The intangible task – a revelatory case of teaching mathematical thinking in Japanese elementary schools

ABSTRACT

This paper deals with the nature of teaching mathematical thinking and presents a case study of a single Japanese lesson where the characteristics of mathematical thinking and the teaching thereof are identified in relation to multiplication. The raison d’être for this teaching is questioned and investigated by looking at how multiplication is described in the curriculum and representative textbook material. It is seen how Japanese teachers are institutionally conditioned to incorporate mathematical thinking in the context of multiplication, something which may appear in contrast to other countries. The lesson is analysed using the notion of praxeologies and didactic co-determination conceptualised in the Anthropological Theory of the Didactic.

Keywords:

• Mathematical thinking
• multiplication
• elementary school
• teacher tasks
• didactic co-determination

Acknowledgements

We would like to thank Yoshikazu Yamamoto for allowing us to observe the lesson and for giving us access to his lesson plan. Takamasa Kondo helped with live translation and subsequent discussion, and Akemi Suengawa translated the lesson plan. Miku Yoshida and Jacob Bahn helped double check findings in the video material.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Klaus Rasmussen http://orcid.org/0000-0003-0907-6581

Notes

1 According to the Free Dictionary (http://www.thefreedictionary.com/).

2 Please take note of the special meaning of technology in ATD, which differs markedly from common usage.