Ainley, J. 2000# Constructing purposeful mathematical activity in primary classrooms

Tikly, C.Wolf, A. eds. The Maths We Need NowBedford Way PapersLondon

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*.

Brousseau, G. 1997Balacheff, N.Cooper, M.Sutherland, R.Warfield, V. eds. *Theory of Didactical Situations*Kluwer Academic PublishersDordrecht

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.

Cooper, C., Dunne, M. 2000Assessing Children’s Mathematical KnowledgeOpen University PressBuckingham

Dettori, G., Garuti, R., Lemut, E. 2001# From arithmetic to algebraic thinking by using a spreadsheet

Sutherland, R.Rojano, T.Bell, A.Lins, R. eds. Perspectives on School AlgebraKluwerDordrecht

Filloy, E., Rojano, T. 1989Solving equations: The transition from arithmetic to algebraFor the Learning of Mathematics91925

Harel, G. 1998Two dual assertions: The first on learning and the second on teaching (or *vice versa*)American Mathematical Monthly105497507

Herscovics, N., Linchevski, L. 1994A cognitive gap between arithmetic and algebraEducational Studies in Mathematics275978CrossRef Kieran, C. 1996# The changing face of school algebra

Alsina, C.Alvares, J.M.Hodgson, B.Laborde, C.A., Pérez eds. *Proceedings of the Eighth International Congress on Mathematics Education: Selected Lectures*S.A.E.M.Seville271290

Nunes, T., Schliemann, A.D., Carraher, D.W. 1993Street Mathematics and School MathematicsCambridge University PressCambridge

Radford, L. 2000Signs and meanings in students’ emergent algebraic thinking: A semiotic analysisEducational Studies in Mathematics42237268CrossRef Radford, L. 2002The seen, the spoken and the writtenA semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics221423

Radford, L. 2003Gestures, speech and the sprouting of signs: A semiotic-cultural approach to students’ types of generalizationMathematical Thinking and Learning53770CrossRef 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.

Sutherland, R. 1991Some unanswered research questions on the teaching and learning of algebraFor the Learning of Mathematics114046

Sutherland, R. (1993). Project AnA–the gap between arithmetic and algebra (R000232132). Final report to ESRC. Institute of Education, University of London.

Sutherland, R., Rojano, T. 1993A spreadsheet approach to solving algebra problemsJournal of Mathematical Behaviour12353383

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.