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International Journal of Learning, Teaching and Educational ResearchVol. 14, No. 2, pp. 163-172, December 2015

A Brief Review of Researches on the Use ofGraphing Calculator in Mathematics
Classrooms*
Jung-Chih Chen and Yung-Ling Lai
National Chiayi University
Chiayi, Taiwan

Abstract The main purpose of this study is to know about the graphingcalculator used for learning mathematics. Many studies have attempted
to find the effect of graphing calculator availability in mathematics
classroom. Also, many educators have explored the role of graphingcalculators. Based on reviews, most researches about the use of graphingcalculators in the mathematics classrooms indicate that graphingcalculators have had positive effect on the learning of mathematics at
any grade levels. However, several reports still revealed that usinggraphing calculators had no significant or negative effects on learning ofmathematics (Averbeck, 2001; Fox, 1998; Norris, 1995; Upshaw, 1994).
This paper may provide many readers a snapshot to capture the use ofgraphing calculators based on research studies.
Keywords: Graphing Calculator, NCTM, CAS, Mathematics Classroom,
Mathematics Learning.

Introduction
In 2000, the National Council of Teachers of Mathematics (NCTM) published thePrinciples and Standards for School Mathematics, a set of recommendations formathematics curricula for Grade K-12. This book states: “Technology is essential
in teaching and learning mathematics, it influences the mathematics that istaught and enhances students’ learning” (p. 24). Also, the Curriculum and
Evaluation Standards for School Mathematics document (NCTM, 1989) states that
“The K-4 curriculum should make appropriate and ongoing use of calculatorsand computers” (p. 19). Thus, technology use in the classroom should be____________________________________________________________*This study was partly supported by the Ministry of Science and Technology (MOST) in
Taiwan. (Grant number: MOST 103-2511-S-415-003). Yet the opinions expressed here are
only those of the authors.
**We are grateful for the helpful comments provided by several anonymous reviewers
on earlier drafts of this article.

© 2015 The authors and IJLTER.ORG. All rights reserved.

164emphasized. Meanwhile, all levels of mathematics teachers should think about
its impact and advantages to students’ learning in the classroom.
In the spring of 2015, the researcher conducted a project to explore theimplementation of mathematics content standards in high school in Taiwan,
surveys were mailed to mathematics teachers. Of the 480 surveys, about 171
were returned. One item teachers were asked about software they used in
Mathematics class. From the analyses in Figure 1 below, we found that mostteachers only used MS Excel, clearly technology use was limited.

90
80
70
60
50
40
30
20
10
Figure 1: Responses to “What kind of software did you use in mathematics class?”

In the past, students usually only use paper and pencil in the mathematics
classroom. But today most people agree that technology can engage students’interest in the learning process of mathematics. For instance, the reality is that
calculator is able to perform operations and execute algebraic symbolic
manipulations quickly and accurately; calculator use allows students andteachers more time to develop mathematical understanding, reasoning and otherhigh level of applications. The fact is that appropriate use of technology
associated with appropriate pedagogy will lead students to think and reason
more mathematically.
This review focuses on the use of graphing calculators. As you may know,
since the mid-1980s, there has been growing interest and attention in graphingcalculators’ potential to facilitate and enhance the teaching and learning ofmathematics in school. From algebra I to pre-calculus, most studies designed
have compared test scores between two groups; one called experiment group inwhich students received instruction with graphing calculators , and the othercalled control group received instruction without a graphing calculator. The
final results of studies mostly suggest that the use of graphing calculators inteaching and learning is quite helpful to students’ cognitive understanding,visualization, and achievement in mathematics classrooms. (Graham & Thomas,
2000; Johnson, 1997; Karadeniz, 2015; Kastberg &Leatham, 2005; Paschal, 1995 ;Wareham, 2016).

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Academic Research
In this section, I have reviewed many researches related to the use of graphingcalculators, especially focusing on some academic dissertations. Although about
fifty dissertations have been carefully reviewed, because of the limitation of
space, here I briefly discuss some significant exemplars as follows:
1. Blozy (2002) conducted his study to analyze performance on calculus
questions by students using computer algebra system (CAS) and non-CAS
groups respectively. In addition, students were given two calculus tests, but
students were only allowed to use graphing calculator on the first test.
Further, Blozy used both quantitative and qualitative methods to analyze thecollected data.
Fifty-six advanced Placement high school calculus students participated in the
study. CAS group included thirty students and non-CAS group included
twenty-six students. All students were given two calculus tests, but students
were only allowed to use graphing calculator on the first test.
Indeed, Blozy found that the CAS students performed better on someindividual questions while non-CAS students performed better on the otherindividual questions. Overall, the results did show that CAS students and nonCAS students approach and answer questions differently. Specifically, the CAS
students consistently used graphical and numerical representations to solve
problems and seemed to perform better on questions requiring this type ofrepresentation. Likewise, non-CAS students consistently used algebraic
approaches to solve problems and seemed to perform better on questions
requiring these types of representations. This study concluded that it was not thetype of question that was significant to performance, but the type ofrepresentation (That is; depending on its graphical, numerical, or algebraic type)that students used to solve the question that was significant to performance.
2. Averbeck (2001) investigated college students’ learning of the function
concept and the role of the graphing calculator in a college algebra course.
He also examined the difference between students with high symbolic
manipulation skills and students’ algebraic skills and academic majors (math& science, business, and liberal arts), twenty five students were involved inthis study, and they were divided into six categories.
To collect data on students’ understanding of functions, students are given a
pretest and posttest. Some test questions consist of three problem situations
given in the numerical, graphical, and symbolic representations. To collect data
about the role of the graphing calculator, Averbeck (2001) conducted dailyclassroom observations. Further, formal and informal interviews with students
and instructor were conducted to verify students’ responses and classroom
observations.
The results indicate that students had difficulties with univalentrequirement in three areas: (a) order of domain and range, (b) preference forsimple algorithms, and (c) the restriction that functions were one-to-one.
Students with high symbolic manipulation skills were more flexible working
between representations of functions. Also, half of the students with low
symbolic manipulation skills perceived a single function given in different
representations as separate entities. Again, students might interpret that
exponential functions possessed a bounded domain because they did not© 2015 The authors and IJLTER.ORG. All rights reserved.

166

explore the behavior of graph.
Averbeck also mentioned that the graphing calculator played a role in allphases of the solution process as follows:(1)
The initial phase: Students used graphing calculators to develop a
symbolic approach.
(2)
The solution-execution phase: Students used graphing calculators to
avoid careless errors.
(3)
The solution-monitoring phase: Students used graphing calculators tocheck answers.
3. Allison(2000) investigated the challenge of the graphing calculator used inhigh school students’ thinking while solving problems. The students were
presented with many different tasks to solve including both contextual, nonroutine problems and non-contextual, exploratory problems. With pertinent
data presented in symbolic, tabular, and textual representations. Students
interviews reflected their perspective on the importance of the use of thegraphing calculators when problem solving.
The results reveal that the graphing calculator gives an impetus to a students’mathematical problem solving. All of the students agreed that the graphingcalculator promoted speed and accuracy to their problem solving process.
Frequently, students attempt to use graphical approaches to solve problems, andtheir thinking ways about tasks are also influenced.
Quite often, students might use the graphing calculator functions that had
been demonstrated in their mathematics classroom. For instance; they used the“regression functions” to find symbolic models in problems with tabular dataand in explorations with graphical data. Also they might use trial-and-error
methods to explore the possible relationships between functions and theircorresponding graphs.
4. Milou (1999) designed a survey of classroom usage involving the graphingcalculator. In this study, he focused on 146 secondary mathematics teachers
who used the graphing calculator in their teaching. In particular, main
attention is to examine algebra teachers’ teaching; their understanding about
the graphing calculators, and to see any changes about their instructional
practices.
Most teachers agreed or strongly agreed that “Graphing calculators allow for
algebra classes to cover additional material.” In addition, all teachers were asked
to tell in which potential topics were appropriately explored. The following
three topics were written by a lot of teachers:(1) Statistics associated with data analysis, curve or best fit, quartiles, and soon.
(2) Some problems using complex applications involving in everyday life orbusiness, something like that.
(3) Mathematical problem solving.
Likewise, teachers were asked about what topics should be ignored or should be
weakened; their answers mostly include(1) Factoring(2) Student produced graphing(3) Rational expressions
In addition, about 72% of the teachers answered “agree” or “strongly” to the© 2015 The authors and IJLTER.ORG. All rights reserved.

167

question: “Students should first solve algebraically and support graphically.”
But, when they were asked if students should solve graphically only whenalgebraic methods are unworkable, 59% answered “disagree” or “strongly
disagree.”
Other important results include (i) Most algebra teachers thought that thegraphing calculator played a motivational tool, (ii) Teachers of algebra II used
the graphing calculators more often than teachers of algebra I, (iii) Algebrateachers are not confident of how to use the graphing calculators in theirteaching.
Milou also concludes that at present the use of the graphing calculator is
not coincident to many algebra teachers. He points out the fact, although manyhigh school teachers and algebra II teachers widely accepted the graphingcalculator, yet there is still much controversy by middle school teachers andalgebra I teachers, they express concerns about whether this technology is reallyappropriate in their mathematics classrooms.
Interestingly enough, two questions shown in this study are listed asfollows: (Milou, 1999)
Q1: “Do you Use Graphing Calculators in Your Classroom?”
Current Teaching Assignment
Algebra Ⅰ
Algebra Ⅱ
Both Algebra I & Algebra II
Neither Algebra I nor Algebra II

Response(Yes)
37
21
19
11

Response(No)45(teachers)2(teachers)3(teachers)
8(teachers)

Q2: “Should Graphing Calculators Be Permitted to Be Used on All Tests?”
Response
Strongly agree
Agree
Neither agree nor disagree
DisagreeStrongly disagree

Frequency
21
31
20
52
20

Percent
14.6
21.5
13.9
36.1
13.9

5. Fox (1998) studied the relations of a graphing calculator used in an active
learning environment on intermediate algebra students’ achievement andattitude. This quasi-experimental study involved six classes of community
college intermediate algebra students (totally 166 persons) during six weeks.
Students in the experimental group used TI-82 in class and on tests. While
students in the control group still used their scientific calculators. Both groups
were taught in active learning environments. Students were given pretest, threeachievement tests and a post-attitude survey.
The results indicated that no significant differences due to treatment were
found between the groups on achievements or attitude toward mathematics.
However, when compared to intermediate algebra classes not involved in thisstudy, 15% more students in the study’s active learning classes completed thecourse successfully.
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Fox also drew the following important conclusions in his studies:(1) Active learning could positively impact learning.
(2) The use of graphing calculators encouraged active learning and could
help students make connections between different representations.
(3) Remedial students might not be accustomed to using calculators forstudying mathematics and should be tested on the basic use of thegraphing calculator before being tested for achievement.
(4) Teachers might struggle to incorporate the use of graphing calculators.
(5) The determination of technology’s appropriate use should allow for thediversity of remedial students’ needs and past experiences.

Highlights From Various Research
According to the research articles, some important findings about the use ofgraphing calculators could be succinctly summarized as follows:(1) The most critical personal factors affecting teachers’ decisions were
professional development, beliefs, mathematical and pedagogical knowledge,
and familiarity with graphing calculators. Note that teaching experience,education background, and personal use of the calculator did not play animportant role in teachers’ decision-making process (Szombathelyi, 2001)(2) The graphing calculator was usually used as an exploring tool to solve
problems related to limit and derivative. When a multiple representational
approach was used, it was very likely to involve of algebraic and graphicalrepresentations (Girard, 2002).
(3) Technology integration with the graphing calculator requires changes inteacher attitudes, course content, instructional methodology, and teacher
preparation. Teachers with limited knowledge and preparation usinggraphing calculator usually exhibited a lack of confidence that affected theirattitude and their effectiveness in using the graphing calculator in theirclassrooms (Bynum, 2002).
(4) CAS students and non-CAS students approach and answer questions
differently. The CAS students consistently used graphic and numericalrepresentations to solve problems (Blozy, 2002).
(5) Students used graphing calculators to develop a symbolic approach, to avoid
careless errors, and to check answers (Averbeck, 20001).
(6) The graphing calculators often can help students visualize the derivative andhence make connections with the other kind of representations (Serhan, 2000).
(7) The results revealed that the graphing calculator served as impetus forstudents’ mathematical problem solving. Graphing calculator could promote
speed and accuracy to their problem solving process. (Allison, 2000).
(8) The graphing calculators could enhance students’ graph interpretation
abilities. Students’ abilities to interpret contextual graphs of functions both
locally and globally improved. Students exhibited very well developed
understanding of the relationship between slope and the rate of change of
one variable (Pullano, 2000).
(9) The graphing calculator proved to be useful tool for achieving an
improvement in student understanding of variable. Some concerns include
the lack of confidence and the lack of resources (Graham & Thomas, 2000).
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169(10) Some algebra teachers are not confident of how to use the graphingcalculator in their instruction. For example: Do concepts and procedures stillneed to be mastered first? Also, teachers agreed that the graphing calculator
should be used to support analytical algebra findings, but they disagreed
that the graphing calculator should only be used when algebraic methods
were difficult. Teachers in the study believed that algebra I students were too
dependent on the graphing calculator and were thus unable to handle basic
algebraic manipulations (Milou, 1999).
(11) The graphing calculator could make the work easier and sooner, it didenhance a student’s visualization about Algebra II concepts. But, somestudents with low performance did have more difficulty in operating thegraphing calculators (Drottar, 1998).
(12) The cognitive benefits about graphing calculator use were still controversial
by some algebra teachers. Most algebra teachers thought that graphingcalculator was useful tool for promoting motivation in mathematics
classrooms (Milou, 1998).
(13) Some results suggested that the graphing calculator (i) could facilitate thelearning of functions and the spatial visualization skills; (ii) could promotemathematical investigation and exploration; and (iii) could reform inemphasis of teaching and learning from algebraic skill to graphicalinvestigation, and exploring the relationship between graphical, algebraic
and geometric representations ( Penglase & Arnold, 1996).
(14) Teachers in high school used graphing calculators to provide graphs andmake generalizations about transformations of the quadratic function inmathematics classroom. (Simmt, 1997).
(15) Currence (1993) found that some teachers have changed the ways theytaught mathematics because of the use of the graphing calculator in theirclassrooms.

Concluding Remarks
In summary, most studies conclude that using graphing calculator has its value
in the mathematics classroom. At least, available research indicates that somebenefits are obvious and straightforward, such as (1) It will provide students
visualization (Karadeniz, 2015) through graphical and numerical approaches tosolve problems, (2) It will reduce the time spent on calculations andmanipulations as well, (3) It will illustrate some mathematical concepts whichlead to a higher level of thinking and understanding, and (4) Results of an indepth study reveal the positive relationships between calculator use andmathematics achievement (Kastberg &Leatham, 2005 ; Wareham, 2016). However,here we emphasize the importance of teacher’s “appropriate use” in teaching.
Teachers should look through the textbooks in advance to find topics where agraphing calculator could be used. Basically those topics should meet content
goals and learning objectives of the students.
Further, some people may wonder if the graphing calculators have thepossibility to reform mathematics education, such as the ways in teaching or thecontent focuses. In order for more significant changes to come through, here we
provide some suggestions as follows:© 2015 The authors and IJLTER.ORG. All rights reserved.

170(1) Students , especially in high schools, should have access to graphingcalculators to perform calculations and to support problem solving activities
in mathematics classroom.
(2) The school and district should support and guide teachers in theappropriate use of the graphing calculators. Professional development can
provide in service workshops, peer tutoring, and new faculty expertise.
(3) Since the graphing calculator becomes more popular by classroom teachers,
so the curriculum needs to be reviewed and aligned, especially for someareas that can be de-emphasized because of the inclusion of the graphingcalculators. On the other hand, in some topics, teachers can better have theopportunity to learn “when” and “how” to use the graphing calculator
appropriately in their mathematics classrooms.
(4) All publishers of textbooks, including all authors of assessments, evaluation,and mathematics instruments, should realize that the graphing calculator
applications certainly affect the mathematics curriculum.
(5) Those people who are responsible for the selection of curriculum materials
should remain cognizant of how the technology eventually affects thecurriculum.
(6) Whether or not students are allowed to use the graphing calculators in theirtests, we believe, is also an incentive factor to determine its prevalence in themathematics classroom.
Finally, the researchers expect that mathematics teachers in high school canunderstand the benefits to integrate graphing calculators in their classrooms.
Indeed, teachers can determine “when” and “how” to use it in class (Karadeniz,2015). More than all, technology use should be considered in new curriculum
documents such as mathematics content standards or guidelines.

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