The design of lessons using mathematics analysis software to support multiple representations in secondary school mathematics

Technology, Pedagogy and Education

Volumn 20, Issue 1, 2011, Pages 95-112

  Pierce, Robyn ^a   Stacey, Kaye ^a   Wander, Roger ^a   Ball, Lynda ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Lesson design; Lesson study; Mathematics analysis software; Multiple representations; Professional development; Secondary mathematics; Technology

Indexed keywords

EID: 79953139048     PISSN: 1475939X     EISSN: 17475139     Source Type: Journal    
DOI: 10.1080/1475939X.2010.534869     Document Type: Article

References (26)

1. Ainsworth, S., Bibby, P.A., & Wood, D.J. (1998). Analysing the costs and benefits of multirepresentational learning environments. In M.W. van Someren, P. Reimann, H.P.A. Boshuizen, & T. de Jong (Eds.), Learning with multiple representations (pp. 120-134). Amsterdam: Pergamon Press.
2. Artigue, M., & Lagrange, J.-B. (1997). Pupils learning algebra with DERIVE: A didactive perspective. Zentralblatt für Didaktik der Mathematik, 29(4), 105-112.
3. Demana, F., & Waits, B.K. (1989). Around the sun in a graphing calculator. The Mathematics Teacher, 82(7), 546-550.
4. Dreyfus, T. (1994). The role of cognitive tools in mathematics education. In R. Biehler, R.W. Scholz, R. Sträßer, & B. Winelmann (Eds.), Didactics of mathematics as a scientific discipline (pp. 201-211). Dordrecht, Netherlands: Kluwer Academic Publishers.
5. Drijvers, P. (2003). Learning algebra in a computer algebra environment. Utrecht, Netherlands: Freudenthal Insititute.
6. Ferrara, F., Pratt, D., & Robutti, O. (2006). The role of technologies for the teaching of algebra and calculus. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education (pp. 237-273). Rotterdam, Netherlands: Sense Publishers.
7. Friedlander, A., & Tabach, M. (2001). Promoting multiple representations in algebra. In A. Cuoco & F. Curcio (Eds.), 2001 yearbook of the National Council of the Teachers of Mathematics: The roles of representation in school mathematics (pp. 173-185). Reston, VA: National Council of Teachers of Mathematics.
8. Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. In A. Cuoco & F. Curcio (Eds.), 2001 yearbook of the National Council of the Teachers of Mathematics: The roles of representation in school mathematics (pp. 1-23). Reston, VA: National Council of Teachers of Mathematics.
9. Gravemeijer, K. (2004). Local instruction theories as means of support for teachers in reform mathematics education. Mathematical Thinking and Learning, 6(2), 105-128.
10. Herman, M. (2007). What students choose to do and have to say about use of multiple representations. The Journal of Computers in Mathematics and Science Teaching, 26(1), 27-54.
11. Isoda, M., Stephens, M., Ohara, Y., & Miyakawa, T. (Eds.). (2007). Japanese lesson study in mathematics. Its impact, diversity and potential for educational improvements. Hackensack, NJ: World Scientific.
12. 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.
13. Kendal, M., & Stacey, K. (2001). The impact of teacher privileging on learning differentiation with technology. International Journal of Computers for Mathematical Learning, 6(2), 143-165.
14. Kieran, C., & Saldanha, L. (2008). Designing tasks for the codevelopment of conceptual and technical knowledge in CAS activity. In G. Blume & K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Volume 2 Cases and perspectives (pp. 393-414). Charlotte, NC: Information Age Publishing.
15. Leikin, R., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics, 66(3), 349-371.
16. National Council of Teachers of Mathematics. (1989). Principles and standards for school mathematics. Reston, VA: Author.
17. Pierce, R., & Stacey, K. (2001). Observations on students' responses to learning in a CAS environment. Mathematical Education Research Journal, 13(1), 28-46.
18. Pierce, R., & Stacey, K. (2009). Lesson study with a twist: Researching lesson design by studying classroom implementation. In M. Tzekaki, M. Kaldrimidou, & C. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education Vol. 4 (pp. 369-376). Thessaloniki, Greece: PME.
19. Seufert, T., Jänsen, I., & Brünken, R. (2007). The impact of intrinsic cognitive load in the effectiveness of graphical help for coherence formation. Computers in Human Behavior, 23, 1055-1071.
20. Shavelson, R., Phillips, D., Towne, L., & Feuer, M. (2003). On the science of design studies. Educational Researcher, 32(1), 25-28.
21. Silver, E.A., Ghousseini, H., Gosen, D., Charalambous, C., & Font Strawhun, B.T. (2005). Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom. Journal of Mathematical Behavior, 24, 287-301.
22. Smith, M.S., Silver, E.A., & Stein, M.K. (2005). Improving instruction in rational numbers and proportionality: Using cases to transform mathematics teaching and learning (Vol. 1). New York: Teachers College Press.
23. Sweller, J., van Merrienboer, J.G., & Paas, F.G.W. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10, 251-296.
24. Thomas, M.O.J. (2008). Conceptual representations and versatile mathematical thinking. In M. Niss (Ed.), ICMI-10 proceedings and regular lectures. Copenhagen, Denmark.
25. Wander, R., & Pierce, R. (2009). Marina's fish shop: A mathematicallyand technologicallyrich lesson. Australian Mathematics Teacher, 65(2), 6-12.
26. Zehavi, N., & Mann, G. (2003). Task design in a CAS environment: Introducing (in)equations. In J.T. Fey, A. Cuoco, C. Kieran, L. McMullin, & R.M. Zbiek (Eds.), Computer algebra systems in secondary school mathematics education (pp. 173-191). Reston, VA: National Council of Teachers of Mathematics.