Institute of Teacher Education Chess Piece and Numeral Dice

MABALACAT CITY COLLEGE
THE USE OF CHESS PIECE AND NUMERAL DICE IN

SOLVING LINEAR EQUATION WITH ONE VARIABLE
An Action Research Presented to the
Faculty of Teacher Education
Mabalacat City College
Mabalacat City, Pampanga
From the Institute of Teacher Education
Major in Mathematics
by:
Garcia, Artlie A.
Sibal, Eric John M.
Institute of Teacher Education Chess Piece and Numeral Dice

APPROVAL SHEET
This thesis entitled “THE USE OF CHESS PIECE AND NUMERAL DICE IN
SOLVING LINEAR EQUATION WITH ONE VARIABLE” prepared and
submitted by Artlie A. Garcia and Eric John M. Sibal has been examined and
recommended for Oral Examination.
ROGER L NUQUI, Ed.D.

Thesis advisory/committee
-------------------------------------------------------------------------------------------------------
ENGR RENALYN N. GACUSAN, Ed.D.

Chairperson
CONRAD M. BURKLEY, MAEd. IRENE CHRISTY M. BACOLOD, LPT

Member Member
Approval in partial fulfillment of the requirements for the degree of Bachelor of

Secondary Education Major in Mathematics.
Date:__________________________ CONRAD M. BURKLEY, MAEd.

Field of study head, BSEd
Date:__________________________ RENALYN N. GACUSAN, Ed. D.

Dean

Acknowledgement
We would like to pay special recognition, gratitude and overwhelming appreciation to the
persons below who assisted us at every point and made our research successful to cherish
our goal:
To their parents, who supported and helped them financially, and for allowing the
researcher to stay at their home for research purposes.
To Mr. Roger l. Nuqui, Ed. D. for guiding them all throughout. As their Research
Adviser.
To the Principal of DALIS Mrs. Carmela Cabrera for signing the request letters
and allowing them to gathered data in Dona Asuncion Lee Integrated School.
To the panel members, for guiding them in their study.
And to the students as their research respondents, who allow them to ask some
questions to support their study.

Dedication
This study is dedicated to the student who undergo linear equation in one variable; to the
teachers’ friends and families who believed in them that they can finished their research
with full of encouragement, support, and love. And specially to God who is always
helping them in times of discouragement, failures, and hopelessness and He gave them
strength, hope, joy, wisdom, knowledge, understanding and encouragement. Truly in
Him, nothing is hard for Him to do. “Never worry about anything. But in every situation
let God know what you need in prayers and requests while giving thanks.” – Philippians
4:6 (GW)

Table of Content Page
Title page .................................................................................................................... i
Approval Sheet ........................................................................................................... ii
Acknowledgement ..................................................................................................... iii
Dedication .................................................................................................................. iv
Table of Content ..........................................................................................................v
Table .......................................................................................................................... vi
Figures ...................................................................................................................... vii
Abstract .....................................................................................................................viii
Chapter 1. The Problem and Review of Related Literature
Introduction ................................................................................................................. 1
Review of Related Literature....................................................................................... 4
Synthesis ......................................................................................................................10
Conceptual/Theoretical Framework ........................................................................... 11
Hypothesis/Assumptions ............................................................................................. 13
Significance of the Study ............................................................................................. 14
Scope and Delimitation of the Study ........................................................................... 14
Definition of Terms ..................................................................................................... 15
Chapter 2. METHOD
Research Design ........................................................................................................... 24
Participants ................................................................................................................... 24
Instrument .................................................................................................................... 24
Data Collection Procedure ........................................................................................... 25
Chapter 3. RESULT AND DISCUSSION

Results .......................................................................................................................... 27
Discussion .................................................................................................................... 27
Statistical Results.......................................................................................................... 27
Chapter 4. SUMMARY, CONCLUSION AND RECOMMENDATION
Summary ...................................................................................................................... 28
Conclusion ................................................................................................................... 28
Recommendation ......................................................................................................... 28
References ................................................................................................................. 31
Appendices ................................................................................................................. 37
Appendix A. Letter for the School Principal................................................................40
Appendix B. The value of Chess Piece…………………….........................................41
Appendix B-1. How to use Chess piece and number dice……………………………42
Appendix C. Lesson Plan (Experimental Group)........................................................ 43
Appendix C-1. Lesson Plan (Controlled Group).......................................................... 53
Appendix D. Instrument...............................................................................................54
Appendix E. Summary of Data.....................................................................................55
Appendix E-1. Summary of Data.................................................................................55
Appendix F. Mean Scores of Pre-test...........................................................................54
Appendix F-1. Mean Scores of Post-test......................................................................54
Appendix I. Documentation.........................................................................................54

Tables
Mean Scores of the Pre-test in the Controlled and Experimental Group………..… 25
Mean Scores of the Post-test in the Controlled and experimental Group…………. 25
The Pre-tests of the Controlled and Experimental Group…………………………. 26
The Post-tests of the Controlled and Experimental Group……………………….... 26
Summary of Data (Controlled Group)……………………………………………... 42
Summary of Data (Experimental Group)…………………………………………... 43

Figures
Conceptual Framework…………………………………………………………...9
Theoretical Framework…………………………………………………………..20

Abstract
This study was quantitative research. It employed a quasi-experimental method where
two groups of the students were used as participants. Both groups were given pretest
prior the discussion about linear equation. Post-test was then administered after the
instruction using the conventional method (control group) and the use of real object.
(Experimental group). Mean and t-test were utilized to analyze and interpret the data.
This study found out that the participants under both methods showed poor scores on the
pretest; moreover, both groups showed improving scores in the post-test. The study
revealed that the students performed better in using real object than the conventional
method.
Keywords: Experimental Method, traditional Method

Chapter 1
The Problem and Review of Related Literature
Introduction
Each learner has his/her own individual differences. These include difference in
terms of intellectual and emotional development, needs, interests and process of learning.
It depends on his/her ability to adjust in a learning environment which can help in molding
one’s uniqueness (Kolb, 1984). There are also differences present in an individual from
birth such as age, socioeconomic background and past experiences. One of the most
essential goals of education is to provide holistic learning to students enhancing his/her full
potential and cater individual difference. Teachers play an essential role in the learning
process. As an instrument agent, teachers should be able to explore appropriate techniques
in addressing students’ needs. However, as a student age, the level of knowledge tends to
increase which assumes that learners are capable of grasping information easily without
using various teaching strategies (Staudinger et al., 2003).
Students in the high school are considered a borderline of adolescence. During this
stage, learners are expected to have higher cognitive level in preparation for the senior high
school . Through that, teachers have the tendency to apply teaching strategies which are
commonly applied in Higher Education Institution. Several studies have proven that
diverse teaching approach enables effective learning of the students. One of the strategies

that commonly employed to students is experiential learning. Mathematics is a subject
which contains abstract information because of that teachers are challenged on how to teach
the subject. Traditional method of teaching using Math textbooks provides examples
without enriching experiences in solving problems.
Effective teaching strategies enhance students’ mastery of the subject and
comprehension. Through this, learners are capable of using constructive reasoning and
applying mathematics in real-life. One of the branches of Mathematics relating real-life
application is linear Equation. Students’ ability to decide or predict a certain phenomenon
is an example of applying Linear equation in real-life situations. Integration of real-life
experiences in teaching Linear equation is an example experiential learning. The purpose
of this study is to determine the performance of the students in Linear equation through the
use of experiential learning. According to an education professor, Dr. Jean Shaw (2009),
the use of concrete examples is efficient in education because it activates various senses,
represents ideas in more than one way, promotes communication among students, and
increases the confidence level of the students, leading to lessened confusion and deepened
understanding.
Furthermore, concrete examples help certain group of students including the
students who hate math and doesn’t have interest in numbers. Based on the learning theory
of Jean Piaget, students are active learners who master concepts by progressing through
three levels of knowledge: concrete, pictorial, and abstract. The use of concrete examples
in probability enables students to explore concepts at first and deepen the level of
understanding. Example is chess piece with different value and numeral dice. When

students manipulate objects, they are taking the necessary first steps toward building
understanding and internalizing math processes and procedures. For example, when
learning addition of probability, students can use actual cards to visualize the answer. After
practicing with these, they can progress to finding product for probability problems. Over
time, students will devise strategies and apply the rule of multiplication in probability
(O’donnell, 2008)
Several studies have proven that the use of various senses and physical action can
increase students’ comprehension. Cooper (2011) stated that the concrete nature of
manipulatives typically requires users to exert physical actions. McNeil and Jarvin (2010)
noted that the incorporation of physical action has been shown to enhance memory and
understanding. Manipulatives allow concrete, hands-on exploration and representation of
mathematical concepts (Rosen & Hoffman, 2009). Abstract ideas such as mathematical
concepts can be hard to grasp. Moreover, human memory is designed to remember concrete
information better than abstract information. Ruzic and O’Connell (2009) found that
long-term use of concrete examples has a positive effect on student achievement by
allowing students to use concrete objects to observe, model, and internalize abstract
concepts. To really nail down an abstract idea, the need to solidify it in a student’s mind
is essential. It can be done by using specific and concrete examples (Weinstein & Smith,
2010).

Review of Related Literature
Foreign Literature
According to Fletcher (2009), various teaching methods are used in teaching
mathematical concepts to varying degrees of success. These methods are ‘transmission’
and ‘interactive’ approaches, and research has shown ‘interactive’ to be more effective
than the ‘transmission’ approach. In the transmission approach which is also known as
traditional teaching method or teacher centered instruction, the teacher acts as a reserve
of knowledge. The teacher who sees himself as the sole supplier of knowledge takes
control over almost every activity in the teaching and learning process. His or her duty is
to transmit or explain facts and procedures to learners. Learners are only asked to check if
they are following the taught procedures. Such approach creates boredom in class,
encourages passive attitude among learners and make them feel they have nothing to
contribute (Fletcher, 2009). This method of teaching is also called non-participatory
teaching method because students do not participate in the lesson. Lesson is however
conducted through explicit teacher explanation through lectures and teacher-led
demonstrations.
John van de Walle and his colleagues (2013) define a mathematical tool as, “any
object, picture, or drawing that represents a concept or onto which the relationship for
that concept can be imposed. Concrete examples are physical objects that students and
teachers can use to illustrate and discover mathematical concepts, whether made
specifically for mathematics (e.g., cards, dice, marbles, wheel) or for other
purposes.”.More recently, virtual manipulative tools are available for use in the

classroom as well; these are treated in this document as a tool for teacher modeling
and demonstration.In addition, research on multiple intelligences and students’ different
learning styles supports the use of manipulatives or concrete examples (Gardner, 1997,
2002; Marzano, 2010). In order to cater various learning styles, concrete example is an
effective instrument suited for kinesthetic and visual learners (Sundstorm, 2012).
Mathematical manipulative is a tool allowing students use their senses such as touching
and playing the objects. This method used in teaching an abstract subject transforming it
to a real representation of mathematical concept. Mathematics concrete manipulatives for
visual learners can include flash cards or color wheel that allow students to gather a
clearer understanding of the mathematics problems (Sundstorm, 2012).
Johnson (2008) reported findings that suggest that when applied appropriately, the
long-term use of manipulative appears to increase mathematics achievement and
improve student attitudes toward mathematics. The utilization of manipulative materials
helps students understand mathematical concepts and processes, increases thinking
flexibility, provides tools for problem-solving, and can reduce math anxiety for some
students. Teachers using manipulative must intervene frequently to ensure a focus on the
underlying mathematical ideas, must account for the “contextual distance” between the
manipulative being used and the concept being taught, and take care not to overestimate
the instructional impact of their use.
Sabean and Bavaria (2005) have synthesized a list of the most significant
principles related to mathematics teaching and learning. This list includes the
expectations that teachers know what students need to learn based on what they know,
teachers ask questions focused on developing conceptual understanding, experiences and
prior knowledge provide the basis for learning mathematics with understanding, students

provide written justification for problem solving strategies, problem based activities
focus on concepts and skills, and that the mathematics curriculum emphasizes conceptual
understanding.
Moyer (2012) states that some teachers use manipulatives in an effort to reform
their teaching of mathematics without reflecting on how the use of representations may
change their own mathematics instruction.
Clements (2009) calls this type of deep understanding “Integrated Concrete”
knowledge. The effective use of manipulative can help students connect ideas and
integrate their knowledge so that they gain a deep understanding of mathematical
concepts.
(Bavaria 2011) The role of discovery and practice and the use of concrete
materials are two additional topics that must be considered when developing a program
directed at improving mathematics achievement. Examined research which suggested that
such a program must be balanced between the practice of skills and methods previously
learned and new concept discovery. This discovery of new concepts, they suggest,
facilitates a deeper understanding of mathematical connections.
Manipulatives are concrete learning materials that allow students to comprehend
abstract concepts through concretizing them (Boggan, Harper, & Whitmire, 2010; Cope,
2015; Hartshorn & Boren, 1990; Laski, Jor’dan, Daoust, & Murray, 2015; McClung,
1998; Moyer, 2001; Ojose & Sexton, 2009; White, 2012), thus help them to establish a
relation between the manipulatives and abstract mathematical concepts by offering
concrete experiences (Holmes, 2013) and eventually, provide long-term permanence of
mathematical skills (Cass, Cates, Smith, & Jackson, 2005).
For these reasons, the idea of concrete examples in teaching linear equation was

conceived, find out what concrete examples are and how they are used in an educational
setting. In the aspect of education, concrete examples in linear equation are defined as
tangible materials used such as chess piece and numeral dice. Which engage students
using their senses. It is similar to a manipulative that is created to utilize motor skills in
understanding abstract concepts particularly in Mathematics (“Manipulative”, 2009).
When students manipulate objects, they are taking the necessary first
steps toward building understanding and internalizing math processes and procedures.
For example, when learning linear equatiuon in one variable, students can use actual
chess piece and numeral dice to visualize the answer. After practicing with these, they
can progress to finding product for linear equation problems. Over time, students will
devise strategies and apply the properties of addition in Linear equation (O’donnell,
2008)
In fact, research shows that using concrete examples can contribute to the
development of well-grounded, interconnected understandings of mathematical ideas.
Students can easily remember and explain the process of solving through the use concrete
examples in solving a given Linear equation problems (Stein, 2008) and according to
Bruner(1996), students comprehend more on a concrete model rather than a symbolic
model. Similarly, the findings of Goracke (2009) supports Bruner’s theory as learners
failed a symbolic algebra assessment while those who use manipulatives yield to a score
of 100%.Several studies have proven that the use of various senses and physical action
can increase students’ comprehension. Cooper (2011) stated that the concrete nature of
manipulatives typically requires users to exert physical actions. McNeil and Jarvin (2010)
noted that the incorporation of physical action has been shown to enhance memory and
understanding. Manipulatives allow concrete, hands-on exploration and representation of

mathematical concepts (Rosen & Hoffman, 2009). Abstract ideas such as mathematical
concepts can be hard to grasp. Moreover, human memory is designed to remember
concrete information better than abstract information. Ruzic and O’Connell (2009) found
that long-term use of concrete examples has a positive effect on student achievement by
allowing students to use concrete objects to observe, model, and internalize abstract
concepts. To really nail down an abstract idea, the need to solidify it in a student’s mind
is essential. It can be done by using specific and concrete examples (Weinstein & Smith,
2010).
This implies that pretest results are expected to be low due to student’s lack of retention
in Mathematics. The result of this study corroborates with the findings of Cluett (2009)
where the students’ pretest results in mathematics scored below 40%.
As I conducted previous research on finding a solution to increasing students’
understanding of mathematics, I found that manipulatives were proven to assist in
helping students eliminate their frustrations and create enjoyment in learning
mathematics. Teachers are constantly looking for ways to improve their teaching and
help students understand Mathematics. Based on research from several countries,
manipulative materials in teaching mathematics to students hold the promise that
manipulatives will help students understand the material being taught (Heddens, 2007).
Local Literature
(Florence 2012) argued that mathematics manipulatives can help engage students
for a longer period of time by helping them stay focused on particular tasks. She believes
that lecture-based teaching can often seem boring but that concrete manipulatives
allowed students to be actively involved in learning.

(Razon 2010) found that manipulatives benefit the learning and teaching of
mathematics. This research also found that the use of mathematics manipulatives links
strongly with concept formation in student learning. ConcreteManipulatives are able to
facilitate the creation of a learning environment that encourages engagement and enables
understanding.
Smith (2009) defines manipulatives as “physical objects that are used as teaching
tool to engage students in hand-on learning of mathematics”. Thus manipulatives
are materials from our own environment that learners can use to learn or form mathematical
concepts. In other word, any material or object that helps learner to understand
mathematics. Such materials help to reduce the abstract nature of mathematics as perceived
my many students.
Synthesis
This study is about improving student’s performance in linear equation using chess
piece and numeral dice. To know what will be more effective chess piece and numeral dice
that needs to be use in teaching linear equation that can help students improve their
academic performance. The purpose of this study is to show the difference between the
control group and experimental group for the learning progress of the students and the
relation of this study on the researches mentioned above is we all want to improve the
academic performance of a student by using chess piece and numeral dice in solving linear
equation.
Conceptual Framework
The problem for educators is to figure out how to make courses such as math enjoyable
and make it easy to understand, and this is where the using of chess piece and numeral

dice in teaching linear equation may be effective. The goal of using chess piece and
numeral dice is to positively change how a subject is taught, allow students to learn in
new ways, and make the learning experience both interesting and exciting. The dynamics
of using chess piece and numeral dice in linear equation allow for many different actions
by the students. While a student may excel in one learning style more than another, it is
still advantageous to the student to experience many different styles of learning
throughout his or her educational development. Students can play educational games
using concrete examples often develop an increased motivation to continue playing and
learning. To summarize, using chess piece and numeral dice in linear equation produces a
state of flow which increases motivation and supports the learning process. Thus, the goal
of using chess piece and numeral dice is to encourage students to complete tasks and
solve problems as well as develop the motivation to continue using concrete examples
through experiential learning to gain further knowledge that’s why both control Group
and experimental group undergone Pre-test and Post test to get the expected result both
control and experimental group in Pre-test are expected to have low scores, while in
experimental group in Post-test is expected to have a highest score compared to the
control group.

Control
Group PERFORMANCE
WITH
Pre test Post test LINEAR

EQUATION
WITH ONE
VARIABLE
Experimental
Group
Paradigm of the Study
The redesign conceptual framework was conceptualized and finalized by one of the
panelist, Prof. Conrad M. buerkley to better understand the flow and the objectives
of the study.
Theoretical Framework
In 1966 another important person named Jerome Bruner where seen the
importance of hands on learning or using manipulatives in the learning process. In his
constructivist theory he stated that learning is an active process in which learners
construct new ideas or concepts based upon their past knowledge. The Jerome Bruner’s
Theory states that children understand and remember concepts that they develop through
their interaction with the environment. This has influenced education by allowing it to be
a hands on learning environment.
Piaget suggests that students pass through four stages of intellectual development

(Cope, 2015; Duchesne & McMaugh, 2016; Ojose, 2008). While age is specified for each
stage, this can vary depending on the individual. The concrete operations stage (7 -12
years), has particular relevance, as this is the stage in which students “utilize their senses
in order to know” (Ojose, 2008, p. 27). At this stage, Piaget suggests students learn most
effectively through multiple representations and hands-on experiences with concrete
materials (Kontas, 2016; Ojose, 2008). As Cope (2015) notes, when students progress to
the formal operations stage (12 years onwards) their need for concrete experiences
“diminishes but never ceases” (p. 14). This implies that manipulatives may hold value in
the lower secondary classroom, a time when students are usually making the transition
from the concrete operations, to the formal operations stage.
Dienes (1960) proposed that learners whose mathematical understandings were
firmly gounded in manipulatives experiences would be more likely to make connections
between the world in which they live and the abstact world of mathematics.
The use of manipulatives also has a theoretical basis in Gardner’s theory of
multiple intelligences. This theory proposes that there are at least eight separate domains
of intelligences that students may work best or prefer learning from (Duchesne &
McMaugh, 2016). For example, transmission teaching of mathematics allows auditory
learners to gain the most from a lesson. In contrast, the use of manipulatives brings in
elements of auditory, visual, tactile and kinesthetic, allowing a wider range of learning
styles to be reached (Kontas, 2016; Witzel, 2005).
Statement of the Problem
This action research generally aims to identify the improving student’s
performance in linear equation using chess piece and numeral dice at Santos ventura

national High School in the year 2018-2019.
Specifically, it will seek answers to the following:
1. How may the pretest scores of the participants in the control and experimental group
be described?
2. How may the Post test of the participants in the control and experimental group
be described?
3. Is there a significant difference between the Pretest and in Post-Test
scores of the control and experimental groups?
4. What manipulative may be proposed for solving linear equation with one variable?
Statement of Hypothesis
Null Hypothesis
1. There is no significant difference between the pretest scores of control and
experimental group, and
2. There is no significant difference between the post-test scores of control and
experimental group.
Alternative Hypothesis
1. There is significant difference between the pretest scores of control and experimental
Group, and
2. There is significant difference between the post-test of control and experimental
Group.
Scope and Delimitation

The study was limited to the level of awareness of 30 Grade 7 students of
Dona Asuncion Lee Integrated School in the second semester of academic year 2018-
2019. The Researcher focused on the control group and experimental group of Grade 7
students towards linear equation with one variable. The researchers determined the level
of awareness of the participants on the word linear equation and will determine the
students’ performance in linear equation using chess piece and numeral dice. It also aims
to enhance the students’ skills and mental abilities and deal with the real-life problems
that they will encounter.
Significance of the Study
This concept paper is beneficial to the following:
To the school administrators: Should implement the use of chess piece and
numeral dice in teaching and learning linear equation as an effective materials in learning
and teaching mathematics .
To the teachers of the school: are encouraged to chess piece and the lower grade
level in teaching mathematics for retention of the basic lessons in probability to the
students.
To the students: are encouraged to participate actively in the discussion and
activities given by the teacher,
To future researchers: To use the gathered information as a guide by the next
researcher for their current research.

Definition of Terms
Chess piece (Conceptual) – any of 16 white and 16 black pieces used in playing the game
of chess.
(Operational) - 16 white and 16 black pieces used white piece for positive
and black piece for negative.
Controlled (Conceptual) A controlled is one which the researcher holds constant
(controls) during an experiment. It is also known as a constant variable or
simply as a "control".
- (Operational) The teacher holds complete control of the student and it is
the traditional way of teaching.

Experiential (Conceptual) involving or based on experience and observation.
(Operational) based on past experiences and by observation the scenario.
Experiential Learning (Conceptual) is the process of learning through experience, and
is more specifically defined as "learning through reflection on doing" (Wikipedia)
(Operational) is the process of learning by doing, discovering by you or within
the group.
Experimental Group (Conceptual)-

(Operational) – will receive treatment and they will be using Chess piece
and numeral dice.
Numeral Dice (Conceptual) - a small cube with each side having a different number of
spots on it, ranging from one to six, thrown and used in gambling and other games
involving chance.
(Operational) a solid cube that has a one to six number that is using for
games.
Real Object/s (Conceptual) - A collection of points which actually serves as a source of
light rays in an optical system. (Operational) a things or an object that is tangible.
CHAPTER II
METHODOLOGY
Research Design
The study used the experimental research design; it is a design that used to
estimate the casual impact of an intervention on its target population (Dinardo, 2008) the
study will be focused only in Quantitative methods to gather the needed data for the
study.
Participants
The researcher employs the purposive sampling technique in choosing the 30
participants of the study. All of the participants were enrolled at Santos Ventura national
High School during the school year 2018-2019. The participants will compose of males
and females regardless of their age. The researcher picks 25 students as the experimental
group and 25 students as the control group.

Instrument
The researcher used a 10-item quiz with 20 points on the Linear equation with one
variable to determine the ability or performance of the Grade 7 students. This quiz will be
validated by the math teacher. The use of Chess piece and numeral dice in solving the
Linear equation with one variable will be used among the experimental group while in
control group is the conventional way of teaching. That will be conducted by the
researcher.
Sampling Design
The study was conducted at Dona Asuncion Lee Integrated School. A total of 50
participants in this study. The researcher used the purposive sampling.
Data Collection Procedure
In gathering data, the researcher administered a 10 - item quiz to the one section
of Grade 7 which is the first Section. The two Class were grouped in two and divide in two
parts, the Pre-test and Post-test. The Pre-test ware used to determine the students’
knowledge on Linear equation. The Pretest has with 10-item questions based on several
topics in linear equation with one variable. After the students took the Pretest, the control
group will not receive treatment while experimental group will receive treatment. Then,
the researcher will teach the Linear equation with one variable using traditional activities
to the control group and will use experiential learning to the experimental group. The

posttest will be used to determine the knowledge acquired by the students through the
process.
Statistical Analysis
The third phase will involve analyzing of the data.
Frequency was used to tally the scores to determine the total responses of the participants
for each statement in the performance.
The differences Mean, standard deviation and percentage were used to determine the
performance and self-efficacy of the students before and after the experiment.
The t-test will be used to analyze the test if there is significant difference in the academic
performance of using chess piece in Linear equation with one variable. Finally, the data
will be analyzed and interpreted with the assistance of the statistician.

Chapter 3
RESULT AND DISCUSSIONS
This chapter presents the result and discussion that the researchers constructed
after administering the study.
1. Pre-test Scores of the Control and Experimental group.
Table 1 shows the number of participants per group, total score of the pre-test,
mean of the scores of two groups on pre-test and the standard deviation of the scores of
each group.
Groups N Total Score Mean Std. Deviation
Control 25 20 6.56 2.48
Experimental 25 20 8.48 3.33
N= 50
The table represents the student’s score of the control and experimental groups in the
pretest. The obtained mean for the control group was 6.56 with a standard deviation of

2.48. The obtained mean of experimental group was 8.48 with the standard deviation of
3.33. This implies that pretest results are expected to be low due to student’s lack of
retention in Mathematics. The result of this study corroborates with the findings of Cluett
(2009) where the students’ pretest results in mathematics scored below 40%.
2. Post-test Scores of the Control and Experimental Group.
Table 2 shows the number of participants per group, total score of the post-test,
mean of the scores of two groups on post-test and the standard deviation of the scores of
each group.
Group N Total Score Mean Std. Deviation
Control 25 20 9.76 3.02
Experimental 25 20 16.48 1.76
N=50
The table presents are the score of the control and experimental group in the post-test.
The obtained mean for the control group was 9.76 with standard deviation of 3.02. The
obtained mean of experimental group was 16.48 with a standard deviation of 1.76.
Therefore, the manipulatives is effective.
3. Different of the Pretest/Posttest result between Control and Experimental
Groups.
t-value was used to determine if there is significant difference between the Post
test of the control and experimental group.

Participants Pretest Post Test
t-value Interpretation t-value Interpretation
Control Group
0.03 Not Significant 0.00 Highly Significant
Experimental Group
Level of significance at 5%
The table shows that the pretest of both groups had a t-value of 0.03. With an
interpretation of Not significant while the post test of both groups have a
t-value of 0.00 with an interpretation of highly significant. This implies that there was no
significant difference between the student’s score of the two groups. it can be inferred
that the students in the experimental group performed better that control group.
What instructional material may be proposed in solving linear equation with one
variable?
The researcher proposed the use of chess piece and numeral dice. The researcher
believed that the use of this materials can help the student to solve fast compare to the
traditional way of solving as this manipulatives helped the student to think and to learn
using their experiential learning.

Chapter 4
SUMMARY, CONCLUSION AND RECOMMENDATION
This chapter presents the summary, conclusion and recommendation that the
researchers constructed after administering the study.
Summary
1. Result of the Pretest of the Control and Experimental group.
Pre-test score on both experimental and control group were close together, which
the researchers conclude that they have the same level of knowledge about solving linear
equation. Almost of the scores on both groups are low, which means that both groups were
having difficulties in solving linear equation.
2. Result of the Posttest of the Control and Experimental group.
The scores of experimental groups is higher than the control group: the mean of
control group is 9.76 while the experimental group is 16.48 and the total number of items
is 20. The researcher conclude that the proposed manipulatives are effective.

3. Significant difference between the Pre-test and Post-test scores of the Control and
Experimental group.
There is no significant difference between the pre-test and the post-test of the
control and experimental group. It can be inferred that the students in the experimental
group performed better that control group.
4. Chess Piece and Numeral Dice.
The chess piece and numeral dice are the manipulatives in solving linear equation.
This method made by the researcher in order for students may easily understand the
concept of solving linear equation not just by mere numbers but through using
manipulatives like chess piece and numeral dice, which represent the variable and
constant.
Conclusion
Based on the finding, the researcher derived at the following conclusions:
1) the participants under both groups showed poor score on the pretest,
2) the participants under experimental group performed better than control group in the
post-test, and
3) the use of Chess piece and numeral dices is an effective way than the conventional
way of teaching linear equation with one variable.
Recommendation
Based on the result and conclusions of the study , the following recommendations are
offered:

1. To the Math Coordinator, this study will help them to assess the effectiveness of
using chess piece and numeral dice as manipulatives in solving linear equation.
2. To the Math Teachers, this study will help the teacher in teaching linear equation to
have an active learning process among the students and to make students achieve optimal
learning by doing. Lastly, the flow of the learning is fun and not boring.
3. To the students, this study will help the students to make the solving in linear
equation easy. Find mathematics interesting and fun. Help them to understand the
concepts of solving linear equation a concrete way.
4. To the future researchers this will serve as a guide for their research and can be a
source of information for this study.
3) the teacher should implement the use of real object in teaching linear equation as an
effective tool n education and explore this tool in other branches of mathematics,
4) the students are encouraged to participate actively in the discussion and activities
given by the teacher,
5) the teacher should incorporate the use of real object to strengthen the students’
understanding in different subjects especially in Mathematics while making learning
enjoyable.

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Appendices
Appendix A. Letter for the School Principal

Appendix B. The value of Chess piece and number dice

Appendix B-1. How to use Chess piece and number dice

Appendix C. Lesson Plan (Experimental Group)

Appendix C-1. Lesson Plan (Controlled Group)

Appendix D. Instrument

Appendix E. Summary of Data
(Pre-test Scores)
STUDEN Contro Experiment 12 6 8
T NO. l al Group 13 2 8
Group 14 10 8
1 4 6 15 6 8
2 4 14 16 8 10
3 6 4 17 8 4
4 6 4 18 10 8
5 4 12 19 10 12
6 4 14 20 8 12
7 6 6 21 8 4
8 6 6 22 8 8
9 2 8 23 8 14
10 4 10 24 10 4
11 6 8 25 10 12

Appendix E-1 Summary of data
(Post-test Scores)
STUDEN Contro Experiment 12 6 18
T NO. l al Group 13 14 16
Group 14 6 16
1 12 12 15 4 18
2 8 14 16 8 18
3 8 18 17 10 16
4 6 18 18 8 16
5 12 14 19 12 18
6 10 14 20 12 18
7 6 18 21 14 16
8 8 18 22 12 16
9 10 16 23 10 18
10 12 14 24 16 16
11 8 18 25 12 18

Appendix F. Mean Scores of Pretest
Appendix F-1. Mean Scores of Post-test

Appendix G. Standard Deviation (Pre-test)
Appendix G-1. Standard Deviation (Post-test)

Appendix H. T-test (Two tailed)

Appendix I. Pictures/Documentation
During Pretest (Control Group)
During Pretest (Experimental Group)

During Demonstration (Control Group)
During Demonstration (Experimental Group)
During Post-test (Control Group)

During Post-test (Experimental Group)

Real Object (Chess piece and number dice)
Using Real object (Experimental Group)

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MABALACAT CITY COLLEGE

THE USE OF CHESS PIECE AND NUMERAL DICE IN

An Action Research Presented to the

Faculty of Teacher Education

Mabalacat City College

Mabalacat City, Pampanga

From the Institute of Teacher Education

Sibal, Eric John M.