THE PROBLEM AND ITS BACKGROUND

Introduction

Many students with learning difficulties in the area of mathematics

demonstrate specific weaknesses with mathematics reasoning (Griffin &

Jitendra, 2009). One aspect of the mathematics curriculum that involves high

levels of reasoning is solving word problems. Word problems, sometimes

referred to as story problems are used to give learners a glimpse of how

mathematics is used in the real world (Bogomolny, 2009).

Word problems consist of a linguistic presentation of hypothetical

situations in which problems are posed that can be solved through the use of

mathematical equations. Some mathematicians conceptualize word problems as

part of a larger problem-solving component of the mathematics curriculum in

which students must overcome barriers in order to obtain and explain a solution

to a mathematical problem that is not directly apparent (Heddens & Speer, 2001).

Based on this conceptualization of solving word problems, the

mathematical equations are sometimes hidden within multifarious, complex

word usage. Sometimes the numerals and numeric operations are difficult to

identify due to unforeseen or unique language structures, especially in the most

advanced word problems. This results in high levels of challenge for many

students, particularly those with learning difficulties in the area of mathematics.

1|Page
 Wherefore, premises considered, the researcher opts to examine the effect

of problem solving strategies on the performance of grade-8 students in

mathematics at Cebu Integrated School.

Statement of the problem

The main purpose of this study is to determine the effects of problem

solving strategies on the performances of grade-8 students in mathematics at

cebu integrated school. Specifically it aims to answer the following questions:

1. What are the strategies use to solve problems in mathematics?

2. What are the performances of grade-8 students in mathematics?

3. What are effects of problem solving strategies on the performance of grade-8

students in mathematics?

Objectives of the Study

Generally, this study aims to determine the effects of problem solving

strategies on the performances of grade-8 students in mathematics at cebu

integrated school.

Specifically, it aims;

1. To know the strategies, use to solve problems in mathematics.

2. To determine the performances of grade-8 students in mathematics.

3. To find the effects of problem solving strategies on the performance of

grade-8 students in mathematics.

2|Page
Significance of the Study

The result of this study provides basis for solving basic mathematical

operations and have a deep-rooted belief that they will never be very good at

solving math problems. One of the goals for this research is for students to

develop confidence in their own ability by helping them to become better

problem solvers. By helping to boost not only their problem-solving abilities but

their own perceptions of their mathematical abilities, we hoped they would

become a bit more tenacious when dealing with a difficult problem and thereby

improve their scores.

Scope and Delimitation of the Study

This study focuses only on knowing the effects of problem solving

strategies on the performance of grade-8 students in mathematics.

This study was limited only on finding the effects of problem solving

strategies on the performance of grade-8 students in mathematics.

Definition of Terms

In order to clarify some terms used in this study, the following are hereby
defined conceptually or operationally:

Problem Solving. The process of finding solutions to difficult or complex

Strategies. A plan of action designed to achieved a major or overall aim.

3|Page
 REVIEW OF RELATED LITERATURE

This chapter presents the literature reviewed and studies which were read

and which has information on the present research.

Related literature

The idea of problem solving within the field of mathematics continued to

advance throughout the 20th century through the research of George Polya

(2000). Polya wrote extensively about mathematics problem solving. He was

a strong advocate for introducing mathematics problem solving to primary

school-aged children. In 2000, Polya published How to Solve It, a four-step

strategy for solving mathematics problems. The four steps in his strategy

were: (a) understand the problem, (b) make a plan, (c) carry out the plan, and

(d) review and respond, or extend (Polya, 2000). Polya continued to develop

his plan for teaching students how to solve mathematics word problems by

expanding the four steps of How to Solve It to six steps: (a) understand the

problem, (b) determine a plan of action, (c) think about possible

consequences of carrying out the plan of action, (d) carry out your plan in a

thoughtful manner, (e) check to see if the desired goal has been achieved, and

(f) reflect on your new knowledge from solving the problem. Polya's word

problem strategy laid the foundation for the use of cognitive strategies within

the mathematics curriculum.

The mathematical model contains only mathematical aspects that can be

acted on using mathematical analysis techniques (Verschaffel et al., 2000).

4|Page
Some examples of mathematical models include graphs and pictures,

symbolic expressions, tables, and verbal statements (Lesh & Doerr, 2003).

Representation use during problem solving is crucially important if a student

expects to find the correct solution (Greeno & Hall, 1997). Effective problem

solvers recognize that some representations are more appropriate or lead to

the solution quicker than others, depending on the task (Greeno & Hall,

1997; Preston & Garner, 2003; Verschaffel et al., 1999). Furthermore, factors

that might impact the mathematical model are more obvious to problem

solvers who fully engage in the problem-solving process. Those who take the

necessary time and energy to understand the text and develop a situation

model are likely to solve the problem (Verschaffel et al., 2000), but that does

not guarantee success. The present study examines students’ representation

use (i.e., mathematical modeling) within the context of the problem-solving

process. Mathematical modeling is a critical step in the process because it

leads to the mathematical analysis technique (i.e., procedures) used to answer

the problem.

Successful problem solvers typically go through all six stages of the

problem-solving process whereas unsuccessful problem solvers typically take

at least one shortcut. Shortcuts are more likely to lead to inappropriate

mathematical models, incorrect use of procedures, and reporting the wrong

answer to the problem (Verschaffel et al., 2000). Some of the common

missteps are discussed here. At the first stage of the superficial problem-

solving process, students read the text and create a mathematical model. This

5|Page
leap in the problem-solving process does not facilitate adequately

understanding the text or determining the key aspects of the problem. At the

third problem-solving stage, some learners employ mathematical

representations that are inappropriate for a problem’s context. For example,

Santos-Trigo (2000) noticed that high school students often tried using

symbolic representations and algorithms to solve complex word problems.

They were frequently unsuccessful and Santos-Trigo argued that if they had

better facility with multiple representations then they might have shown

better problem-solving performance. The role of mathematical

representations is critically important for problem solver’s success and it is a

focus of this study.

During mathematical analysis, learners often combine numbers

inappropriately because they do not consider alternate representations or their

situation model is inaccurate (Verschaffel et al., 2000). Another common

mistake is that problem solvers employ a representation, conduct procedures,

and report the result as the problem’s solution without interpreting it. For

example, an individual might indicate 16 as a word 33 problem’s solution;

however, the correct response requires meaningful units such as dollars,

blocks, or people. This expedited problem-solving process takes less time but

it also leads to far more incorrect answers (Verschaffel et al., 2000). A

common error that can be made at any stage of the problem-solving process

is not devoting the necessary cognitive energy to each stage of the process.

6|Page
One error made by many students is not taking time and cognitive energy to

sufficiently understand a problem’s text (Pape, 2004).

Today, mathematical word problems are taught, emphasized, and valued

greatly in the United States public education system (NCTM, 2009). The

emphasis on solving mathematical word problems is supported through local,

regional, state, and national mathematics standards. The National Council of

Teachers of Mathematics has been at the forefront of establishing these

standards and has articulated the importance of problem solving within all of

their standards for school mathematics (NCTM, 2009). The NCTM further

notes the importance of linking mathematics problems to contexts other than

school. Solving mathematical word problems is viewed as one way to

promote this type of high-level thinking. Word problem scenarios frequently

describe events that occur outside of school and thus have the potential to

assist students in understanding that mathematics may be used in a variety of

contexts.

Hypothesis

1. Null Hypothesis

There is no significant effect on the use of problem solving

2. Alternative Hypothesis

There is a significant effect on the use of problem solving

7|Page
 METHODOLOGY
RESEARCH DESIGN

The research study will use the descriptive survey wherein she will use a survey
questionnaire in gathering the data and finding out the effects of problem solving
strategies on the performances of grade-8 students in mathematics

RESPONDENT OF THE STUDY

The respondent of this study will be the Grade-8 students of Cebu Integrated
School who has undergone the subject math.

DATA GATHERING

The research study will use a survey questionnaire as an instrument in gathering

There is a liker scale that will use in gathering data from the said respondent.

Here are the following:

 5 – Strongly Disagree
 4 - Disagree
 3 - Unsure
 2 - Agree
 1 – Strongly Agree

 3 – Never Used
 2 – Seldom Used
 1 – Frequently Used

8|Page
 BIBLIOGRAPHY
References

Bottge, B. A. (2001). Reconceptualizing mathematics problem solving for low-achieving

students. Remedial and Special Education, 22(2), 102-112.

Cuoco, A., Goldenberg, E. P. & Mark, J. (1996). Habits of mind: An organizing

principle for mathematics curricula. Journal of Mathematical Behavior, 15, 375-402.

Fraivillig, J. L., Murphy, L. A. & Fuson, K. C. (1999). Advancing children’s

mathematical thinking in everyday mathematics classrooms. Journal for Research in

Mathematics Education, 30(2), 148-170.

Gersten, R. & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for

students with mathematical disabilities. The Journal of Special Education, 33(1), 18-28.

Jitendra, A. K., Griffin, C. C., McGoey, K., Gardill, M. C., Bhar, P. & Riley, T.

(1998). Effects of mathematical word problem solving by students at risk or with mild

disabilities. The Journal of Educational Research, 91(6), 345-355.

National Council of Teachers of Mathematics. (2000). Principles and Standards for

School Mathematics. Reston, VA:

Pape, S. J. (2004) . Middle school children’s problem solving behavior: A cognitive

analysis from a reading comprehension perspective. Journal for Research in Mathematics

Education, 35(3), 187-219.

Reynolds, A. J. & Walberg, H.J. (1992). A process model of mathematics achievement

and attitude. Journal for Research in Mathematics Education, 23(4), 306-328.

Schullo, S. A. & Alperson, B. L. (April, 1998). Low SES algebra1 students and their

teachers: Individual and a bi-directional investigation of their relationship and implicit

beliefs of ability with final grades. Paper presented at Annual Meeting of the American

9|Page
Educational Research Association, San Diego, CA.

Woodward, J. & Montague, M. (2002). Meeting the challenge of mathematics reform

for students with LD. The Journal of Special Education, 36(2), 89-101.

Williams, S., & Baxter, J. (1996). Dilemmas of discourse-oriented teaching in one

middle school mathematics classroom. The Elementary School Journal, 97, 21-38.

Yackel, E., & Cobb, P. (1996). Socio mathematical norms, argumentation, and

autonomy in mathematics. Journal for Research in Mathematics, 27, 458-477.

Zusho, A., & Pintrich, P. (2002). Motivation in the second decade of life: The Role of

multiple developmental trajectories. In T. Urdan & F. Pajares (Eds.), Adolescence and

education: General issues in the education of adolescents (pp. 163-199) Greenwich, CT:

Information Age.

10 | P a g e