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The calculator's role in mathematics attitude.

Abstract

The results of twenty-seven studies on the effect of calculators on students' attitudes toward mathematics are summarized in this article. The statistical process of meta-analysis was used to determine the overall trend of the collection of studies. The results show that access to calculators during mathematics instruction does benefit students' attitudes toward mathematics. Also, there is statistical support for the fact that students enjoy using calculators while learning mathematics.

Introduction

Students attitudes toward mathematics are influenced by a variety of factors including family involvement (Ma, 1999) and grade level (Ma, 1997). The relationship between attitude and achievement has been established (Ma, 1997) but is, nevertheless, complex. Many factors are out of the teacher's control but instructional methods and their effect on attitude can be influenced by educators and administrators. Over the last twenty years, the topics covered and the instructional methods implemented in the mathematics classroom have changed as the role of technology, the calculator in particular, has increased in the study of mathematics. Currently, the focus is not if calculators should be used but how to make use of calculators meaningful to the learning experience. The significance of the relationship between calculators and the study of mathematics was emphasized in the National Council of Teachers of Mathematics Standards (NCTM, 1989) document where it was noted that calculators allow for exploration of different problem solving approaches and a more meaningful study of relationships between mathematics problems and real world applications.

The question raised in this study is, with the technological advances in the mathematics classroom, has access to calculators also helped students improve their attitudes toward mathematics? With research conducted during the early years of calculator use, this question was addressed by Hembree and Dessart (1986) and favorable results were reported for students' attitudes toward mathematics after instruction with calculators. The answer to the question outlined below was determined through a statistical analysis of research studies that assessed students' attitudes toward mathematics after instruction with calculators. The research studies featured in this analysis were conducted in the last two decades during which the calculator's role in the classroom has been well established.

Statistical Method

The research studies were identified through a search of education-related computer databases including the Education Resources Information Center (ERIC), Psych Info, and Dissertation Abstracts International. A study was selected for inclusion if it featured the use of a basic, scientific, or graphing calculator; it involved students in a mainstream K-16 classroom; and it was a quasi-experimental research project with treatment group data being compared to control group data. The search yielded two possibilities: (1) a treatment group with access to calculators and a control group who participated in the same instruction without access to calculators and (2) a treatment group with access to graphing calculators and a control group with access to scientific calculators. Since graphing calculators without computer algebra system (CAS) capabilities are often featured in lower level mathematics courses taken by populations of mostly non-science majors with the potential of weaker attitudes toward mathematics, the search was limited to non-CAS graphing calculators. The noncalculator control studies were used to compare the attitudes of students with access to calculators with the attitudes of students who did not have access to calculators. The scientific calculator control studies were used to determine if non-CAS graphing calculators have more influence on students attitudes toward mathematics when compared to scientific calculators. Each study used a Leikert scale survey instrument designed according to the Mathematics Attitude Inventory (Sandman, 1980) or other available attitude measures like the scales developed by Aiken (1974) and Fennema and Sherman (1976). The Mathematics Attitude Inventory evaluates six attitudinal factors. Most researchers did not base their survey instruments on all six factors of the Mathematics Attitude Inventory but developed instruments on the broadly defined attitude towards mathematics factor.

The methods outlined by Lipsey and Wilson (2001) were used to code and statistically analyze the studies. The studies were coded according to the following study characteristics: treatment group calculator type (basic, scientific, graphing); control group calculator type (scientific, none); educational division (elementary, middle school, high school, college); treatment length (0-7 weeks, 8-15 weeks, 16 or more weeks). Once the studies were coded, effect sizes were calculated. The standardized mean difference was the effect size used since the means and standard deviations of student responses to the Leikert scale attitude questions were available. A positive effect size was generated for studies in which the treatment group reported a better attitude towards mathematics than their control group counterparts. A negative effect size reflected the control group's more positive attitude. An effect size value near zero represented no difference in the attitudes of the two groups.

Effect sizes were grouped according to attitudinal factor and each group was statistically analyzed including a test for homogeneity, calculation of a weighted mean effect size, and a 95% confidence interval. Hedges Q statistic was used to determine which data sets were homogeneous (Hedges & Olkin, 1985). Each effect size in a homogeneous data set is considered an estimate of the effect size for the population from which the data was gathered. The population effect size is, therefore, best represented by the weighted mean effect size of the data set. If the corresponding confidence interval does not contain zero, then there is a statistically significant difference in the treatment group and control group attitude toward mathematics.

Study Characteristics

Twenty-seven studies conducted between 1983 and 2000 satisfied the criteria for inclusion in the analysis. With the exception of five studies (Coston, 1994; Fox, 1998; Hersberger, 1983; Liu, 1993; Whisenant, 1989) each study provided one effect size representing students' attitudes toward mathematics. Coston (1994) and Liu (1993) studied groups of students involved in two different treatments with each treatment group being compared to a control group. One treatment group used calculators but was taught with the same instruction methods as the control group while the other treatment group learned with the addition of special calculator instruction materials that were not used by the control group. Since the two treatment groups differed significantly in the method of treatment, the two effect sizes for each study were not averaged into one value. For these two studies, the two independent treatment/control group comparisons were considered separate primary studies for purpose of analysis. Fox (1998), Hersberger (1983), and Whisenant (1989) provided data on other attitudinal factors but did not analyze students overall attitude toward mathematics.

While none of the studies were conducted under rigorous experimental conditions, over 80% of the studies used random techniques to assign treatment conditions to intact classes. Eleven of the studies used a readily available survey instrument (Aiken, 1974; Fermema & Sherman, 1976; Sandman, 1980) and the remaining researchers developed their own survey instrument based on the Mathematics Attitude Inventory. Eleven studies were conducted in colleges with four taking place in a community college. Most of the college researchers analyzed students in college algebra and precalculus classes but three studies were conducted in developmental mathematics classes. High school students participated in seven studies of algebra, precalculus, and statistics classes. The remaining nine studies took place at the elementary and middle school level. Rich (1991) studied a group of high ability students who used graphing calculators while learning precalculus. All of the other researchers evaluated students in mainstream mixed ability classrooms. Twenty studies took place over fifteen weeks or less. Students in three studies (Bartos, 1986; Lim, 1992; Whisenant, 1989) were evaluated over the course of an entire school year. Four researchers (Hersberger, 1983; Rich, 1991; Riley, 1992; Szetela & Super, 1987) conducted studies in which K-12 students had access to calculators for two school years. The sample involved in each study was fairly small with nineteen studies evaluating no more than 100 students. All of the research reported here was conducted with combined treatment and control group samples of 250 students or less.

Statistical Results

Nineteen studies compared a treatment group with access to calculators to a control group with no calculator access. These studies were conducted with students at all levels of the educational spectrum with the majority being high school and college students. The results best reflect attitudes after calculators were used for eight weeks or more. Hedges Q statistic revealed that the effect sizes were heterogeneous. One study (Aldridge, 1991) was determined to be an outlier through a process outlined by Huffcutt and Arthur (1995) and the remaining eighteen studies were a homogeneous data set with a weighted mean effect size of 0.11. The confidence interval did not contain zero. Therefore, students who used calculators during instruction reported better attitudes toward mathematics on attitude survey instruments than students who studied the same topic with similar instruction but did not have access to calculators.

With respect to type of calculator, seven studies compared a graphing calculator treatment group to a control group that had access to scientific calculators. These studies took place at the high school and college level and most of them lasted fifteen weeks or more. The test for homogeneity revealed that the group of studies was homogeneous. The weighted mean effect size of 0.21 had a corresponding confidence interval that did not contain zero. Therefore students who used graphing calculators while learning mathematics had better attitudes toward mathematics than their counterparts who used scientific calculators during the same class taught under similar instructional conditions. Six studies included survey questions on students' attitudes toward using calculators in mathematics. The control group in three studies had access to scientific calculators while the other three studies used no calculator control groups. One study was conducted with elementary students, one with middle school students, and the remaining research took place at the college level. A homogeneous data set was determined by Hedges Q statistic. The statistical analysis was conducted three times. Once with the entire set of studies, once with the scientific calculator control group studies, and once with the no calculator control group studies. In all three cases, the weighted mean effect size (0.30, 0.25, 0.31, respectively) and corresponding confidence intervals reveal that students enjoyed using calculators when learning mathematics. The three scientific calculator control group studies, all of which were conducted at the college level, reflect that students with graphing calculators have better attitudes toward using calculators during instruction than students who use scientific calculators.

A small number of studies reported survey results for other attitude factors of the Mathematics Attitude Inventory. Specifically, four studies looked at mathematics anxiety, three researchers reported results on student motivation to increase mathematical knowledge, two studies contained information on student self-concept in mathematics, and two studies reported on students beliefs related to the value of mathematics in society. For all four attitudinal factors, the test for homogeneity revealed a homogeneous data set. However, each weighted mean effect size had a corresponding confidence interval that contained zero. Therefore, for each attitudinal factor, the attitudes reported by students using calculators were no different than the attitudes of students who did not have access to calculators.

Summary

The results of this statistical summary reveal that students who use calculators report more positive attitudes toward mathematics on end of treatment surveys than their noncalculator counterparts. For students at the high school and college level, the use of graphing calculators has a more significant influence on students' attitudes toward mathematics than using scientific calculators. The results also support the fact that students enjoy having access to calculators while learning mathematics. Calculators are useful tools in the study of mathematics. Therefore, it is worthwhile knowing that allowing students' access to calculators will enhance their attitudes toward studying mathematics. The results of this study do not diminish the complexity of student attitudes and related factors. These results do add a new dimension to the established fact that calculators are beneficial to students' mathematics achievement (Hembree & Dessart, 1986; Ellington, 2003) and reveal that calculator use is influential to students in non-academic ways as well. Further research is needed on the role of the calculator in improving students' views with respect to other attitudinal factors like mathematics anxiety, student self-concept in mathematics, motivation to increase mathematical knowledge, and student perception of the value of mathematics in society.

References

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* Aldridge, W.B. (1991). The effects of utilizing calculators and a mathematics curriculum stressing problem solving techniques. Dissertation Abstracts International, 54, 0404A. (UMI No. AAC91-18846)

* Alkhateeb, H. (1995). The effect of using graphics calculators on student's attitudes towards mathematics and students' achievement in introductory calculus. Dissertation Abstracts International, 56, 2155.

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* Bartos, J.J. (1986). Mathematics achievement and the use of calculators for middle elementary grade children. Dissertation Abstracts International, 47, 1227A. (UMI No. AAC86-14912)

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Fennema, E., & Sherman, J. (1976). Mathematics attitude scales: Instruments designed to measure attitudes toward the learning of mathematics by males and females. Journal for Research in Mathematics Education, 7, 324-326.

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* Hylton-Lindsay, A.A. (1997). The Effect of the graphing calculator on metacognitive aspects of student performance in precalculus for business. Dissertation Abstracts International, 58, 3449.

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* Lim, C. (1992). Effects of using calculators on computational ability on non-college bound students, their attitudes toward mathematics and achievements on unit tests in probability and statistics. Dissertation Abstracts International, 52, 2450A. Lipsey, M., & Wilson, D. (2001). Practical meta-analysis. Thousand Oaks, CA: Sage.

* Liu, S.T. (1993). Effects of teaching calculator use and problem solving strategies on mathematics performance and attitude of fifth grade Taiwanese male and female students. Dissertation Abstracts International, 54, 4354A.

Ma, X. (1999). Dropping out of advanced mathematics: The effects of parental involvement. Teachers College Record, 101, 60-81.

Ma, X., & Kishor, N. (1997). Assessing the relationship between attitude toward mathematics and achievement in mathematics: A meta-analysis. Journal for Research in Mathematics Education, 28, 26-47.

* Merckling, W.J. (1999). Relationship(s) between the perceptual preferences of secondary school students and their achievement in functions using a graphing calculator. Dissertation Abstracts International, 60, 0371.

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* Norris, C.W. (1994). The impact of using graphic calculators as an aid for the teaching and learning of precalculus in a university setting. Dissertation Abstracts International, 55, 1862.

* Rich, S.B. (1991). The effect of the use of graphing calculators on the learning of function concepts in precalculus mathematics. Dissertation Abstracts International, 52, 0835.

* Riley, A.G. (1992). Effects of integrating TI Math Explorer calculators into the grades 3 through 6 mathematics curriculum on achievement and attitude. Dissertation Abstracts International, 54, 1661A.

* Rodgers, K.V. (1996) The effects on achievement, retention of mathematical knowledge, and attitudes toward mathematics as a result of supplementing the traditional algebra II curriculum with graphing calculator activities. Dissertation Abstracts International, 57, 0091.

Sandman, R.S. (1980). The mathematics attitude inventory: Instrument and user's manual. Journal for Research in Mathematics Education, 11, 148-149.

* Scott, B.A. (1994). The effect of graphing calculators in algebra II classrooms: A study comparing achievement, attitude, and confidence. Dissertation Abstracts International, 55, 2755.

* Seavertson, P. (1995). Comparing the use of the graphics calculator and scientific calculator in college algebra. Dissertation Abstracts International, 56, 4309.

* Starr, S. (1989). The effects of including calculators on the problem-solving instruction for low-income sixth-grade students. (ERIC Document Reproduction Service No. ED309070)

* Szetela, W., & Super, D. (1987). Calculators and instruction in problem solving in grade 7. Journal for Research in Mathematics Education, 18, 215-229.

* Thomasson, S.J. (1992). The effects of the graphing calculator on the achievement and attitude of college students enrolled in elementary algebra. Dissertation Abstracts International, 53, 3835.

* Vazquez, J.L. (1991). The effect of the calculator on student achievement in graphing linear functions. Dissertation Abstracts International, 51, 3660.

* Weber, T.E. (1999). Graphing technology and its effect on solving inequalities. Dissertation Abstracts International, 60, 0088.

Whisenant, M.A. (1989). The effects of the use of calculators in algebra I classes on basic skills maintenance and algebra achievement. Dissertation Abstracts International, 54, 0450A.

* Studies included in the meta-analysis

Aimee J. Ellington, Virginia Commonwealth University

Aimee Ellington is assistant professor mathematics education. Her research interests include the use of meta-analysis in education and technology in the mathematics classroom.
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Author:Ellington, Aimee J.
Publication:Academic Exchange Quarterly
Geographic Code:1USA
Date:Jun 22, 2004
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