Syllogistic Analysis and Cunning of Reason in Mathematics Education

Publicerad:2013-09-18

Uppdaterad:2013-10-07

I en ny avhandling från Karlstads universitet undersöks frågan om det är möjligt att bedriva matematikundervisningen genom syllogism: Att från två premisser dra en slutsats.

Författare

Yang Liu

Handledare

Arne Engström, Docent, Karlstads universitet

Opponent

Jiansheng Bao, Professor

Disputerat vid

Karlstads universitet

Disputationsdag

2013-09-12

Titel (eng)

Syllogistic Analysis and Cunning of Reason in Mathematics Education

Institution

Institutionen för matematik och datavetenskap

Syllogistic Analysis and Cunning of Reason in Mathematics Education

This essay explores the issue of organizing mathematics education by means of syllogism. Two aspects turn out to be particularly significant. One is the syllogistic analysis while the other is the cunning of reason. Thus the exploration is directed towards gathering evidence of their existence and showing by examples their usefulness within mathematics education.

The syllogistic analysis and the cunning of reason shed also new light on Chevallard’s theory of didactic transposition. According to the latter, each piece of mathematical knowledge used inside school is a didactic transposition of some other knowledge produced outside school, but the theory itself does not indicate any way of transposing, and this empty space can be filled with the former.

A weak prototype of syllogism considered here is Freudenthal’s change of perspective. Some of the major difficulties in mathematics learning are connected with the inability of performing change of perspective. Consequently, to ease the difficulties becomes a significant issue in mathematics teaching. The syllogistic analysis and the cunning of reason developed in this essay are the contributions to the said issue.