********************************* NOTE: The ICMI Study 22 on Task Design in Mathematics Education is underway. The ICMI Study Conference will be held in Oxford, UK, on July 22-26. The proceedings of this conference are already available and can be accessed at http://hal.archives-ouvertes.fr/docs/00/83/74/88/PDF/ICMI_STudy_22_proceedings_2013-FINAL_V2.pdf . The Introduction in the proceedings is attached for your information. ********************************************** Task Design in Mathematics Education. Proceedings of ICMI Study 22
Claire Margolinas (07/2013)
There has been a recent increase in interest in task design as a focus for research and development in mathematics education. This is well illustrated by the success of theoretically based long term design research projects in which design and research over time have combined to develop materials and approaches that have appealed to teachers. One area of investigation is how published tasks are appropriated by teachers for complex purposes and influences mathematics teaching. Tasks generate activity which affords opportunity to encounter mathematical concepts and also to use and develop mathematical thinking and modes of enquiry. Tasks also arise spontaneously in educational contexts, with teachers or learners raising questions or providing prompts for action by drawing on a repertoire of past experience. We are interested in how these are underpinned with implicit design principles. It is important to address also the question of sequences of tasks and the ways in which they link aspects of conceptual knowledge. The communities involved in task design are naturally diverse: designers, professional mathematicians, teacher educators, teachers, researchers, learners, authors, publishers and manufacturers, and individuals acting in several of these roles. We wish to illuminate the diverse communities and methods that lead to the development and use of tasks. [ http://hal.archives-ouvertes.fr/hal-00834054 ]
Margolinas, C. (Ed.). (2013). Task Design in Mathematics Education. Proceedings of ICMI Study 22 (Vol. 1). Oxford.
Anne Watson University of Oxford, UK
Minoru Ohtani Kanazawa University, Japan
Janet Ainley School of Education, University of Leicester, UK
Janete Bolite Frant LOVEME Lab, UNIBAN, Brazil
Michiel Doorman Utrecht University, Netherlands
Carolyn Kieran Université du Québec à Montréal, Canada
Allen Leung Hong Kong Baptist University, Hong Kong
Claire Margolinas Laboratoire ACTé, Université Blaise Pascal, France
Peter Sullivan Monash University, Australia
Denisse Thompson University of South Florida, USA
Yudong Yang Shanghai Academy of Educational Sciences, China
The study aims to produce a state-of-the-art summary of relevant research and to go beyond that summary to develop new insights and new areas of knowledge and study about task design. In particular, we aim to develop more explicit understanding of the difficulties involved in designing and implementing tasks, and of the interfaces between the teaching, researching, and designing roles - recognising that these might be undertaken by the same person, or by completely separate teams.
Ainley, J., Bills, L., & Wilson, K. (2004). Algebra for a Purpose: using spreadsheets KS2 & 3. Derby: ATM Publications.
Ainley, J., Bills, L., & Wilson, K. (2005). Designing Spreadsheet-Based Tasks for Purposeful Algebra. International Journal of Computers for Mathematical Learning, 10(3), 191-215.
Anderson, J. R., & Schunn, C. D. (2000). Implications of the ACT-R learning theory: No magic bullets. In R. Glaser (Ed.), Advances in instructional psychology: Educational design and cognitive science (Vol. 5, pp. 1-34). Mahwah, NJ: Lawrence Erlbaum Associates.
Artigue, M., & Perrin-Glorian, M.-J. (1991). Didactic engineering, research and development tool: some theoretical problems linked to this duality. For the learning of Mathematics 11(1), 3-17.
ATM (various dates). Points of departure 1,2,3,4. Derby, UK: Association of Teachers of Mathematics.
Becker, J. P., & Shimada, S. (1997). The open-ended approach: A new proposal for teaching mathematics. Reston, Virginia: National Council of Teachers of Mathematics.
Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer Academic Publishers.
Brousseau, G., Brousseau, N., & Warfield, V. (2004). Rationals and decimals as required in the school curriculum. Part 1: Rationals as measurement. Journal of Mathematical Behavior, 20, 363 - 411.
Brousseau, G., Brousseau, N., & Warfield, V. (2007). Rationals and decimals as required in the school curriculum: Part 2: From rationals to decimals. The Journal of Mathematical Behavior, 26(4), 281-300. http://www.sciencedirect.com/science/article/B6W5B-4R5G38N- 1/2/89f8fa55b19b428152a164aa16a029bb
Brousseau, G., Brousseau, N., & Warfield, V. (2008). Rationals and decimals as required in the school curriculum: Part 3. Rationals and decimals as linear functions. The Journal of Mathematical Behavior, 27(3), 153-176. http://www.sciencedirect.com/science/article/B6W5B-4TN5MH1- 1/2/8b7c9f4fd5b0182ea2ce54a8657b515b
Brousseau, G., Brousseau, N., & Warfield, V. (2009). Rationals and decimals as required in the school curriculum: Part 4: Problem solving, composed mappings and division. The Journal of Mathematical Behavior, 28(2-3), 79-118. http://www.sciencedirect.com/science/article/B6W5B-4XBWW66- 1/2/e8ed54e6e9f5ab39f8c336c70805a027
Chevallard, Y. (1999). L'analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en Didactique des Mathématiques, 19(2), 221-266.
Choppin, J. (2011). The impact of professional noticing on teachers' adaptations of challenging tasks. Mathematical Thinking and Learning, 13(3), 175-197.
Christiansen, B., & Walter, G. (1986). Task and activity. In B. Christiansen, A. G. Howson & M. Otte (Eds.), Perspectives on mathematics education: Papers submitted by members of the Bacomet Group (pp. 243- 307). Dordrecht: D. Reidel.
Corey, D. L., Peterson, B. E., Lewis, B. M., & Bukarau, J. (2010). Are there any places that students use their heads? Principles of high-quality Japanese mathematics instruction. Journal for Research in Mathematical Education, 41, 438-478.
De Lange, J. (1996). Using and applying mathematics in education. In A. Bishop, K. Clements, C. Keitel, J. Kilpatrick & C. Laborde (Eds.), International Handbook of Mathematics Education (pp. 49-98). Dordrecht: Kluwer Academic Publishers.
Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics? Mathematical Thinking and Learning, 1(2), 155-177.
Gueudet, G., & Trouche, L. (2009). Towards new documentation systems for mathematics teachers? Educational Studies in Mathematics, 71, 199-218.
Gueudet, G., & Trouche, L. (2011). Teachers' work with resources: Documentational geneses and professional geneses. In G. Gueudet, B. Pepin & L. Trouche (Eds.), From Text to 'Lived' Resources. New York: Springer.
Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal of Research in Mathematics Education, 28(5), 524-549.
Huang, R., & Bao, J. (2006). Towards a model for teacher professional development in China: Introducing Keli. Journal of Mathematics Teacher Education, 9, 279-298.
Kieran, C., Tanguay, D., & Solares, A. (2011). Researcher-designed resources and their adaptation within classroom teaching practice: Shaping both the implicit and the explicit. In G. Gueudet, B. Pepin & L. Trouche (Eds.), From Text to 'Lived' Resources (pp. 189-213). New York: Springer.
Kilpatrick, J., Swafford, J., & Findell, B. (2011). Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy Press.
Lagrange, J.-B. (2002). Etudier les mathématiques avec les calculatrices symboliques. Quelle place pour les techniques? In D. Guin & L. Trouche (Eds.), Calculatrices symboliques. Transformer un outil en un instrument du travail mathématique : un problème didactique (pp. 151-185). Grenoble: La Pensée Sauvage.
Leont'ev, A. (1975). Dieyatelinocti, soznaine, i lichynosti [Activity, consciousness, and personality]. Moskva: Politizdat.
Margolinas, C., Abboud-Blanchard, M., Bueno-Ravel, L., Douek, N., Fluckiger, A., Gibel, P., Vandebrouck, F., & Wozniak, F. (Eds.). (2011). En amont et en aval des ingénieries didactiques. Grenoble: La pensée sauvage.
Mason, J., & Johnston-Wilder, S. (2006). Designing and using mathematical tasks. York, UK: QED Press.
Renkl, A. (2005). The worked-out-example principle in multimedia learning. In R. Mayer (Ed.), The Cambridge handbook of multimedia learning (pp. 229-246). Cambridge, UK: Cambridge University Press.
Runesson, U. (2005). Beyond discourse and interaction. Variation: a critical aspect for teaching and learning mathematics. The Cambridge Journal of Education, 35(1), 69-87.
Schoenfeld, A. H. (1980). On useful research reports. Journal for Research in Mathematical Education, 11(5), 389-391.
Sierpinska, A. (2003). Research in Mathematics Education: Through a Keyhole. In E. Simmt & B. Davis (Eds.), Proceedings of the Annual Meeting of Canadian Mathematics Education Study Group: Acadia University.
Sullivan, P. (1999). Seeking a rationale for particular classroom tasks and activities. In J. M. Truran & K. N. Truran (Eds.), Making the difference. Proceedings of the 21st Conference of the Mathematics Educational Research Group of Australasia (pp. 15-29). Adelaide: MERGA.
Sullivan, P., Zevenbergen, R., & Mousley, J. (2006). Teacher actions to maximise mathematics learning opportunities in heterogeneous classrooms. International Journal in Science and Mathematics Teaching, 4, 117-143.
Tirosh, D., & Wood, T. (Eds.). (2009). The International Handbook of Mathematics Teacher Education (Vol. 2). Rotterdam: Sense publishers.
Tzur, R., Sullivan, P., & Zaslavsky, O. (2008). Examining Teachers' Use of (Non-Routine) Mathematical Tasks in Classrooms from three Complementary Perspectives: Teacher, Teacher Educator, Researcher. In O. Figueras & A. Sepúlveda (Eds.), Proceedings of the Joint Meeting of the 32nd Conference of the International Group for the Psychology of Mathematics Education, and the 30th North American Chapter (Vol. 1, pp. 133-137). México: PME.
Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H., & Houang, R. T. (2002). According to the Book. Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Dordrecht: Kluwer Academic Publishers.
Van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: an example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54, 9-35.
Vergnaud, G. (1982). Cognitive and developmental psychology and research in mathematics education: some theoretical and methodological issues. For the Learning of Mathematics, 3(2), 31-41.
Watson, A., & Mason, J. (2006). Seeing an Exercise as a Single Mathematical Object: Using Variation to Structure Sense-Making. Mathematical Thinking and Learning, 8(2), 91-111.