Do teachers find that the use of dynamically linked multiple representations enhances their students’ relational understanding of the mathematics involved in their lessons and what evidence do they provide to support their findings? Throughout session 2008–2009, this empirical research project involved six Scottish secondary schools, two mathematics teachers from each school and students from different ages and stages. Teachers used TI-Nspire PC software and students the TI-Nspire handheld technology. This technology is specifically designed to allow dynamically linked multiple representations of mathematical concepts such that pupils can observe links between cause and effect in different representations such as dynamic geometry, graphs, lists and spreadsheets. The teachers were convinced that the use of multiple representations of mathematical concepts enhanced their students’ relational understanding of these concepts, provided evidence to support their argument and described changes in their classroom pedagogy.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Adu-Gyamfi, K. (2002). External multiple representations in mathematics teaching. Unpublished thesis, North Carolina State University, Raleigh.
Amit, M., & Fried, M. N. (2005). Multiple representations in 8th grade algebra lessons: Are learners really getting it? In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 57–64). Melbourne: PME.
Brenner, M. E., Mayer, R. E., Moseley, B., Brar, T., Duran, R., Smith Reed, B., et al. (1997). Learning by understanding: The role of representations in learning algebra. American Educational Research Journal, 34(4), 663–689.
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. Dallas, TX: Texas Instruments.
Clark-Wilson, A. (2008). Evaluating TI-Nspire in Secondary Mathematics Classrooms. Chichester: University of Chichester.
Cresswell, J. W., & Plano Clark, V. L. (2007). Designing and Conducting Mixed Methods Research. London: Sage Publications Ltd.
Davis, R. B., & Maher, C. A. (1997). How students think: The role of representations. In L. D. English (Ed.), Mathematical Reasoning: Analogies, Metaphors, and Images (pp. 93–115). Mahwah, NJ: Lawrence Erlbaum Associates.
Drijvers, P., & Trouche, L. (2008). From artifacts to instruments. A theoretical framework behind the orchestra metaphor. In: G. W. Blume & M. K. Heid (Eds.), Research on Technology and the Teaching and Learning of Mathematics, Cases and Perspectives, Vol. 2. Charlotte, NC: National Council of Teachers of Mathematics, Information Age Publishing.
Duncan, A. G. (2010). Teachers’ views on dynamically linked multiple representations and relational understanding of mathematics—an investigation into the use of TI-Nspire in Scottish secondary schools. Aberdeen: University of Aberdeen.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103–131.
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.
Even, R. (1998). Factors involved in linking representations of functions. Journal of Mathematical Behavior, 17(1), 105–121.
Farrell, A. M. (1996). Roles and behaviors in technology-integrated precalculus classrooms. The Journal of Mathematical Behavior, 15(1), 33–53.
Guin, D., & Trouche, L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematics Learning, 3, 195–227.
Hegedus, S., & Kaput, J. (2007). Lessons from SimCalc: What Research Says, Research Note 6. Dallas, TX: Texas Instruments.
Hegedus, S., Kaput, J., Dalton, S., Brookstein, A., Moniz, J., & Roschelle, J. (2007). SimCalc Classroom Connectivity Project 2: Understanding Classroom Interactions among Diverse, Connected Classroom Technologies, Overview of Present Findings of a 4 Year Study (2004–2008). Dartmouth, MA: University of Massachusetts.
Hembree, R., & Dessart, D. J. (1986). Effects of hand-held calculators in pre-college mathematics education: A meta-analysis. Journal for Research in Mathematics Education, 17(2), 83–99.
Hollar, J. C., & Norwood, K. (1999). The effects of a graphing-approach intermediate algebra curriculum on students’ understanding of function. Journal for Research in Mathematics Education, 30(2), 220–226.
Johnson, R. B., & Onwuegbuzie, A. J. (2004). Mixed methods research: A research paradigm whose time has come. Educational Researcher, 33(7), 14–26.
Kaput, J. (1992). Technology and mathematics education. In D. Grouws (Ed.), A Handbook of Research on Mathematics Teaching and Learning (pp. 515–556). New York: MacMillan.
Kaput, J., Noss, R., & Hoyles, C. (2002). Developing new notations for a learnable mathematics in the computational era. In L. D. English (Ed.), Handbook of International Research on Mathematics Education (pp. 51–75). Mahwah, NJ: Lawrence Erlbaum Associates.
Kieran, C. (1993). Functions, graphing, and technology: Integrating research on learning and instruction. In T. A. Romberg, T. P. Carpenter, & E. Fennema (Eds.), Integrating Research on the Graphical Representation of Functions (pp. 189–237). Hillsdale, NJ: Erlbaum.
Kozma, R., Russell, J., Jones, T., Marx, N., & Davis, J. (1996). The use of multiple, linked representations to facilitate science understanding. In S. Vosniadou, E. De Corte, R. Glaser, & H. Mandl (Eds.), International Perspectives on the Design of Technology-Supported Learning Environments (pp. 41–60). Mahwah, NJ: Lawrence Earlbaum Associates.
National Council of Teachers of Mathematics (undated). Principles and Standards for School Mathematics. Accessed 19 July 2010. http://standards.nctm.org/document/chapter3/rep.htm.
Roschelle, J. (1992). Learning by collaborating: Convergent conceptual change. Journal of the Learning Sciences, 2(3), 235–276.
Roschelle, J., & Gallagher, L. (2005). A research perspective on using graphing calculator interventions to improve mathematics achievement, SRI Report P11961.560, California, USA.
Roschelle, J., Pea, R., Hoadley, C., Gordin, D., & Means, B. (2000). Changing how and what children learn in school with computer-based technologies. The Future of Children, 10(2), 76–101.
Ruthven, K. (1990). The influence of graphic calculator use on translation from graphic to symbolic forms. Educational Studies in Mathematics, 21(5), 431–450.
Ruthven, K., Deaney, R., & Hennessy, S. (2009). Using graphing software to teach about algebraic forms: a study of technology-supported practice in secondary-school mathematics. Educational Studies in Mathematics, 71, 279–297.
Ruthven, K., & Hennessy, S. (2003). Successful ICT use in secondary mathematics—a teacher perspective. Micromath, 19(2), 20–24.
Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
Skemp, R. R. (1987). The Psychology of Learning Mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.
Tall, D. O., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular references to limits and continuity. Educational Studies in Mathematics, 12, 151–169.
Tashakkori, A., & Teddlie, C. (Eds.). (2003). Handbook of Mixed Methods in Social and Behavioural Research. Thousand Oaks, CA: Sage.
Weber, K. (2002). The Role of Instrumental and Relational Understanding in Proofs about Group Isomorphisms, Proceedings of the 2nd International Conference in Teaching Mathematics, Greece. Accessed 27 January 2010. http://www.math.uoc.gr/~ictm2/.
Williams, S. R. (1993). Some common themes and uncommon directions. In T. A. Romberg, T. P. Carpenter, & E. Fennema (Eds.), Integrating Research on the Graphical Representation of Functions (pp. 313–338). Hillsdale, NJ: Erlbaum.
About this article
Cite this article
Duncan, A.G. Teachers’ views on dynamically linked multiple representations, pedagogical practices and students’ understanding of mathematics using TI-Nspire in Scottish secondary schools. ZDM Mathematics Education 42, 763–774 (2010). https://doi.org/10.1007/s11858-010-0273-6
- Mathematics Teacher
- Classroom Practice
- Continue Professional Development
- Multiple Representation
- Lesson Evaluation