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Using Calculators for Teaching and Learning Mathematics

 

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This research brief is based on a synthesis of nearly 200 research studies, dating from 1976 to 2009, on calculator use in the classroom. Our goal here is to provide advice to practitioners and researchers on how the existing research base can be used to guide classroom practice and support future research. (See Rakes et al., 2011 for a full description of the literature review.) We address the common question of practice: Are there consistent findings in mathematics education technology research about the use of calculators? In general, we found that the body of research consistently shows that the use of calculators in the teaching and learning of mathematics does not contribute to any negative outcomes for skill development or procedural proficiency, but instead enhances the understanding of mathematics concepts and student orientation toward mathematics.

We divided the studies by types of calculator features (four-function, scientific, graphing, and advanced features such as CAS, dynamic geometry, and classroom connectivity) and by the year of the study in order to provide a sense of how calculator research has progressed over time (see figure 1). Earlier studies in the period were conducted on hand-held, four-function, and electronic calculators, and focused on student basic skills and/or orientation measures (e.g., mathematics anxiety) as outcomes (e.g., Hutton, 1976; Jamski, 1976; Jones, 1976; Lunder, 1978). With the advent of the graphing calculator, an overwhelming proportion of studies focused on the new features offered (e.g., dynamic geometry, statistics, CAS).

ResBrief_18_Fig1 

Examining such a large body of work makes the task of synthesizing difficult, but structured reviews of research make patterns, themes, and consistent effects much simpler to recognize. As a starting point, we reviewed three existing research syntheses to identify important trends and effects observed over time. Hembree and Dessart (1986) conducted one of the first calculator meta-analyses, considering 79 studies to assess the effects of calculators on student achievement and attitude. This study showed that using a calculator with traditional instruction improves students’ basic skills with paper and pencil, both in working exercises and in problem solving (with an exception for Grade 4) and that students at all grade levels and ability levels improved in self-concept and attitude. Hembree and Dessart analyzed more than a simple measure of student achievement. They captured categories of basic operations and problem solving across various conditions (e.g., skills acquisition with and without calculators and skills retention and transfer).

Ellington (2003) conducted a subsequent meta-analysis of 54 studies reported after the sample from Hembree and Dessart (1986) to determine if the effects of calculators noted by Hembree and Dessart on student achievement and attitude were consistent over time. She found that students’ operational skills and problem-solving skills improved when calculators were an integral part of testing and instruction. She also found that calculator use did not hinder the development of basic mathematical skills and additionally improved student attitudes toward mathematics.

In 2006, Ellington presented a meta-analysis that specifically targeted studies examining graphing calculators in middle, secondary, and post-secondary mathematics classes. Her meta-analysis of 42 studies showed that, regardless of the mode of testing, graphing calculators helped students understand mathematical concepts. Most strikingly, Ellington found, “There were no circumstances under which the students taught without calculators performed better than the students with access to calculators” (p. 24).

Collectively, these three meta-analyses provide a striking level of consistent findings across more than150 studies spanning several decades. Our current study incorporates the studies from each meta-analysis along with almost 50 additional studies, which included a wide range of research quality, methodologies, and contexts. The result: we found no evidence to contradict the previous analyses’ findings (Rakes, et al., 2011).

Few areas in mathematics education technology have had such focused attention with such consistent results, yet the issue of whether the use of calculators is a positive addition to the mathematics classroom is still questioned in many areas of the mathematics community, as evidenced by continually repeated studies of the same topic. As a result, we concluded that future practitioner questions about calculator use for mathematics teaching and learning should advance from questions of whether or not they are effective to questions of what effective practices with calculators entail. Another question to explore is how their capabilities can be combined with other technologies to produce learning experiences not possible without the technology (e.g., probeware, classroom response systems). Researchers, on the other hand, should build on the existing base by pursuing questions about such effective practices and the structures needed at the classroom and school level to support calculator use in the classroom.

One particular line of research illustrates this point clearly. A four-year longitudinal study involving teacher professional development included both student and teacher outcomes, measured both quantitatively and qualitatively (Irving, Sanalan, & Shirley, 2009; Irving et al., 2010; Owens et al., 2008; Pape, Bell, Owens, & Sert, 2011; Pape, et al., 2010; Pape, Irving, Owens, et al., 2011; Shirley, Irving, Sanalan, Pape, & Owens, 2011). This line of research went beyond merely measuring effect sizes quantitatively or describing patterns of teacher behavior through classroom observation. These studies also examined the components of professional development that increased teacher knowledge about technology (such as TPACK: see Mishra & Koehler, 2006; Niess, 2005; Niess et al., 2009) and how that knowledge translated into practices that were more or less effective for enhancing student achievement, learning, orientation, and learning behaviors in mathematics (Pape, Irving, Bell, et al., 2011).  

Authors of practitioner journal articles should also begin to take advantage of the solid research base for calculator usage in the mathematics classroom. For example, more explicit links to research should be included in articles and book chapters for practitioners presenting teaching strategies and in resource books for teachers on how to use technology in the classroom. Such a practice is not currently held as a standard: Only 18 of the 100 such papers in our sample made any connections to research. The dearth of such connections in practitioner articles points to a need for the field to begin concentrating on enhancing the use of the existing research base for informing practice and disseminating ideas to others.

In summary, a wide array of evidence of nearly four decades points to the usefulness of calculators for enhancing student achievement, learning concepts, orientation towards mathematics, and learning behaviors in mathematics. This evidence could propel practitioners to begin to produce robust, dynamic learning environments in which students learn mathematics with understanding and emerge ready to apply mathematics to issues unique to the 21st century. Meanwhile, new lines of research should investigate phenomena beyond whether or not calculators are effective; instead, we can begin to explore the conditions, resources, and contexts needed to maximize the degree to which calculator use can enhance the teaching and learning of mathematics.

By Robert N. Ronau
University of Louisville

Christopher R. Rakes
Institute of Education Sciences

Sarah B. Bush
Bellarmine University

Shannon Driskell
University of Dayton

Margaret L. Niess
Oregon State University

David Pugalee
University of North Carolina–Charlotte 

Karen D. King, Series Editor 

 

References 

Ellington, A. (2003). A meta-analysis of the effects of calculators on students in precollege mathematics classes. Journal for Research in Mathematics Education, 34, 433–463.

Ellington, A. J. (2006). The effects of non-CAS graphing calculators on student achievement and attitude levels in mathematics: A meta-analysis. International Journal of Instructional Media, 106, 16–26.

Hembree, R., & Dessart, D. (1986). Effects of hand-held calculators in precollege mathematics education: A meta-analysis. Journal for Research in Mathematics Education, 17, 83–99.

Hutton, L. A. (1976). The effects of the use of mini-calculators on attitude and achievement in mathematics. Dissertation Abstracts International-A, 37(08), 4934. (UMI No. AAT 7703347)

Irving, K. E., Pape, S. J., Owens, D. T., Abrahamson, A. L., Silver, D., & Sanalan, V. A. (2010, May). Longitudinal study of classroom connectivity in promoting mathematics and science achievement: Years 1–3. Paper presented at the Annual Meeting of the American Educational Research Association, Denver, CO.

Irving, K. E., Sanalan, V. A., & Shirley, M. L. (2009). Physical science connected classrooms: Case studies. Journal of Computers in Mathematics and Science Teaching, 28, 247–275.

Jamski, W. D. (1976). The effect of hand calculator use on the achievement of seventh-graders learning rational number-decimal-percent conversion algorithms. Dissertation Abstracts International-A, 37(08), 4934. (UMI No. AAT 7703349)

Jones, E. W. (1976). The effect of the hand-held calculator on mathematics achievement, attitude and self-concept of sixth grade students. Dissertation Abstracts International-A, 37(03), 1387. (UMI No. AAT 7619885)

Lunder, D. A. (1978). The impact of the calculator on test anxiety for high school consumer mathematics students. Dissertation Abstracts International-A, 39(11), 6607. (UMI No. AAT 7910673)

Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108, 1017–1054.

Niess, M. L. (2005). Preparing teachers to teach science and mathematics with technology: Developing a technology pedagogical content knowledge. Teaching and Teacher Education, 21, 509-523.

Niess, M. L., Ronau, R. N., Shafer, K. G., Driskell, S. O., Harper, S. R., & Johnston, C. (2009). Mathematics teacher TPACK standards and development model. Contemporary Issues in Technology & Teacher Education, 9, 4–24.

Owens, D. T., Pape, S. J., Irving, K. E., Sanalan, V.A., Boscardin, C. K., & Abrahamson, L. (2008, July). The connected algebra classroom: A randomized control trial. In C. Laborde & C. Knigos (Eds.). Proceedings for Topic Study Group 22, Eleventh International Congress on Mathematics Education. Monterrey, Mexico. Retrieved July 2, 2009 from http://tsg.icme11.org/document/get/249 

Pape, S. J., Bell, C. V., Owens, S. K., Bostic, J. D., Irving, K. E., Owens, D. T., et al. (2010, May). Examining verbal interactions within connected mathematics classrooms. Paper presented at the Annual Meeting of the American Educational Research Association, Denver, CO.

Pape, S. J., Bell, C. V., Owens, D. T., & Sert, Y. (2011). Examining teachers’ use of the TI-Navigator™ to support students’ understanding of quadratic equations and parabolas. Manuscript in preparation.

Pape, S. J., Irving, K. E., Bell, C. V., Shirley, M. L., Owens, D. T., Owens, S. K., Bostic, J. D., & Lee, S. C. (2011). Principles of Effective Pedagogy within the Context of Connected Classroom Technology: Implications for Teacher Knowledge. In R. N. Ronau, C. R. Rakes, & M. L. Niess (Eds.), Educational technology, teacher knowledge, and classroom impact: A research handbook on frameworks and approaches (pp. 176–199). Hershey, PA: IGI Global.

Pape, S. J., Irving, K. E., Owens, D. T., Boscardin, C. K., Sanalan, V. A., Abrahamson, A. L., et al. (2011). Classroom connectivity in algebra I classrooms: Results of a randomized control trial. Manuscript submitted for publication. 

Rakes, C. R., Ronau, R. N., Niess, M. L., Driskell, S. , Pugalee, D., & Bush, S. (2011, January). Research in mathematics instructional technology: Current trends and future demands. Symposium presented at the annual meeting of the Association of Mathematics Teacher Educators, Irvine, CA.

Shirley, M. L., Irving, K. E., Sanalan, V. A., Pape, S. J., & Owens, D. T. (2011). The practicality of implementing connected classroom technology in secondary mathematics and science classrooms. International Journal of Science and Mathematics Education, 9, 459–481.  


 

 The development of this brief was supported by the National Science Foundation under Grant No. 0946875

Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).

 

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