Freudenthal (1981)

Major Problems of Mathematics Education

• Author: Hans Freudenthal
• Journal: Educational Studies in Mathematics
• Year: 1981
• Source: http://link.springer.com/article/10.1007%252FBF00305618

Abstract

The article does not have an abstract.

Summary

In this article, Hans Freudenthal articulates 11 major problems of mathematics education.

1. Why can Jennifer not do arithmetic?

   In this problem, Freudenthal critiques educators from trying to diagnose students' difficulties as a doctor would diagnose an illness, claiming educators too often diagnose for what is wrong, not why something is wrong. Instead, Freudenthal suggests we rely on the "vast resources of human experience" (p. 135) to build "paradigmatic cases, paradigms of diagnosis and prescription, for the benefit of practitioners and as bricks for theory builders" (p. 135).

2. How should children learn?

   Freudenthal extends this to "How should people learn?" and how we learn to observe learning processes. He suggests answers lie in "observing learning processes, analysing them and reporting paradigms — learning processes within the total educational system, learning processes of pupils, groups, classes, teachers, school teams, councillors, teacher students, teacher trainers, and of the observer himself" (pp. 136-137).

3. How to use progressive schematisation and formalisation in teaching any mathematical subject whatever?

   This question receives Freudenthal's longest reply, including illustrations of what he means by schematisation. Freudenthal claims that the "history of mathematics has been a learning process of progressive schematising, (p. 140) but claims that "Youngsters need not repeat the history of mankind but they should not be expected either to start at the very point where they preceding generation stopped" (p. 140). He clarifies that schematising should be seen as a psychological progression or network of possible progressions.

4. How to keep open the sources of insight during the training process, and how to stimulate retention of insight, in particular in the process of schematising?
5. How to stimulate reflecting on one's own physical, mental and mathematical activities?
6. How to develop a mathematical attitude?
7. How is mathematical learning structured according to levels and can this structure be used in attempts at differentiation?
8. How to create suitable contexts in order to teach mathematising?
9. How can calculators and computers be used to arouse and increase mathematical understanding?
10. How to design educational development as a strategy for change?

Also

APA

Freudenthal, H. (1981). Major problems of mathematics education. Educational Studies in Mathematics, 12(2), 133–150. doi:10.1007/BF00305618

BibTeX

@article{Freudenthal1981,
author = {Freudenthal, Hans},
doi = {10.1007/BF00305618},
journal = {Educational Studies in Mathematics},
number = {2},
pages = {133--150},
title = {{Major problems of mathematics education}},
url = {http://link.springer.com/article/10.1007\%2FBF00305618},
volume = {12},
year = {1981}
}