Exploration and Development for the Applications of Japanese Sangaku Culture in Secondary Mathematics Teaching

This project will explore the contents and teaching applications of a unique mathematical culture from Japan called “Sangaku” (mathematical tablets). Samurais and commoners in Japan’s Edo period (1603-1807) gave plaques to temples or shrines as religious offerings to thank the deities’ grace, and mathematicians offered mathematical tablets to express their gratitude, and also to publicly announce their achievements. Problems on those mathematical tablets are usually related to secondary school geometry, with topics such as Euclidean geometry, trigonometry, ellipses and volumes of solids. Therefore, the research questions of this project are (1) What are the unique geometrical problems and methods in Japan’s Sangaku culture? (2) From the perspective of the theories of geometry teaching and learning, how can one understand and organise the geometrical problems and methods in the Sangaku culture? (3) Among the organised Sangaku problems, which ones could be developed as material for secondary school mathematics teaching and learning? As for research methods, the project leader will interpret the Sangaku contents with the usual textual analysis method. Moreover, ‘van Hiele model of geometric thinking’ and ‘spatial reasoning’ shall be two main theories as the framework of analysis. Also, the project leader will go to Japan to collect material and work with scholars specialising in Sangaku and its educational applications. The project will also hold Sangaku reading seminar with a group of secondary school teachers who are interested in using history in mathematics teaching, and discuss how we can transform Sangaku problems into material for classroom use. Finally, the research team will share the developed material online, and write papers to be read in international conferences and to be published in academic journals.