Dave Hewitt, Loughborough University, UK
Learner difficulties with algebra: are they really about algebra and do they really have to be difficult?
There have been several studies from the 1980s onwards which have identified difficulties that many learners have with algebra (e.g. Küchemann, 1981; Herscovics, 1989; Cooper et al., 1997). Yet some studies in the 2000s give a clear sense that relatively young learners can successfully work with algebraic situations (e.g. Carraher et al., 2001; Schliemann et al., 2003). So what is difficult about working algebraically? Are there other factors which affect success with algebraic tasks but which are not essentially algebraic in nature? In this talk I will present an argument that not all difficulties with algebra are to do with algebra, and that there may be more productive ways to go about teaching algebra than are commonly found in many school classrooms.
Carraher, D., Schliemann, A., D. and Brizuela, B., M. (2001). Can young students operate on unknowns? In M. van den Heuvel-Panhuizen (Ed.) Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 1, pp. 130-140). Utrecht, The Netherlands: PME.
Cooper, T. J., Boulton-Lewis, G. M., Atwah, B., Pillay, H., Wilss, L. and Mutch, S. (1997). The transition from arithmetic to algebra: initial understanding of equals, operations and variable. In E. Pehkonen (Ed.) Proceedings of the 21st conference of the International Group for the Psychology of Mathematics Education, (Vol. 2, pp. 89-96). Lahti, Finland: PME.
Herscovics, N. (1989). Cognitive Obstacles Encountered in the Learning of Algebra. In S. Wagner and C. Kieran (Eds), Research Issues in the Learning and Teaching of Algebra, Reston, Virginia: National Council of Teachers of Mathematics, Lawrence Erlbaum Associates, pp. 60-86.
Küchemann, D. (1981). Algebra. In K. M. Hart (Ed.), Children's understanding of mathematics: 11-16, London: John Murray, pp. 102-119.
Schliemann, A., Carraher, D., Brizuela, B., Earnest, D., Goodrow, A., Lara-Roth, S. and Peled, I. (2003). Algebra in elementary school. In N. A. Pateman, B. J. Dougherty and J. T. Zilliox (Eds), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education held jointly with the 25th Conference of PME-NA, (Vol. 4, pp. 127-134). Hawai'i, USA: PME.