The Role of Technology in Supporting Students’ Mathematical Thinking: Extending the Metaphors of Amplifier and Reorganizer
ARTICLE
Milan Sherman, Drake University, United States
CITE Journal Volume 14, Number 3, ISSN 15285804 Publisher: Society for Information Technology & Teacher Education, Waynesville, NC USA
Abstract
The use of instructional technology in secondary mathematics education has proliferated in the last decade, and students’ mathematical thinking and reasoning has received more attention during this time as well. However, few studies have investigated the role of instructional technology in supporting students’ mathematical thinking. In this study, the implementation of 63 mathematical tasks was documented in three secondary and one middle school mathematics classroom, and the Mathematical Tasks Framework (Stein & Smith, 1998) was used to correlate the cognitive demand of mathematical tasks with the use of technology as an amplifier or reorganizer of students’ mental activity (Pea, 1985, 1987). Results indicate that the use of technology generally aligned with teachers’ current practice in terms of the distribution of low and highlevel tasks enacted in their classrooms. However, the use of technology as a reorganizer of students’ thinking was strongly correlated with these teachers’ attempts to engage their students with highlevel tasks. The distinction between using technology as an amplifier or a reorganizer is refined and extended through its application at the grain size of mathematical tasks, and implications for mathematics teacher education are discussed.
Citation
Sherman, M. (2014). The Role of Technology in Supporting Students’ Mathematical Thinking: Extending the Metaphors of Amplifier and Reorganizer. Contemporary Issues in Technology and Teacher Education, 14(3), 220246. Waynesville, NC USA: Society for Information Technology & Teacher Education. Retrieved March 24, 2019 from https://www.learntechlib.org/primary/p/130321/.
© 2014 Society for Information Technology & Teacher Education
References
 BenZvi, D. (2000). Toward understanding the role of technological tools in statistical learning. Mathematical Thinking and Learning, 2(1 & 2), 127–155.
 Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. The Teachers College Record, 110(3), 608–645.
 Boston, M.D., & Smith, M.S. (2009). Transforming secondary mathematics teaching: Increasing the cognitive demands of instructional tasks used in teachers’ classrooms. Journal for Research in Mathematics Education, 40(2), 119–156.
 Boutell, M., & Clifton, C. (2011). SPLICE: Selfpaced learning in an inverted classroom environment. In Proceedings of the 42nd ACM Technical Symposium on Computer Science Education. New York, NY: Association for Computing Machinery.
 Burrill, G., Allison, J., Breaux, G., Kastberg, S., Leatham, K., & Sanchez, W. (2002). Handheld graphing technology in secondary mathematics: Research findings and implications for classroom practice. Retrieved from the Texas Instruments website: http://education.ti.com/sites/UK/downloads/pdf/References/Done/Burrill,G.%20(2002).pdf
 Chazan, D. (1999). On teachers’ mathematical knowledge and student exploration: A personal story about teaching a technologically supported approach to school algebra. International Journal of Computers for Mathematical Learning, 4, 121–149.
 Chazan, D. (2000). Toward a “conceptual understanding” of school algebra. New York, NY: Teachers College Press.
 Common Core State Standards Initiative. (2010). Common core state standards (Mathematics standards). Retrieved from http://www.corestandards.org/thestandards/mathematics
 Cuban, L., Kirkpatrick, H., & Peck, C. (2001). High access and low use of technologies in high school classrooms: Explaining an apparent paradox. American Educational Research Journal, 38(4), 813.
 Cuoco, A., Goldenberg, E.P., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. Journal of Mathematical Behavior, 15, 375–402.
 Deslauriers, L., Schelew, E., & Wieman, C. (2011). Improved learning in a largeenrollment physics class. Science, 332(6031), 862–864.
 Doerr, H.M., & Zangor, R. (2000). Creating meaning for and with the graphing calculator. Educational Studies in Mathematics, 41(2), 143–163.
 Earle, R.S. (2002). The integration of instructional technology into public education: Promises and challenges. Educational Technology, 42(1), 5–13.
 Farrell, A.M. (1996). Roles and behaviors in technologyintegrated precalculus classrooms. The Journal of Mathematical Behavior, 15(1), 35–53.
 Foertsch, J., Moses, G., Strikwerda, J., & Litzkow, M. (2002). Reversing the lecture/homework paradigm using eTEACH® webbased streaming video software. Journal of Engineering Education, 91(3), 267–274.
 Galbraith, P. (2006). Students, mathematics, and technology: Assessing the present– challenging the future. International Journal of Mathematical Education in Science and Technology, 37(3), 277–290.
 Gannod, G.C., Burge, J.E., & Helmick, M.T. (2008). Using the inverted classroom to teach software engineering. In Proceedings of the 30th International Conference on Software Engineering (pp. 777–786). New York, NY: Association for Computing
 Goos, M., Galbraith, P., Renshaw, P., & Geiger, V. (2003). Perspectives on technology mediated learning in secondary school mathematics classrooms. The Journal of Mathematical Behavior, 22(1), 73–89.
 Heid, M.K. (1988). Resequencing skills and concepts in applied calculus using the computer as a tool. Journal for Research in Mathematics Education, 19(1), 3–25.
 Heid, M.K. (1997). The technological revolution and reform of school mathematics. American Journal of Education, 106, 5–61.
 Henningsen, M.A., & Stein, M.K. (1997). Mathematical tasks and student cognition: Classroombased factors that support and inhibit highlevel mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549.
 Hollebrands, K.F., Conner, A.M., & Smith, R.C. (2010). The nature of arguments provided by college geometry students with access to technology while solving problems. Journal for Research in Mathematics Education, 41(4), 324–350.
 Hollebrands, K.F., Laborde, C., & StraBer, R. (2008). Technology and the learning of geometry at the secondary level. In M.K. Heid & G.W. Blume (Eds.), Research on technology in the teaching and learning of mathematics: Research syntheses (Vol. 1, pp. 155–205). Charlotte, NC: Information Age Publishing.
 Huntley, M.A., Rasmussen, C.L., Villarubi, R.S., Sangtong, J., & Fey, J.T. (2000). Effects of standardsbased mathematics education: A study of the CorePlus Mathematics Project Algebra and Functions strand. Journal for Research in Mathematics Education, 31(3), 328–61.
 Judson, P.T. (1990). Elementary business calculus with computer algebra. Journal of Mathematical Behavior, 9(2), 153–157.
 Kastberg, S., & Leatham, K. (2005). Research on graphing calculators at the secondary level: Implications for mathematics teacher education. Contemporary Issues in Technology and Teacher Education, 5(1), 25–37.
 Koehler, M.J., & Mishra, P. (2008). Introducing technological pedagogical content knowledge. In AACTE Committee on Innovation and Technology (Ed.), Handbook of technological pedagogical content knowledge (TPCK) for educators (pp. 3–29). New
 Lage, M.J., Platt, G.J., & Treglia, M. (2000). Inverting the classroom: A gateway to creating an inclusive learning environment. The Journal of Economic Education, 31(1), 30–43.
 Lappan, G., Fey, J., Fitzgerald, W., Friel, S., & Phillips, E.D. (2006). Connected mathematics 2: Grade 6. Pearson Prentice Hall.
 Lee, H.S., & Hollebrands, K.F. (2008). Preparing to teach mathematics with technology: An integrated approach to developing technological pedagogical content knowledge. Contemporary Issues in Technology and Teacher Education, 14(3) Contemporary Issues in Technology and Teacher Education, 8(4), 326–341. Retrieved from http://citejournal.org/vol8/iss4/mathematics/article1.cfm
 Mishra, P., & Koehler, M.J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017–1054.
 Monaghan, J. (2004). Teachers’ activities in technologybased mathematics lessons. International Journal of Computers for Mathematical Learning, 9(3), 327–357.
 Moore, A.J., Gillett, M.R., & Steele, M.D. (2014). Fostering student engagement with the flip. Mathematics Teacher, 107(6), 420.
 National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.
 National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
 National Council of Teachers of Mathematics. (2009). Focus in high school mathematics: Reasoning and sensemaking. Reston, VA: Author.
 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.
 Norton, S., McRobbie, C.J., & Cooper, T.J. (2000). Exploring secondary mathematics teachers’ reasons for not using computers in their teaching: Five case studies. Journal of Research on Computing in Education, 33(1), 87–109.
 Novak, G.M., Patterson, E.T., Gavrin, A.D., Christian, W., & Forinash, K. (1999). Just in time teaching. American Journal of Physics, 67, 937.
 O’Callaghan, B.R. (1998). Computerintensive algebra and students’ conceptual knowledge of functions. Journal for Research in Mathematics Education, 29(1), 21–40.
 Palmiter, J.R. (1991). Effects of computer algebra systems on concept and skill acquisition in calculus. Journal for Research in Mathematics Education, 22(2), 151–156.
 Pea, R.D. (1985). Beyond amplification: Using the computer to reorganize mental functioning. Educational Psychologist, 20(4), 167–182.
 Pea, R.D. (1987). Cognitive technologies in mathematics education. In A.H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 89–122). Hilldale, NJ:
 Peressini, D., & Knuth, E.J. (2005). The role of technology in representing mathematical problem situations and concepts. In W.J. Masalski & P.C. Elliott (Eds.), Technologysupported mathematics learning environments, 2005 Yearbook of the National Council of Teachers of Mathematics (pp. 277–290). Reston, VA: National Council of Teachers of
 Prober, C.G., & Heath, C. (2012). Lecture halls without lectures—a proposal for medical education. New England Journal of Medicine, 366(18), 1657–1658.
 Romberg, T.A. (1994). Classroom instruction that fosters mathematical thinking and problem solving: Connections between theory and practice. In A.H. Schoenfeld (Ed.), Mathematical thinking and problem solving (pp. 287–304). Hillsdale, NJ: Erlbaum.
 Russell, M., Bebell, D., O’Dwyer, L., & O’Connor, K. (2003). Examining teacher technology use: Implications for preservice and inservice teacher preparation. Journal of Teacher Education, 54(4), 297–310.
 Schwarz, B.B., & Hershkowitz, R. (1999). Prototypes: Brakes or levers in learning the function concept? The role of computer tools. Journal for Research in Mathematics Education, 30(4), 362–389.
 Sherman, M.F. (2012). Supporting students’ mathematical thinking during technologyenhanced investigations using DGS. In D. Martinovic, D. McDougall, & Z. Karadag (Eds.),
 Stein, M.K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50–80.
 Stein, M.K., & Smith, M.S. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School, 3(4), 268–75.
 Stein, M.K., Smith, M.S., Henningsen, M.A., & Silver, E.A. (2009). Implementing standardsbased mathematics instruction: A casebook for professional development (2nd ed.). New York, NY: Teachers College Press.
 Stigler, J.W., & Hiebert, J. (2004). Improving mathematics teaching. Educational Leadership, 61(5), 12–17.
 Strayer, J.F. (2012). How learning in an inverted classroom influences cooperation, innovation and task orientation. Learning Environments Research, 15(2), 171–193.
 Suh, J. (2010). Leveraging cognitive technology tools to expand opportunities for critical thinking in elementary mathematics. Journal of Computers in Mathematics and Science Teaching, 29(3), 14.
 Weiss, I.R., & Pasley, J.D. (2004). What is highquality instruction? Educational Leadership, 61(5), 24–28.
 Weiss, I.R., Pasley, J.D., Smith, P.S., Banilower, E.R., & Heck, D.J. (2003). Looking inside the classroom: A study of K12 mathematics and science education in the United States. Chapel Hill, NC: Horizon Research Inc. Available at http: www.horizonresearch.com
 Winterbottom, S. (2007). Virtual lecturing: Delivering lectures using screencasting and podcasting technology. Planet, (18), 6–8.
 Zbiek, R.M., Heid, M.K., Blume, G.W., & Dick, T.P. (2007). Research on technology in mathematics education: The perspective of constructs. In F.K. Lester (Ed.), Second handbook of research in mathematics teaching and learning (pp. 1169–1207). Charlotte,
These references have been extracted automatically and may have some errors. If you see a mistake in the references above, please contact info@learntechlib.org.
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