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INTERNATIONAL ELECTRONIC JOURNAL OF MATHEMATICS EDUCATION

e-ISSN: 1306-3030. 2018, Vol. 13, No. 3, 139-148

OPEN ACCESS https://doi.org/10.12973/iejme/2704

Impact of Using Graphing Calculator in Problem Solving

Mary Ann Serdina Parrot 1, Kwan Eu Leong 1*

1 University of Malaya, Kuala Lumpur, MALAYSIA

* CORRESPONDENCE: rkleong@um.edu.my

ABSTRACT

The purpose of this study is to investigate the impact of graphing calculator on students' problem

solving success in solving linear equation problems and their attitude toward problem solving in

mathematics. A quasi-experimental non-equivalent control and treatment group using the pre-

test post-test design was employed in this study to test the hypotheses. The sample of the study

involved two Form Four classes from one public secondary school in Sarawak, Malaysia. Students

in the experimental group received problem solving based instruction using graphing calculator

while the control group students underwent the traditional chalk and talk method without the

graphing technology. Two instruments were used in this study, namely the Linear Equation

Problem Solving Test and the Mathematical Problem Solving Questionnaire. Findings of this study

show existence of a significant difference in the mean scores between the two groups; students

who used graphing calculator performed better in problem solving tasks compared to students

without access to graphing calculator. Furthermore, a questionnaire was used to obtain students'

attitude toward problem solving in mathematics. Results from the survey revealed that students

who use graphing calculator have a better attitude toward problem solving in mathematics. This

study is pertinent as it investigates a different approach in teaching linear equation through

problem solving while integrating the latest graphing calculator technology in the lessons.

Keywords: graphing calculator, linear equations, problem solving success, secondary students

INTRODUCTION

Almost everything in life is a problem and it has become the central part of human life as well as in the

mathematics field. The beginning of mathematics has been influenced by mathematicians making an effort to

work out challenging problems. For most mathematical scholars, mathematics is tantamount to solving

problems in such a way when we are doing mathematics; looking for patterns, interpreting diagrams, word

problem, proving theorem and so on. A remark made by Paul Halmos, "The mathematician's main reason for

existence is to solve problems" (Halmos, 1980). The ability to solve problems cannot be learnt separately; it

has to be taught along with other skills as an on-going process building up of experience in acquiring strategies

to solve problems. Hence, the expression of "problem solving" has to be understood as a long-term goal to

achieve and hopefully this skill will be used in everyday life.

With advances in information and communications technology, it is impossible to avoid the impact of

technology on mathematical problem solving. Technology use also contributes to mathematical reflection,

problem identification, and decision making. With guidance from effective mathematics teachers, students at

different levels can use these tools to support and extend mathematical reasoning and sense making, gain

access to mathematical content and problem-solving contexts, and enhance computational fluency. Recently,

a steady increase in interest in using hand-held technologies in particular graphic calculators, has been seen

among mathematics educators, curriculum developers, and teachers (Kissane, 2000). Use of graphing

Article History: Received 20 March 2016 Revised 12 November 2016 Accepted 1 January 2017

? 2018 The Author(s). Open Access terms of the Creative Commons Attribution 4.0 International License

(http://creativecommons.org/licenses/by/4.0/) apply. The license permits unrestricted use, distribution, and reproduction in

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Creative Commons license, and indicate if they made any changes.

Parrot & Leong

calculators in learning mathematics will allow students to explore and model mathematical problems and view

multi representation of mathematical problems. Technology that supports multiple representations can

increase students' use of visualization in problem solving and lead to gains in understanding (Center for

Technology in Learning, 2007).

PROBLEM STATEMENT

In real life, students need to solve problems because this is a skill needed in the 21st century to succeed in

life. Skills endow people to face with challenges of everyday life, related to making decisions, solving problems

and dealing with unexpected events. To become a good problem solver in mathematics, one must develop a

base of mathematics knowledge (Wilson, Fernandez, & Hadaway, 1993). According to Mayer, there are four

types of knowledge pertaining to problem solving, namely: (1) linguistic and factual knowledge, (2) schema

knowledge, (3) algorithmic knowledge, and (4) strategic knowledge (Mayer, 1982). Difficulty in problem solving

might happen throughout the following phases of knowledge, that is, reading, comprehension, choosing

strategy, executing strategies, transformation, process skill and solution (Newman, 1983).

Mathematics skills such as language, number fact, information and arithmetic are vital in problem-solving.

Deficiency in any of these skills could cause difficulties among students who want to become good problem

solvers (Tambychik, Meerah, & Aziz, 2010). Past research indicated that many students who are lacking in

mathematical skills face difficulties in carrying out mathematical tasks involving problem solving

(Tambychik, 2005; Tay, 2005). The ability to use cognitive abilities in learning is crucial for meaningful

learning to take place. However, many students face hindrances in using these cognitive abilities. They were

reported to face difficulties in making accurate perceptions and interpretations, memorizing and retrieving

facts, concentrating and using their logical thinking (Andersson & Lyxell, 2007; Bryant, 2009; Tambychik,

2005). Students did not totally acquire mathematics skills needed especially in problem-solving; failure in

problem-solving generally resulted from failing to organize the mathematical operations, to choose the most

effective method, to analyze, to understand the point of the problem and to monitor and control operations

carried out (Victor, 2004).

In Malaysia, studies had shown that students faced difficulty in mathematics especially in problem-solving

because they had problems in understanding and retrieving concepts, formulas, facts and procedure; they lack

the ability to visualize mathematics problems and concepts, are inefficient in logic-thinking and lack the

strategic knowledge in problem-solving (Kadir et al., 2003; Tambychik, 2005; Tay, 2005). A study conducted

on 242 Form Four students to evaluate the level of Malaysian students' problem solving ability showed that

students have fairly good command of basic knowledge and skills but they did not show the use of problem

solving strategies. The common strategy used by students was algorithms and procedures as well as counting;

these students did not use more suitable and effective strategies. Generally, the mastery of problem solving

skills among Malaysian students is still low (Zanzali & Lui, 1999). In the Programme for International Student

Assessment (PISA) on problem solving, Malaysia ranked 39 out of 44 countries, with a mean score of 422

which is below the average (OECD, 2014). It was found that more than one in five Malaysian students could

not even reach basic levels of problem solving.

LITERATURE REVIEW

The information processing theory is the theoretical framework underpinning this study. The basic

characteristics of information processing theory that shape the problem solving efforts are reflected in the

process of receiving, storing and locating new information. It also focuses on the mechanism of the problem

solving process (Laurillard, 2002). In addition, understanding the procedures that students adopt helps

integrate these into a more deterministic account of how students solve problems. Consequently, Polya (1965)

promoted the idea that the application of general problem-solving strategies was important in developing

problem-solving expertise and intellectual performance. The four steps in the problem solving process as

suggested by Polya: understand the problem, devise the plan, carry out the plan and looking back.

Graphing Calculator

Graphic calculators are handheld, battery powered devices equipped with functions to plot graphs, give

numerical solutions to equations and perform statistical calculations, operations on matrices and perform

more advanced mathematical functions such as algebra, geometry and advanced statistics (Kor & Lim, 2003).

In fact, Mitchelmore and Cavanagh noted that the first graphing calculators appeared in the mid-1980s and

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INT ELECT J MATH ED

since then such calculators have become more affordable and powerful (Cavanagh & Mitchelmore, 2000). With

this new technology, the graphing calculator brought many new and exciting changes in the mathematics

curriculum (Choi-Koh, 2003).

Graphing calculators were first seen in 1985, when they were developed by Casio, and later were developed

even further by Texas Instruments in 1995. With the invention of graphing calculators came a new way to

deal with mathematics that provided access to mathematical problem solving that, before this time, could only

be done on computers (Waits & Demana, 1998). Several varieties of graphing calculators exist, but all graphing

calculators have certain functions and capabilities in addition to computation such as graphing, viewing

tables, and running programs and applications. The most recent handheld graphing technology from Texas

Instruments is the TI-Nspire CX. These graphing calculators have all of the capabilities of other graphing

calculators in addition to the ability to view multiple representations on the same screen, to construct and

animate geometric figures, and to receive documents that allow visualizations of solids of revolution.

In a study conducted to investigate the use of graphing calculator (TI-Nspire), there are five roles of

graphing calculator in classroom mathematical practice based on the findings; namely: exploratory tool 1 role,

graphing tool 2, confirmatory tool 3, problem-solving tool 4, and multi-dimensional tool 5 (Ng, 2011). The

researcher concluded that graphing calculator (TI-Nspire) is an effective tool for developing mathematical

concepts, promote learning and problem solving. Doerr and Zangor found that five patterns and modes of

graphing calculator use emerged in the practice: computational tool, transformational tool, data collection and

analysis tool, visualizing tool and checking tool (Doerr & Zangor, 2000).

Past Research

Researchers in different settings have investigated various studies regarding graphing calculator usage in

teaching, learning, achievement and attitude in various domains of mathematics. Even more significantly,

vast research has shown that using graphing calculator has a positive effect on students' performance in

problem solving. Rich, in a study of two high school pre-calculus classes, found that students were more willing

to tackle problem-solving activities when they had access to graphing calculators (Rich, 1991). The students

were also able to solve non-routine problems that might have been too difficult for them without the

availability of a graphing utility; this permitted the introduction of problem-solving situations that were of

interest to the students.

Carter found that the graphing calculator seemingly led to improved problem-solving, as less time was

consumed with algebraic manipulations (Carter, 1995). He also reported that the students used the calculators

as a monitoring aid while solving word problems. Bitter and Hatfield also found that students using calculators

showed improved problem-solving skills (Bitter & Hatfield, 1991). Szetela and Super found a better attitude

toward problem-solving when the calculator was used. However, the scores were not significantly higher for

those students using the calculators than for their counterparts who did not use them (Szetela & Super, 1987).

Allison conducted a case study to determine the impact of graphing calculator on four students'

mathematical thinking while solving problems. The researcher adapted Schoenfeld's model of mathematical

thinking and Berger's interpretive model of graphing calculator as the theoretical framework. Data were

collected through task-based clinical interviews and the task includes contextual non routine problems, non-

contextual non-routine problems and exploratory problems. The results indicate that graphing calculator is

integrated and serves as impetus for a students' mathematical problem solving (Allison, 2000). Some of the

researcher's findings were:

i. Graphing calculator amplified the speed and accuracy of problem solving strategies

ii. Graphing calculator encouraged participants to use graphical approaches to solve problems and

influenced their ways of thinking

iii. Graphing calculator enhanced the participants' ability to focus on reasoning and to look back at their

answer.

The participants agreed that the graphing calculator added speed and accuracy to their problems solving

efforts.

In an experimental study involving graphing calculator in learning probability, the graphing calculator

formed a "thinking tool" which enabled students to develop conceptual understanding and problem-solving

abilities in mathematics. It provided the opportunity for exploring problem solving and increased the students'

confidence in solving more challenging problems (Tan, Harji, & Lau, 2011).

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