Abstract
We describe the design of a sequence of spreadsheet-based pedagogic tasks for the introduction of algebra in the early years of secondary schooling within the Purposeful Algebraic Activity project. This design combines two relatively novel features to bring a different perspective to research in the use of spreadsheets for the learning and teaching of algebra: the tasks which are purposeful for pupils and contain opportunities to appreciate the utility of algebraic ideas, and careful matching of the affordances of the spreadsheet to the algebraic ideas which are being introduced. Examples from two tasks are used to illustrate the design process. We then present data from a teaching programme using these tasks to highlight connections between aspects of the task design and the construction of meanings for variable.
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J. Ainley (2000) Constructing purposeful mathematical activity in primary classrooms C. Tikly A. Wolf (Eds) The Maths We Need Now Bedford Way Papers London
Ainley, J. and Pratt, D. (2002). Purpose and utility in pedagogic task design. In A. Cockburn and E. Nardi (Eds), Proceedings of the 26th Annual Conference of the International Group for the Psychology of Mathematics Education, Vol. 2 (pp. 17–24). UK.
Ainley, J., Pratt, D. and Hansen, A. (forthcoming). Connecting engagement and focus in pedagogic task design. British Educational Research Journal
Ainley, J., Wilson, K. and Bills, L. (2003). Generalising the context and generalising the calculation. In N.A. Pateman, B.J. Dougherty and J. Zilliox (Eds), Proceedings of the 27th Annual Conference of the International Group for the Psychology of Mathematics Education, Vol. 2 (pp. 9–16). Honolulu.
Ainley, J., Bills, L. and Wilson, K. (2005). Purposeful task design and the emergence of transparency. Proceedings of the 29th Annual Conference of the International Group for the Psychology of Mathematics Education.
G. Brousseau (1997) NoChapterTitle N. Balacheff M. Cooper R. Sutherland V. Warfield (Eds) Theory of Didactical Situations Kluwer Academic Publishers Dordrecht
Carraher, D., Schliemann, A. and Brinzuela, B. (2001). Can young students operate on unknowns? In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Annual Conference of the International Group for the Psychology of Mathematics Education, Vol. 1 (pp. 130–140). Netherlands.
C. Cooper M. Dunne (2000) Assessing Children’s Mathematical Knowledge Open University Press Buckingham
G. Dettori R. Garuti E. Lemut (2001) From arithmetic to algebraic thinking by using a spreadsheet R. Sutherland T. Rojano A. Bell R. Lins (Eds) Perspectives on School Algebra Kluwer Dordrecht
E. Filloy T. Rojano (1989) ArticleTitleSolving equations: The transition from arithmetic to algebra For the Learning of Mathematics 9 IssueID2 19–25
G. Harel (1998) ArticleTitleTwo dual assertions: The first on learning and the second on teaching (or vice versa) American Mathematical Monthly 105 497–507
N. Herscovics L. Linchevski (1994) ArticleTitleA cognitive gap between arithmetic and algebra Educational Studies in Mathematics 27 59–78 Occurrence Handle10.1007/BF01284528
C. Kieran (1996) The changing face of school algebra C. Alsina J.M. Alvares B. Hodgson C. Laborde Pérez A. (Eds) Proceedings of the Eighth International Congress on Mathematics Education: Selected Lectures S.A.E.M. Seville 271–290
T. Nunes A.D. Schliemann D.W. Carraher (1993) Street Mathematics and School Mathematics Cambridge University Press Cambridge
L. Radford (2000) ArticleTitleSigns and meanings in students’ emergent algebraic thinking: A semiotic analysis Educational Studies in Mathematics 42 IssueID3 237–268 Occurrence Handle10.1023/A:1017530828058
L. Radford (2002) ArticleTitleThe seen, the spoken and the written A semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics 22 IssueID2 14–23
L. Radford (2003) ArticleTitleGestures, speech and the sprouting of signs: A semiotic-cultural approach to students’ types of generalization Mathematical Thinking and Learning 5 IssueID1 37–70 Occurrence Handle10.1207/S15327833MTL0501_02
Radford, L., Bardini, C. and Sabena, C. (2005). Perceptual semiosis and the microgenesis of algebraic generalizations. Proceedings of the 4th congress of the European society for Research in Mathematics Education. Barcelona, Spain.
Schliemann, A. (1995). Some concerns about bringing everyday mathematics to mathematics education. In L. Meira and D. Carraher (Eds), Proceedings of the 19th Annual Conference of the International Group for the Psychology of Mathematics Education, Vol. 1 (pp. 45–60). Brazil.
Stacey, K. and MacGregor, M. (1997). Multiple referents and the shifting meanings of unknowns in students’ use of algebra. In E. Pehkonen (Ed.), Proceedings of the 21st Annual Conference of the International Group for the Psychology of Mathematics Education, Vol. 4 (pp. 190–197). Finland.
R. Sutherland (1991) ArticleTitleSome unanswered research questions on the teaching and learning of algebra For the Learning of Mathematics 11 IssueID3 40–46
Sutherland, R. (1993). Project AnA–the gap between arithmetic and algebra (R000232132). Final report to ESRC. Institute of Education, University of London.
R. Sutherland T. Rojano (1993) ArticleTitleA spreadsheet approach to solving algebra problems Journal of Mathematical Behaviour 12 IssueID4 353–383
Tabach, M. and Friedlander, A. (2004). Levels of student responses in a spreadsheet-based environment. In M. Johnsen Høines and A.B. Fuglestad (Eds), Proceedings of the Twenty Eighth Annual Conference of the International Group for the Psychology of Mathematics Education, Vol. 2 (pp. 423–430). Bergen University College.
Ursini, S. and Trigueros, M. (2001). A model for the uses of variable in elementary algebra. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Annual Conference of the International Group for the Psychology of Mathematics Education, Vol. 4 (pp. 335–342). Netherlands.
Wilson, K., Ainley, J. and Bills, L. (2004). Spreadsheet generalising and paper and pencil generalising. In M. Johnsen Høines and A. B. Fuglestad (Eds), Proceedings of the 28th Annual Conference of the International Group for the Psychology of Mathematics Education, Vol. 4 (pp. 441–448). Norway.
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Ainley, J., Bills, L. & Wilson, K. Designing Spreadsheet-Based Tasks for Purposeful Algebra. Int J Comput Math Learning 10, 191–215 (2005). https://doi.org/10.1007/s10758-005-8420-9
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DOI: https://doi.org/10.1007/s10758-005-8420-9