**Tinkering with the Problem: Key Experience in Mathematics Activities with the Joy of Learning**

**Yoshinori SHIMIZU**

#### Tsukuba University

Japan

Published in The Mathematician Educator, 2022, Vol 3, No. 1, pp 30-40.

### Abstract

Authentic mathematical activities include key experiences of finding alternative solutions of a mathematical problem, changing the conditions of the problem, and even exploring the origin of the problem. As such experiences provide students new perspectives on the problem, analyzing not only the answer to the problem but also the problem itself is an important activity in the classroom. In this paper, the author argues the significance of examining the problem from multiple perspectives as mathematical habits of mind. A particular attention is given to the act of tinkering with the problems with a hope that students in mathematics classrooms may experience the joy of learning by engaging on such an activity. Examples of tinkering with problems are provided with some practical ideas of Japanese approach to teaching mathematics via problem solving. It is noted that the teacher is the one who ‘tinkers’ with the problems at hand to facilitate students in doing mathematics with the intent that they may experience the joy of learning.

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