Dörfler W. (1987) Empirical investigations of the construction of cognitive schema from actions. In: Bergeron J. C., Herscovics N. & Kieran C. (eds.) Proceedings of the Eleventh Conference of the International Group for the Psychology of Mathematics Education, Volume 3\>Proceedings of the Eleventh Conference of the International Group for the Psychology of Mathematics Education, Volume 3. University of Montreal, Montreal: 3–9.

The theoretical basis of the interviews reported about here is a Piagetian-like approach to the origin and genesis of cognitive schemata representing mathematical concepts. Such schemata are postulated to reflect the abstract and general structure of material, imagined or mental actions and of relations induced by these actions. The main cognitive tools for the mental construction of such schemata are seen to be: Actions, symbolic representations, prototypes of objects, reflection and abstraction, schematization, generalization. The interviews were devised such that the subjects were guided appropriately in their individual cognitive constructions. The mathematical topics treated are: Place value system, divisibility, word problems, geometric sequence, Riemann integral. In general the results support the view that the individual construction of cognitive schemata is possible and effective in the proposed way.

Kilpatrick J. (1987) What constructivism might be in mathematics education. In: Bergeron J. C., Herscovics N. & Kieran C. (eds.) Proceedings of the Eleventh Conference of the International Group for the Psychology of Mathematics Education\>Proceedings of the Eleventh Conference of the International Group for the Psychology of Mathematics Education. University of Montreal, Montreal: 3–27. Fulltext at https://cepa.info/2977

Excerpt: It is tempting to begin by comparing the constructivist movement in mathematics education, at least as it is being manifested in the United States, to any of the waves of religious fundamentalism that have swept our society in its three-and-a-half-century history. A siege mentality that seeks to spread the word to an uncomprehending, fallen world; a band of true believers whose credo demands absolute faith and unquestioning commitment, whose tolerance for debate is minimal, and who view compromise as sin; an apocalyptic vision that governs all of life, answers all questions, and puts an end to doubt-these are some of the parallels that might be drawn.

Sinclair H. (1987) Constructivism and the psychology of mathematics. In: Bergeron J. C., Herscovics N. & Kieran C. (eds.) Proceedings of the Eleventh Conference of the International Group for the Psychology of Mathematics Education\>Proceedings of the Eleventh Conference of the International Group for the Psychology of Mathematics Education. University of Montreal, Montreal: 28–41.

Vergnaud G. (1987) About constructivism. In: Bergeron J. C., Herscovics N. & Kieran C. (eds.) Proceedings of the Eleventh Conference of the International Group for the Psychology of Mathematics Education\>Proceedings of the Eleventh Conference of the International Group for the Psychology of Mathematics Education. University of Montreal, Montreal: 42–54.