数学的理解の超越的再帰理論に関する一考察

On Transcendent Recursive Theory of Understanding Mathematics

小山 正孝

広島大学教育学部紀要. 第二部

Bulletin of the Faculty of Education, Hiroshima University. Part 2

There has been much interest in mathematical understanding and a variety of approaches to study of it in the area of research on mathematics education. The aim of this paper is to study the transcendent recursive theory of understanding mathematics which has been developed and elaborated by S. Pirie and T. Kieren in their work over the past six years.

The theory and its model are examined thoroughly from view points of its foundamental ideas, features and usefulness as a theory of understanding mathematics in order to answer the following questions.

1) Why does this theory regard the growth of child' s understanding mathematics as a whole, dynamic, levelled but non-linear, transcendently recursive process?

2) What are features of this theory? In particular, what are properties of eight potential levels or distinct modes as basic elements of this theory?

教育 [ 370 ]

日本語

広島大学教育学部

[ISSN] 0440-8713

[NCID] AN0021336X