 items that are too easy and another 6 items that are too difficult.

These results yield a 0.51 over-all difficulty index, which implies an average

difficulty for the entire test. On the other hand, in terms of the discrimination,

there are only 2 items that are considered to be very good items, 8 good, 11

marginal and 29 poor. Collectively, this gives an over-all discrimination index of

0.14.

Table 3

Item Analysis of the Test Administered to I-Joule Students

ITEM

#

UPPER

%

LOWER

%

DIFFICUL

TY REMARKS

DISCRIMINA-

TION REMARKS

33% 33% INDEX INDEX


1 9 0.69 9 0.69 0.69 Average Accepted 0.00 Poor

2 0 0.00 3 0.23 0.12 Too

Difficult Rejected -0.23 Poor



5 1 0.08 5 0.38 0.23 Average Accepted -0.31 Poor


7 11 0.85 8 0.62 0.73 Average Accepted 0.23 Marginal

8 9 0.69 4 0.31 0.50 Average Accepted 0.38 Good


10 3 0.23 2 0.15 0.19 Too

Difficult Rejected 0.08 Poor








18 13 1.00 0 0.00 0.50 Average Accepted 1.00 Very Good

19 13 1.00 11 0.85 0.92 Too Easy Revise 0.15 Poor



22 3 0.23 1 0.08 0.15 Too

Difficult Rejected 0.15 Poor


24 1 0.08 2 0.15 0.12 Too

Rejected -0.08 Poor


Difficult


26 12 0.92 9 0.69 0.81 Too Easy Revise 0.23 Marginal








34 11 0.85 12 0.92 0.88 Too Easy Revise -0.08 Poor



37 3 0.23 0 0.00 0.12 Too

Difficult Rejected 0.23 Marginal

38 11 0.85 5 0.38 0.62 Average Accepted 0.46 Very Good




42 12 0.92 9 0.69 0.81 Too Easy Revise 0.23 Marginal





57 3 0.23 1 0.08 0.15 Too

Difficult Rejected 0.15 Marginal





Total Number of Accepted/Average Items 38

Total Number of Revised /Too Easy Items 6

Total Number of Rejected/Too Difficult Items 6

Over-all Difficulty Index 0.51

Total Number of Very Good Items 2

Total Number of Good Items 8

Total Number of Marginal Items 11

Total Number of Poor Items 29

Over-all Discrimination Index 0.14

III. The Strengths and Weaknesses of the Students in Learning

Elementary Algebra

Table 4 specifies the performance of each student in each of the levels of

Benjamin Bloom’s cognitive domain namely knowledge, comprehension,

application, analysis, synthesis and evaluation. The data on each field are

computed using mean/average by dividing the score of each student by the

total number of items in every level. This indicates that there is a variety of

performance across each student and each level; thus, pointing to the

individual differences of the students in terms of mastery of the required

concepts and skills in Elementary Algebra.


Table 4

Frequency Distribution of Students’ Mean Scores across the Six (6)

Levels of the Cognitive Domain S

tud

en

t #

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Ap

pli

cati

on

An

aly

sis

Syn

thesis

Evalu

ati

on

1 0.50 0.30 0.40 0.70 0.20 0.20

2 0.50 0.80 0.60 0.90 0.80 0.20

3 0.40 0.20 0.50 1.00 0.20 0.27

4 0.50 0.40 0.60 0.60 0.20 0.80

5 0.50 0.60 0.60 0.60 0.50 0.73

6 0.50 0.30 0.30 0.30 0.50 0.33

7 0.30 0.50 0.50 0.50 0.40 0.20

8 0.60 0.30 0.50 0.50 0.30 0.27

9 0.50 0.50 0.70 0.70 0.10 0.47

10 0.50 0.30 0.70 0.70 0.70 0.73

11 0.60 0.60 0.70 0.70 0.40 0.47

12 0.40 0.30 0.50 0.50 0.20 0.27

13 0.60 0.60 0.50 0.50 0.70 0.53

14 0.40 0.20 0.50 0.50 0.40 0.47

15 0.20 0.50 0.50 0.50 0.10 0.33

16 0.60 0.70 0.90 0.90 0.80 0.73

17 0.40 0.40 0.70 0.70 0.40 0.67

18 0.80 0.30 0.70 0.70 0.40 0.47

19 0.60 0.40 0.80 0.80 0.40 0.67

20 0.50 0.50 0.50 0.50 0.20 0.33

21 0.50 0.30 0.50 0.70 0.50 0.60

22 0.30 0.40 0.50 0.50 0.20 0.20

23 0.50 0.50 0.50 0.30 0.80 0.53

24 0.50 0.30 0.60 0.70 0.20 0.47

25 0.40 0.50 0.60 0.60 0.40 0.40

26 0.50 0.50 0.60 0.50 0.30 0.73


27 0.60 0.20 0.30 0.60 0.20 0.60

28 0.60 0.30 0.70 0.80 0.10 0.27

29 0.60 0.60 0.50 0.70 0.30 0.20

30 0.70 0.40 0.40 0.60 0.40 0.47

31 0.30 0.60 0.70 0.60 0.30 0.07

32 0.50 0.50 0.50 0.60 0.60 0.20

33 0.60 0.50 0.80 0.60 0.40 0.00

34 0.50 0.40 0.30 0.60 0.40 0.27

35 0.60 0.50 0.70 0.60 0.40 0.40

36 0.50 0.50 0.90 0.70 0.60 0.27

37 0.80 0.60 0.70 0.60 0.30 0.40

38 0.50 0.50 0.50 0.40 0.50 0.40

39 0.30 0.50 0.40 0.70 0.60 0.20

40 0.40 0.40 0.60 0.30 0.30 0.80

Table 5 supports the previously presented data and summarizes the

statistical descriptions of the over-all performance of the students in the test

administered to them. Analysis of the aforementioned data illustrates below

satisfactory ranking as evidenced by the median and mean percentage ratings

below the prescribed percentage by the Department of Education Order No. 33,

S. 2004, which is 75%. The lowest mean and median percentage ratings both

fall under the synthesis level, whereas the highest mean percentage lies in the

analysis level, while the highest median percentage is found under the

application level.

The computed standard deviations of the test scores ranged from 13.94%

to 20.88%, which imply a relatively wide variability of the students’ mean scores.

These values suggest that there are mean scores both below and above the

mean percentage rating. In due course, this proves that the respondents


possess diversity in the mastery of the six (6) levels. Furthermore, the highest

mean score obtained by the respondents, which is 1.00, fall under the

application level, while the minimum mean score, which is 0.00, is obtained

under the evaluation level.

Based from the observations above, it can be concluded that the

respondents are weak in all of the cognitive levels because no level reached the

specified standard. It, therefore, follows that students are considered weak in all

the content areas covered in the test; hence, accommodations and adjustments

must be done to deal with these difficulties.

Table 5

Descriptive Statistics for Test Scores across the Six (6) Cognitive Levels

Kn

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sis

Syn

thesis

Evalu

ati

on

MEDIAN (%) 50.00 50.00 55.00 60.00 40.00 40.00

MEAN (%) 50.25 44.25 57.50 61.25 39.25 41.55

STD.DEV. (%) 13.94 14.81 15.39 0.15 19.40 20.88

MIN 0.20 0.20 0.30 0.30 0.10 0.00

MAX 0.80 0.80 0.90 1.00 0.80 0.80


IV. The Implications of the Results of the Study for Learning and Teaching

Elementary Algebra

Based from the presented data above, the study at hand revealed that the

students performed weakly in all the levels of Bloom’s cognitive domain as

signified by mean percentage ratings below the 75% standard rating. It is also

noteworthy to state that the students garnered the highest performance in the

analysis level, while they obtained the lowest statistics in the synthesis and

evaluation levels. These values are suggestive of the diversity of the students’

mastery and retention of the concepts and skills in Elementary Algebra.

The aforementioned data must be the benchmark of Mathematics

educators in teaching Elementary Algebra in such a way that the weaknesses

can be further converted into strengths. In this regard, teachers must be

sensitive, responsive and eventually, adaptive to the calls for changes and

adjustments in terms of the various facets of the curriculum and instruction.

Inability to adhere to these advocacies could lead to shallow learning; thus,

hampering us to move along and with the advancements of other fields in this

global city.

The performance of the sample population may have been caused by

some factors that could, in any way, affect, or worse, inhibit the occurrence of

life-long learning. The students’ learning styles and the teachers’ teaching style

must always be congruent with each other to suit the needs of the former.

Should there be a mismatch of styles, both parties, to ensure success in the


teaching-learning process, must conduct proper reconsiderations and

accommodation. Teachers should always know where their students are and

so, diagnosis is mandatory. This will aid them to locate the strong and weak

points of the learners and consequently, to plan learning activities, with

provisions to strengthen weaknesses and reinforce areas of high mastery.

Related literatures often state that students personally consider

Mathematics as a dreaded subject. Possessing such negative mindset, students

also hold lower levels of interest and lesser focus on the subject that can both

lead to poor performance in any math-related subjects. Such cases pose a

variety of challenges to teachers, majority of which are tests of creativity and

patience. To mention some, teachers must always be updated with the current

innovations and breakthroughs in the teaching of Mathematics and be open to

study, learn and apply them in their own classrooms. To increase interest and

attention, educators must employ motivational strategies, ranging from tangible

to intangible motivators that campaign for higher level of class performance.

Having students belonging to the 21st century period, Mathematics educators

must use student-centered tasks, explorations, discoveries and active learning

since these will also greatly help in keeping the learners engaged in the learning

process. Moreover, enrichment activities can also be designed and

implemented to the students to enhance their present learning status. If despite

creative efforts to further the instruction students still perform below the

satisfactory level, intervention programs such as remedial and tutorial programs


can be installed, where tutors can provide more drills to help students make the

skills permanent and automatic.

Other factors such as socio-cultural influences (parents, peers and

significant others) can also impede good performance. In this light, teachers

must encourage building of strong relationship with others and maintaining a

positive outlook to keep healthy and balanced emotional and social structures.

Self-help and individual accountability also counts in the pursuit of better

performance.

Should these implications be considered, Mathematics teachers start

actualizing the hope of alleviating any weaknesses; hence, welcoming a better

and highly performing Mathematics class.

V. Proposed Enrichment Activities in Enhancing the Students’ Skills in

Elementary Algebra

As stated in the implications above, one of the strategies that Algebra

teachers can do to increase active engagement and focus of the subject is

through the administration of various enrichment activities. Each activity

indicates the level of the cognitive level it targets. The researchers decided to

focus on the following topics since these areas serve as the foundation of other

Algebra skills; thus, intensifying the need to strengthen them to alleviate

difficulties in more complex lessons that require these skills. Moreover, these

are the topics, which contain skills that can highly be applied in the real world on


a daily context. The researchers further believe that the implementation of these

activities will greatly contribute to the success of instruction.

Note: The output of the students in each activity is highly dependent upon the

individual teacher. The following templates, therefore, can still be altered,

depending upon the preferences of the teachers and the students.,

1. Properties of Equalities (Remembering, Understanding and Applying

Level)

Title: Property Match

Objective:

a. Perform fundamental operations on integers: addition, subtraction,

multiplication and division;

b. State and illustrate the different properties (commutative, associative,

distributive, identity, inverse)

Materials:

For the walls (or stations): one sign for each property covered, listing the name

of the property and showing the property in symbolic notation.

For the students: each student or pair will need a list containing one numerical

example to demonstrate each property. To avoid students following each other

around the room, these lists may be prepared and cut into individual strips of

paper, each containing one example. These strips can be bundled and stapled

in advance, varying the order in each bundle so that students who have the


same property on one strip will not match up again on the next. Students should

also carry pencils to label each strip as the correct property name is found.

Procedure:

Pre- Activity

1. Set up workstations with each property sign. Then after students identify

the correct property, they would have a small number (4-6) of problems related

to that property to complete. These problems could be prepared in advance,

copied onto half-sheets of paper, and stacked at each station.

2. On each identifying sign list only the name of the property, giving no

symbolic representation. This encourages students to learn the proper

terminology for steps they take in their work. It may also help them to start

recognizing properties in more general situations, thereby increasing the

properties usefulness to them.

Activity

1. Prepare the student materials as described above. Place property signs in

visible locations around the room. Students will need to move to each sign.

2. Students may work individually, or be assigned to work in pairs. Each

student or pair should get one bundle of property strips before beginning.

3. Students should start from their desks. Then when the teacher says

“Begin”, each student finds the sign corresponding to the example on his or her

first property strip, and goes to that sign.


4. Students may compare strips when they arrive, to make sure that each

student at their sign belongs there.

5. Students may write the correct property name on the first strip. The teacher

should be prepared to mediate in case of disagreement. If an aide is in the

room, that person might circulate to verify student responses.

6. Next, the teacher can say, “OK, turn to the next strip. Ready, and move.”

The procedure repeats until each student has identified each property example.

Post Activity

Discuss which properties were difficult, which got confused with one another,

and why. Verify that all students got all of the properties labeled correctly.

These property strips may serve as a study guide, or as a testing aid.

Available at http://www.math.wichita.edu/history/Activities/algebra-act.html#irr

2. Solving First Degree Equations (Remembering, Understanding and

Applying Level)

Title: Let Us Solve Together

Objectives:

a. Introduce first-degree equations and in one variable;

b. Distinguish between expressions and equations;

http://www.math.wichita.edu/history/Activities/algebra-act.html#irr


c. Determine the solution set of first degree equations in one variable

by applying the properties of equality.

Materials:

3 X 5 cards, enough for the class, Worksheets

Procedure:

Pre- Activity

Before class, teacher makes up the 3 X 5 cards. On the back of two

cards, write the letter "A." Do the same with "B" and "C" and so on until you

have enough for each student to get one card. The purpose of this is so that

each student will be paired up with another student that has that same letter.

On one of the cards, write an equation that your level can solve such as:

2x + 5 =

3x - 18 =

x² + 5 =

On the corresponding card for that letter, write a number from 20 to 100. Mix up

the cards at random, making sure that half the kids will get an equation, and

half the kids will get a number.


Activity:

1. The teacher will give brief introduction and overview of the activity and will

discuss the rules and guidelines.

2. Students are to pair up with the person that has the same letter on the

back of their card. They put them together and solve the equation. For example,

suppose one "A" had 5x + 3 =, and the other "A" had 35, their equation would

be 5x + 3 = 35. They then solve for x.

3. Teacher then picks random students to present their problems on the

board. If there is an odd number of students, just add another "A" card and put

a number on the back of it.

4. Three people would then be grouped as "A's". They would then combine

their numbers together. In other words, using the above example, let's say you

add another "A" card and write -24 on it. Then the three "A" cards would make:

5x + 3 = 35-24.

Post- Activity

The students will be given a worksheet related to the activity

conducted that will serve as seatwork to be done individually. This is to assess

if each student have mastered the lesson based from the activity done.

Available at [email protected].

mailto:[email protected]


3. Conversions and Measurement (Applying, Analyzing, Evaluating and

Creating Level)

Title: Biggest, Strongest, Fastest

Objective:

a. Express relationships between two quantities using ratios;

b. Convert measurements from one unit to another;

c. Round off measurements; round off numbers to a given place (e.g. nearest ten, nearest tenth);

d. Solve problems involving measurement.

Materials: Biggest, Strongest, Fastest worksheet and answer key Procedure:

1. Challenge students to name which animal they believe to be the biggest,

strongest and fastest in the animal kingdom and to defend their reasoning.

Begin a brief discussion about how species have evolved such that they

have become the biggest, strongest, and fastest.

2. Read the Biggest, Strongest, Fastest. After reading the text that states

which animal is the biggest (or fastest, or longest, etc) let students guess

just how big (or how fast, or how long etc.) before reading the smaller

accompanying text that specifies the statistic that earns the animal its title.

3. Provide students with a copy of the Biggest, Strongest, Fastest worksheet.

Students work in pairs to estimate (and then record the first column) the


speed of each of the items listed. Students then rank (and record in the

second column) the items in order from slowest to fastest.

4. Prior to sharing the solutions, students as a class discuss their

estimations, ranking and defend their reasoning.

5. Provide students with the answers using the Biggest, Strongest, Fastest

answer key. Students should draw comparisons between and among the

speeds of various items on the list and express them using ratios, giving

their speeds more meaning (e.g., the ratio of the speed to a car traveling

on a freeway is approximately 1 to 1 or 1:1. this means that both objects

travel at the same rate. The ratio of a commercial airliner at cruising

altitude to the fastest official lap speed at Indy 500 is approximately 2 to 1

or 2:1. This means that the airliner travels twice as fast as the fastest Indy

car.)

6. Place students in pairs and assign each student an animal form Jenkins’s

book. Students research facts about each animal, including a description

of the animal’s habitat, characteristics of the species, unique

characteristics resulting from adaptation and evolution, food web,

possibility of extinction, and so on, and present their findings to the class.

Students present their findings as a poster, diorama, or a slideshow

presentation.

7. After the presentation, every pair is required to convert speed of all the

animals presented; to be written on the other worksheet provided by the


teacher. After converting the students will answer some worded problems

that related to the passage that requires a complete solution every item.

4. Addition and Subtraction of Decimals (Applying Level) Title: Bingo Blitz

Objectives:

a. Perform fundamental operations on integers: addition, subtraction,

multiplication, and division;

b. Review operations on decimals.

Materials:

*Bingo Cards and Answer List (directions for making are below)

*Beans (or other items to use for markers)

*Pencils (one for each student)

*Overhead projector or chalkboard

Procedure:

Pre- Activity

1. Draw a grid consisting of 25 squares. The squares need to be big enough

for the students to write decimal numbers. You can fit 4 grids on one sheet

of paper, or you can draw two grids and leave some room for students to

work out the problems.

2. Develop about 50 decimal sum and difference problems. You can find

these in workbooks and textbooks, or you can make up your own! Write

the answers on an overhead transparency. The students will copy answers

randomly on their bingo cards. Write or type the problems AND ANSWERS


on paper and cut the problems apart. Put the problems in a paper bag or

hat.

Activity

1. Pass out bingo cards and beans to each student. One handful of beans is

plenty! Make sure students have a writing utensil.

2. Put the answer list on the overhead projector or write the answers on the

chalkboard. Have students RANDOMLY write answers in squares on their

boards. Do one board at a time. You can use the same board over and

over or copy new numbers for each game.

3. Pull out a problem from the bag or hat and write it on the overhead or

chalkboard. Students will use scratch paper (or their bingo cards) to work

the problem. If the answer they get is on their card, they get to put a bean

on that square. Note: Teacher may set a time limit or have them use

mental math. These details are up to the individual teacher.

4. When a student has a bingo, have him/her read the answers and the

teacher can check for accuracy.

Post- Activity

The teacher will facilitate a class sharing where everyone is free to share

the things they learned and experienced during the activity. This will serve as

an assessment of the cognitive and affective domains in their learning. The

teacher can also give an assignment about the activity done.

Available at

http://www.lessonplanspage.com/MathDecimalAddSubBingoBlitzIdea34.htm



5. Polynomials and Algebraic Expressions (Applying Level)

Title: X Equals Objectives:

a. Simplify numerical expressions involving exponents and grouping symbols;

b. Translate verbal phrases to mathematical expressions and vice- versa;

c. Evaluate mathematical expressions for given values for the variable(s)

involved;

d. Simplify monomials using the laws on exponents.

Materials:

Board Game

Cards for the game (Word Cards, Simplify Cards, Solve Cards, Factor Cards).

Procedure:

Pre- Activity

The teacher will be the one who will make the board game and the cards

using these drawing. (It is up to the teacher on what expressions and equations

he/she will be using). Here is an example:


Activity/ Game:

The teacher will discuss and explain the rules and guidelines of the activity/

game. The class will be divided into 4 groups, which means problems will be

answered by the group.

1. Place Simplify cards on appropriate rectangle. Place Factor cards on

appropriate rectangle. Place Solve cards on appropriate rectangle. Place

Word cards on appropriate rectangle. Stack Determiner cards next to board.


Deal three Equation cards to all players and stack the remainder next to

board.

2. Each player chooses a color piece and chips. Each player rolls the dice to

see who goes first. Highest roller goes first with play continuing to the left.

Each player chooses a different corner to start on.

3. The Play On each players turn, they roll the dice and head for a category

(simplify, factor, solve, or word expressions) of their choice. Below is a list of

what happens on all the different squares:

4. Roll again - The player's turn continues.

5. Category - Draw a card from the appropriate pile and answer the question.

6. Have the other players check the answer on the answer page. If the player

gets the correct answer, they place their color chip on that category square.

The player then takes another turn. If the answer was wrong, the player's turn

ends.

7. Once a player has received a correct answer for all four categories, they try to

land on the Player's Choice Square. When they do, the other player's choose

a category for the player to answer.

8. * Number - Let "x" equal the number just landed on. Draw one Determiner

card. Substitute the "x" value into your three Equation cards. Simplify the

answers until the player finds one that works with the inequality on the

Determiner card.


9. If one works, draw a new Equation card and place the matching one at the

bottom of the pile. The player takes another turn. If no equation cards will

work, the player's turn ends.

10. The player to correctly answer all four categories and the Player's Choice

question wins the game.

6. Addition of Fractions With Unlike Denominators (Applying and Creating

Level)

Title: Pattern Block

Objectives:

a. Review simplification of and operations on fractions

b. Perform fundamental operations on integers: addition, subtraction,

multiplication and division;

Materials:

Pattern blocks and worksheets with outline

Procedure:

Pre- Activity

The teacher will create the following blocks for the discussion and the

activity. The teacher can make variety of blocks creatively following these

figures:


Triangle Parallelogram

Trapezoid Hexagon

Figure 1

These blocks will serve as a model for every problem. The following should be

considered:

*Triangle represents 1/6

*Parallelogram represents 1/3

*Trapezoid represents 1/2

*Hexagon represents 1 whole

Figure 2.


Activity

1. The teacher will present and explain the different pattern blocks shown in

the figure 1 using the following value for every block:

a. Triangle represents 1/6

b. Parallelogram represents 1/3

c. Trapezoid represents 1/2

d. Hexagon represents 1 whole

2. The teacher will show many examples by modeling some pattern blocks

formed together.

3. The teacher will discuss the rules and guidelines of the activity. Then,

he/she will distribute the pattern blocks per student.

4. The teacher will write on the board different fractions and outlines of

figures. Then, the student will imitate the shown figure by filling the outline with

the pattern blocks.

5. The class will be divided into 10 groups and will work as a group in

answering the worksheet provided by the teacher.

6. Before answering the worksheets, the teacher will display an outlined

figure (Figure 2) that will serve as their guide for the whole worksheet.


Post Activity

The teacher will give a take home activity by answering the following:

By covering figure 2 with different combinations of pattern blocks, add the

following fractions. Make a picture to show how you covered the outline.

Describe in words or pictures the method you used. To be done in a long size

bond paper and to be submitted next meeting.

a. ½ + ¼

b. 2/3 + 1/6

c. 3/12 + 1/3

d. ¾ + 1/6


CHAPTER 5

SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

This chapter contains the summary, conclusions and recommendations in

determining the strengths and weaknesses of high school students in learning

Elementary Algebra.

SUMMARY OF FINDINGS

The study at hand employed the descriptive method to determine the

strengths and weaknesses of the first year high school students, specifically I-

Joule, of Angeles City Science High School. In doing so, the researchers

drafted the test (covering only the lessons in the first two grading periods) with

respect to the basic principles in test construction and considering the

psychometric properties of a good test such as validity and item analysis.

Selected teachers then validated the test for suggestions and improvement of

test items. After the validation, the examination was administered to the

respondents. Prior to the administration, the researchers sent letters seeking

for permission and endorsement to administer the validated test. Afterwards,

the data underwent proper organization and presentation and eventually,

analysis and interpretation with the hope of attaining the set research

objectives. The following results of the study were used as the basis in

modifying and/or designing enrichment activities:


1. 12.5% of the students obtained an above average rating in their Elementary

Algebra class during the second grading period, while 42.5% obtained an

average performance rating and 45% of them obtained poor ratings;

2. The test developed is highly acceptable as evidenced by high ratings, both

in the over-all difficulty and discrimination index;

3. The students obtained the low mean percentage ratings ranging from

39.25% to 61.25% only, in all of the six (6) levels of the cognitive domain.

4. The highest mean score obtained by the respondents, which is 1.00, fall

under the application level, while the minimum mean score, which is 0.00, is

obtained under the evaluation level.

CONCLUSIONS

Based from the preceding conclusions, the researchers came up with

following conclusions:

1. Majority of the respondents obtained below average ratings for the second

grading period in Elementary Algebra.

2. The students possess varying abilities and mastery of the content areas as

evidenced by the assorted mean scores of each student across each

cognitive level.


3. The selected first year students are weak in all the cognitive levels and all

the content areas included in the coverage of the test;

4. Six enrichment activities in Elementary Algebra are designed to enhance the

present learning status of the students in the subject.

RECOMMENDATIONS

The subsequent recommendations are suggested based fro the above-

mentioned conclusions:

1. To further the assessment of the strengths and weaknesses of high school

students in Elementary Algebra, including the topics in the third and the

fourth grading periods can widen the scope of the test developed.

2. The test developed in this study can be administered as a diagnostic or an

achievement test.

3. Educators should consider the results of the assessment during instructional

planning to suit and adjust to the needs of the students.

4. The results of the assessment can be communicated to the students as a

feedback to their performance in the subject;

5. The proposed enrichment activities designed should be used and

implemented by Elementary Algebra teachers to enhance the present status

of the learners;


BIBLIOGRAPHY


BIBLIOGRAPHY

A. BOOKS

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mathematics. USA: McGraw- Hill Book Company.

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Leigh, Elyssebeth& Kinder, Jeff (1999).Learning through fun and games.

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Malaborbor, Pearl et.al.(2002). Elementary algebra. Malabon City: Diamond

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Nivera, Gladys. C. (2003). Elementary algebra: Explorations and applications.

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Oxford University.(2005). Oxford Advanced Learner’s Dictionary. USA: Oxford

University.

Peng, Yee Lee (2006).Teaching secondary school mathematics: A resource

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Reganit, Arnulfo Aaron et.al.(2004). Measurement and evaluation in teaching

and learning. Valenzuela City: Mutya Publishing House.

Sharan, Ram. & Manju, Sharma. (2006). Teaching of mathematics. New Delhi:

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Torralba, Antonio N. (1998). The joys of teaching. Quezon City: UNI-

GRAPHICS Printing Press.

Tucker, Kate (2005). Mathematics through play in the early years. London:

Paul Chapman Publishing A SAGE Publications Company.

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pm).

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Gibson, Jason. (2006). How to Teach Algebra?, Available at

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December 2010, 6:20pm).

Huetinck, Linda & Munshin, Sara N. (2008). Teaching mathematics for the 21st

century. USA: Pearson Inc.

Kobizsyn, Tom & Borich, Dave (2010, October). Educational Testing and

Measurement.Available at http://www.shvoong.com/social-

sciences/education/1635953-educational-testing-measurement/ (23

December, 2010, 5: 45 pm).

Kortering, Larry J. et. al. (2005, June).Improving performance in high school

algebra: what students with learning disabilities are saying.Learning

Disability Quarterly.Available at http://www.highbeam.com/doc/1G1-

135126449.html (23 December, 2010, 5:30pm).

Matthews, Michael S. & Farmer, Jennie S. (2008).Factors Affecting the Algebra

I Achievement of Academically Talented Learners. Journal of Advanced

Academics, v19 n3 p. 472-501. Available at

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&_&ERICExtSearch_SearchValue_0=EJ810758&ERICExtSearch_Searc

hType_0=no&accno=EJ810758 (23 December, 2010, 6: 23pm).

Maushard Mary (2009, August). Calculating the best way for teaching

algebra.Center for Social Organization of Schools.Available

athttp://gazette.jhu.edu/2009/08/17/calculating-the-best-way-for-

teaching-algebra/ (29 December, 2010, 6:45pm).

Poon, Kin-Keung & Leung Chi-Keung (2009, November).Pilot study on algebra

learning among junior secondary students. International Journal of

Mathematical Education in Science and Technology V

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b=issueslist~branches=41 - v4141, Issue 1 p. 49 – 62. Available at

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http://www.highbeam.com/doc/1G1-135126449.html

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http://www.eric.ed.gov/ERICWebPortal/search/detailmini.jsp?_nfpb=true&_&ERICExtSearch_SearchValue_0=EJ810758&ERICExtSearch_SearchType_0=no&accno=EJ810758



http://gazette.jhu.edu/author/marymaushard/

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http://gazette.jhu.edu/2009/08/17/calculating-the-best-way-for-teaching-algebra/

http://gazette.jhu.edu/2009/08/17/calculating-the-best-way-for-teaching-algebra/

http://www.informaworld.com/smpp/title~db=all~content=t713736815~tab=issueslist~branches=41#v41

http://www.informaworld.com/smpp/title~db=all~content=g918005250


http://www.informaworld.com/smpp/content~db=all~content=a91657491

1 (29 December, 2010, 6:27pm).

Roberts, William (2010). Productive Strategies for Raising Student

Achievement in Algebra.National Association Secondary School

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(23 December, 2010, 5:40pm).

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December, 2010, 7:15 pm).

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with other content areas. USA: Pearson Inc.

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Learning Difficulties: An Investigation of an Explicit Instruction

Model.Learning Disabilities: Research & Practice, v18 n2 p121-31.

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&_&ERICExtSearch_SearchValue_0=EJ669603&ERICExtSearch_Searc

hType_0=no&accno=EJ669603 (29 December, 2010, 7:25pm).

C. UNPUBLISHED THESES/DISSERTATIONS

Dimal, Divina. V. “Making Selected Topics In High School Algebra More

Appealing And Interesting Through Simulations Games.” Unpublished

Master’s Thesis, Angeles University Foundation, Angeles City,

Pampanga, May 2007.



http://bul.sagepub.com/content/92/4/305.abstract

http://www.annasierpinska.wkrib.com/pdf/HongYueVanier111108.pdf





Mesina, Luzon G. “Difficulties Of Students In Learning College Algebra:

Implications To Classroom Instructions,” Unpublished Master’s Thesis,

Angeles University Foundation, Angles City, Pampanga, September,

2004.

Ruybibar, Rodrigo “A Proposed Instructional Manual for Integrated

Mathematics.” Unpublished Master’s Thesis. Angeles University

Foundation, Angeles City, Pampanga, May 2001.

Calara, Rebecca C. &Garcia,Maricel M. “Factors Affecting Mathematical

Comprehension on Algebra of the Fourth Year High School Students of

Francisco G. Nepomuceno Memorial High School.” Unpublished

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Pampanga, October 2003.

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htm (April 4, 2011, 1:00pm)

Carr, Stephen. (1998). Let us solve together. Available at [email protected]

(April 3, 2011, 9: 30am).

Isaac, Blake. Cardboard Cognition. Available at

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2011, 1:15pm).

.Kiss, Laurie. (2000). Property match. Available at at

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mailto:[email protected]

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(29 December, 2010, 6:20pm).

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http://www.brookes.ac.uk/schools/education/rescon/cpdgifted/docs/secondarylaunchpads/8enrichment.pdf



CURRICULUM

VITAE


LOVELY GACETA MERCADO Block 2 Lot 3 Phase 1 Sapang Biabas Resettlement, Mabalacat, Pampanga, 2010 0935-248-6545 [email protected]

PERSONAL PROFILE: Age: 18 years old Date of Birth: October 1, 1992 Place of Birth: Mabalacat, Pampanga Gender: Female ` Citizenship: Single Height: 4’11’’ Weight 100 lbs. Name of Father: Rodolfo N. Mercado (deceased) Name of Mother Flordeliza A. Gaceta

EDUCATION: Tertiary:

Angeles University Foundation Angeles City Bachelor of Secondary Education (Major in Mathematics) 2008-present

Secondary:

Camachiles Resettlement High School Camachiles, Mabalacat, Pampanga 2004-2008

Elementary:

Sapang Biabas Resettlement Elementary School Sapang Biabas Resettlement, Mabalacat, Pampanga 1998-2004


SEMINARS ATTENDED:

Discovering the Joys of Teaching

Luzviminda F. Tantoco, Ed.D

University of Assumption, CSFP

July 16, 2010

Research Made Easy

Ms. Madonna Villanueva

Main Library, AUF, Angeles City

December 02, 2010

Early Childhood Literacy through Story Telling

Prof. Shirley Equipado

AUF, Professional School 517

January 26, 2011

Instructional Design Using UBD

Dr. Marilyn Balagtas

Professional School 308, AUF, Angeles City

February 05, 2011

Current Thrusts in Basic Education

Dr. Yolanda Quijano,

St. Cecilia Auditorium, AUF, Angeles City

February 09, 2011

Moving Forward with Backward Design Using UBd

Mr. John David M. Ong

IT- Building 1st Floor, AUF, Angeles City

February 16, 2011

Ang Sining ng Pagtatanghal sa Entablado: Implikasyon sa Pagtuturo

Prof. Patrocinio V. Villafuerte


March 02, 2011

Making Sense of Web. 2.0 Tools Leveraging Social Media in

Teaching/Learning

Prof. Amelia T. Buan



March 26, 2011

What Every Teacher should Know about Special Education

Prof. Rolando Mina Mamaat, Jr.


April 02, 2011


JOSEL VASQUEZ OCAMPO

1943 Kuliat St. Lourdes Sur Angeles City Pampanga

0927-651-0042

[email protected]

PERSONAL PROFILE:

Age: 19 years old Date of Birth: December 11, 1991 Place of Birth: Angeles City, Pampanga Gender: Male ` Citizenship: Single Height: 5’7” Weight 143 lbs. Name of Father: Jose P. Ocampo

Name of Mother Elizabeth M. Vasquez

EDUCATION:

Tertiary:

Angeles University Foundation

Angeles City, Pampanga

S.Y 2008-Present

Secondary:

Angeles City National Trade School

Fil-Am Friendship Hi-way, Angeles City, Pampanga

S.Y 2004-2008

Elementary:

Sto. Rosario Elementary School

Miranda St. Sto. Rosario, Angeles City, Pampanga

S.Y 1998-2004


SEMINARS ATTENDED:




July 16, 2010

Research Made Easy



December 02, 2010




January 26, 2011




February 05, 2011




February 09, 2011




February 16, 2011




March 02, 2011


Teaching/Learning




March 26, 2011




April 02, 2011


JEMIMA DE GUZMAN NICASIO 12980 Duhat St. dau Homesite, Mabalcat, Pampangan 0905-947-9249\ [email protected]

PERSONAL PROFILE: Age: 19 years old Date of Birth: September 6, 1991 Place of Birth: Mabalacat, Pampanga Gender: Female ` Citizenship: Single Height: 4’11’’ Weight 80 lbs. Name of Father: Reynaldo M. Nicasio Name of Mother Adeliana de Guzman

EDUCATION: Tertiary:

Angeles University Foundation Angeles City Bachelor of Secondary Education (Major in Mathematics) 2008-present

Secondary:

Mabalacat National High School Mabalacat, Pampanga 2004-2008

Elementary:

Dau Homesite Elementary School Dau, Mabalacat, Pampanga 1998-2004


SEMINARS ATTENDED:




July 16, 2010

Research Made Easy



December 02, 2010




January 26, 2011




February 05, 2011




February 09, 2011




February 16, 2011




March 02, 2011


Teaching/Learning




March 26, 2011




April 02, 2011


APPENDICES


Angeles University Foundation Angeles City

COLLEGE OF EDUCATION Center of Excellence in Teacher Education

Ms. Amor C. Martin Director, University Library Angeles University Foundation

Dear Ma’am:

Greetings of Peace!

We, the undersigned, are currently conducting an action research in Mathematics entitled “The Strengths and Weaknesses of High School Students in Elementary Algebra”. At this point, we are at the process of completing chapters one to three and we appreciate you and your staff on the Circulations and Filipiñana Section for assisting us in finding related references for our study.

In this light, we are again asking your assistance through seeking a permission from your good office to allow us to borrow the following theses that we consider of high significance to our research from the Graduate School Library:

1. A Proposed Instructional Material For Integrated Mathematics, Ruybibar, Rodrigo 2001.

2. Difficulties Of Students In Teaching College Algebra, Mesina, Luzon G. 2004.

3. Making Selected Topics In High School Algebra More Appealing And Interesting Through Simulation Games, Dimal, Divira V. 2007.

May this merit the most favorable response from your end. Your permission will be a very big help to the success of our endeavor. Thank you very much and God bless!

Respectfully yours,

(SGD.) Lovely G. Mercado

(SGD.) Jemima D. Nicasio (SGD.) Josel V. Ocampo BSEd Mathematics 3

Noted by:

(SGD.) Filipinas L. Bognot, Ph.D Teacher, Action Research in Mathematics

(SGD.) Angelita D. Romero, Ph.D Dean of the College of Education


Angeles University Foundation Angeles City

COLLEGE OF EDUCATION Center of Excellence in Teacher Education

March 14, 2011

Mrs. Esperanza S. Malang Principal Angeles City Science High School Dear Madam: We, the undersigned, are currently enrolled in the course Action Research in Mathematics (MATH20) and are working on the undergraduate study entitled “The Strengths and Weaknesses of High School Students in Learning Algebra: Basis for Enrichment Activities”. As stipulated in the title, our study aims to determine the strengths and weaknesses of first year students in your school and their implications to Mathematics Education. Based from the results, we also hope to administer enrichment activities to these students to enrich their learning. In this regard, we are asking permission from you good office to allow us to administer a test and enrichment activities to selected first year students of your school as a means for data collection. Rest assured that the data that we will obtain from these administrations will be treated with utmost confidentiality and will solely be used for academic purposes. Your permission will be of great help to this academic endeavor. May this merit the most favorable response from your end. Thank you and God bless. Sincerely yours, (SGD.) Lovely G. Mercado (SGD.) Jemima D. Nicasio (SGD.) Josel V. Ocampo BSEd Mathematics 3 Noted by: (SGD.) Filipinas L. Bognot, Ph.D Professor, MATH20


March 28, 2011. The researchers administered the 60-item test to the

I-Joule Students of Angeles City Science High School

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