Games for integers – Games for integers PME95

More games for integers – MoreGamesforIntegers_PME98

On the epistemology of integers – Integers Recherches Abstract

These papers, two in PME and one in *Recherche en didactique des mathématiques*, focus on the question *why minus times minus make plus?*

Can we say that Freudenthal and Dienes were looking for *explanations *of the sign rule? Does the criticism of Glaeser indicate that they simply did not succeed? Or is the whole discussion a symptom that no explanation ultimately exists and that some degree of arbitrariness will somewhere be necessary? If so, precisely where? If we read Freudenthal’s chapter back from its final remarks about “instruction on negative numbers”, it seems that all his project to produce adequate meaning for negative numbers has been abandoned in favor of stressing the importance of rule teaching. We contend that *rule teaching* is exactly the route to failure. When the student comes to the point of asking *why does minus times minus equal plus? *it is already too late: he has learned the solution without knowing the problem and is “fed up” with rules (Baldino, 1997, p. 125).

That was a time when mathematics education did not reject criticism. Through four games we provide the arithmetic basis sufficient for the students themselves to answer the question once we ask them. These games were tested in classroom by Linardi (1998).

Baldino, R. R. (1997). On the epistemology of integers. *Recherches en Didactique des Mathématiques*, N.17/2, 1997, p. 211-249.

Carrera, A. C., Mometti, A. L. Scavazza, H. A. & Baldino, R. R. (1995). Games for integers: conceptual or semantic fields? *Proceedings of PME,* 1995, v. 2, p. 232-239. Recife: UFPE

Linardi P. R. & Baldino, R, R. (1998). More games for integers. *Proceedings of PME22*, Vol. 3 p. 207-214. (30/06/1998)

Linardi, P. R. (1998). Quatro jogos para números inteiros; uma análise (Four games for integers, an anlysis). Master’s Degree Dissertation. UNESP, Rio Claro, Brazil.