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Impact of Using Graphing Calculator in Problem …-geometry calculators and solvers

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
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
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
any medium, on the condition that users give exact credit to the original author(s) and the source, provide a link to the
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).
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.
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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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
The participants agreed that the graphing calculator added speed and accuracy to their problems solving
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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