The need for evidence-based research in the area of mathematics achievement is very important, yet our review of the literature reveals that there is a lack of current research concerning students with special needs and their uses of technology in this area. Read more about CITEd’s approach to the literature review in mathematics.
The review is organized into the following subtopics, each with a short practitioner-friendly article:
K-2 Calculator Technology
3-5 Calculator Technology
6-8 Calculator Technology
9-12 Calculator Technology
9-12 Calculator Technology: Algebra
9-12 Calculator Technology: Geometry
9-12 Calculator Technology: Data Analysis & Probability
The work presented here provides information about the level of evidence (i.e., emerging, promising, or evidence-based research) available to support the use of calculator types for specific subtopics within mathematics, by grade level. See the Overview for our research approach.
CITEd's review identified four broad calculator types: (1) basic, (2) scientific, (3) graphing, and (4) other, which is consistent with Ellington's (2003) work. Basic calculators are common and tend to perform basic operations, have minimal memory, and usually have an LCD screen. Scientific calculators are equipped to perform more complex functions and have larger memory stores. Graphing calculators tend to be the most advanced and can handle complex formulae, often have large screens to display graphs, and have more advanced capacities for memory. Other calculators might include ones that are specialized in financial and accounting fields, or are not easily represented in the typology scheme.
Ellington's work yielded several findings, but perhaps the most important one was that calculators had positive effects on operational and problem-solving skills when they were part of both instruction and later testing. In short, calculators appear to have positive effects on mathematics achievement, as long as they are used in instruction and testing. We reviewed some of the works in the meta-analysis and our conclusions were consistent. To provide some descriptive information, we discuss below some of the studies Ellington reviewed.
Ellington, A. J. (2003). A meta-analysis of the effects of calculators on students' achievement and attitude levels in precollege mathematics classes. Journal for Research in Mathematics Education, 34(5), 433-463.
We found three examples of how teachers have incorporated calculator use into their mathematics lessons, from teaching K-2 students how to count, to presenting them with basic algebraic concepts. In one class, two teachers worked with kindergarteners and first graders to use a calculator to explore numbers. As a result, students demonstrated increased familiarity with calculators and their functions. In another class, a two-line calculator was used. These calculators can be helpful by allowing students to see a whole formula or equation because there are two lines of text visible in the window. Finally, a third article described a way to use calculators to teach multiplication concepts. To learn more, click here and/or see the references below.
Huinker, D. (2002). Calculators as learning tools for young children's explorations of number. Teaching Children Mathematics, 8(6), 316-321.
St. John, D. & Lapp D.A. (2000). Developing numbers and operations with affordable handheld technology. Teaching Children Mathematics, 7(3)November 162-164.
McNamara, D.S. (1995). Effects of prior knowledge on the generation advantage: Calculators versus calculation to learn simple multiplication. Journal of Educational Psychology, 87(2), 307-318.
We found examples of how some researchers think calculators can be incorporated into math lessons to help students in grades 3-5 better understand numbers and operations. We found three articles that may be of interest. One looked into whether fifth graders thought graphing calculators helped them learn. Two articles describe types of calculators we think might support student learning because they display formulas and output at the same time. To learn more, click here and/or see the references below.
Graham, T., & Smith, P. (2004). An investigation into the use of graphics calculators with pupils in key stage 2. International Journal of Mathematical Education in Science and Technology, 35(2), 227-237.
Orton-Flynn, S. & Richards, C.J. (2000). The design and evaluation of an interactive calculator for children. Digital Creativity, 11(4), 205-217.
St. John, D. & Lapp D.A. (2000) Developing numbers and operations with affordable handheld technology. Teaching Children Mathematics, 7(3), November 162-164.
A single evidence-based practice using graphing calculators for algebra in grades 6-8 was found. Supporting this practice are three randomized controlled trials. One of these, Graham and Thomas (2000), studied a curriculum designed to promote students' ability to understand what a variable is by using the "store" function of a graphing calculator. The sample included 189 students (ages 13 and 14) of mixed ability; participants in the treatment group did significantly better from pre- to post-testing than those in the control group. This study demonstrated that using graphing calculators helps students understand what a variable is. In another randomized controlled trial, Owens (1995) compared multi-line, multi-operation calculators (classified here as a type of graphing calculator) to last-entry-or-result calculators (scientific) to see if the former would improve algebra and pre-algebra students' understanding of basic order of operation problems. Four eighth-grade classes participated, of which two were pre-algebra (lower ability) and two were algebra (higher ability). Sixty-one students were used in the analysis. Overall, there was a significant difference on algebra performance, favoring the treatment group. This demonstrated that graphing calculators are better than scientific calculators in helping students understand order of operations. To learn more, click here and/or see the references below.
Graham, A. T., & Thomas, M. O .J. (2000). Building a versatile understanding of algebraic variables with a graphic calculator. Educational Studies in Mathematics, 41(3), 265-282.
Owens, J. (1995, October). The day the calculator changed: Visual calculators in pre-algebra and algebra. Paper presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Columbus, OH.
Subtopic: 9-12 Calculator Technology
We found several examples of how some researchers and teachers think calculators can be incorporated into math lessons to help students in grades 9-12. In fact, there are too many to summarize here, so we developed three documents to give a feel for what is available in the broader literature. Specifically, we cover calculator applications that might help students learn (1) algebra (2) geometry and (3) data analysis and probability.
We found eighteen articles that summarize ideas some teachers and/or researchers thought were helpful. Five of these were actual studies that, in one way or another, considered whether calculators make a difference when teaching algebra. Although none of the studies used designs that can definitively answer the question, four of them supported the use of calculators (keep in mind these conclusions were reached under specific circumstances), and one study suggested it depends on the students' ability levels. Each study might provide some useful teaching strategies. We describe the other articles using an annotated bibliography and provide full citations so you can get the original work if you are intrigued by the teaching idea. To learn more, click here and/or see the references below.
Cedillo, T.E. (2001). Toward an algebra acquisition support system: A study based on using graphic calculators in the classroom. Mathematical Thinking and Learning, 3(4), 221-259.
Goos, M., Galbraith P., Renshaw, P., & Geiger, V. (2003). Perspectives on technology mediated learning in a secondary school mathematics classroom. Journal of Mathematical Behavior, 22,73-89.
Hubbard, D. (1998). Improving student knowledge of the graphing calculator's capabilities. An action research project submitted to the Graduate Faculty of the Saint Xavier University School of Education. Unpublished master's thesis, Saint Xavier University.
Lagrange, J. (1999). Techniques and concepts in pre-calculus using CAS: A two year classroom experiment with the TI-92. International Journal of Computer Algebra in Mathematics Education, 6(2), 143-165.
Mok, I.A.C. (1999, December). Learning opportunities with graphing calculators: The case of asymptotes. Research Report. Paper presented at the Asian Technology Conference on Mathematics. Guangzhou, China.
Several articles are available that provide ideas about how calculators can help teach geometry in grades 9-12; however, few are supported by research evidence. We found that the journal, Mathematics Teacher, is a rich source of information (although not the only one). It holds many descriptions of how teachers used (primarily) graphing calculators to teach about concepts such as polygons, graphing the curve of a basketball shot, quadratic functions, linear models, and so on. We provide a brief overview of these activities and full citations. To learn more, click here and/or see the references below.
Barnes, S. (1996). Perimeters, patterns, and pi. Mathematics Teacher, 89(4), 284-288.
Berthgold, T. (2004/2005) Curve stitching: Linking linear and quadratic functions, Mathematics Teacher, 98(5) 348-353.
Choi-Coh, S.S. (2003) Effect of a graphing calculator on a 10th grade student's study of trigonometry. The Journal of Educational Research, 96(6), 359-369.
Felsager, B. (2001). Mapping stars with TI-83. Micromath, 17(2), 26-31.
Marty, J. F. (1997). Centers of triangles exploration on the TI-92. Wisconsin Teacher of Mathematics, 48(2), 30-33.
Graphing calculators offer several strategies for teaching data analysis and probability concepts, possibly because data analysis has a visual component. One author shows how to use the calculators to illustrate the central limit theorem; another describes an activity using statistics from professional basketball to teach stochastic (i.e., random) concepts; yet another sets up Monte Carlo simulations; and so on. To learn more, click here and/or see the references below.
Barrett, G. B. (1999). Investigating distributions of sample means on the graphing calculator. Mathematics Teacher, 92(8), 744-747.
Doerr, H.M. & Zangor, R. (2000). Creating meaning for and with the graphing calculator. Educational Studies in Mathematics, 41(2), 143-163.
Teppo, A. R., & Hodgson, T. (2001). Dinosaurs, dinosaur eggs, and probability. Mathematics Teacher, 94(2), 86-92.