Theories of Equation in Traditional Korean Mathematics and Its Implications in Mathematics Education

This project aims to analyse the theory of equations in traditional Korean mathematics, with frameworks from modern theories of algebra learning and teaching. The transformation from arithmetic thinking to algebra thinking for students has always been an important issue in the research and practice of mathematics education. There are many features of continuity and discontinuity between arithmetic and algebra, and both procedural and structural thinking are used interchangeably in different steps of arithmetic and algebraic problem-solving. All these phenomena create problems in school algebra learning. Tianyuan shu 天元術 and jiegenfang 借根方 in pre-modern East Asian algebra have different calculation tools (rod counting vs. brush counting) and representations (place-value algebra vs. syncopated algebra). Tianyuan shu does not even use ‘symbols’ or the ‘equal sign’, and it has strong procedure-structure duality. Also, compared to traditional Chinese mathematics, tongsan 東算 (traditional Korean mathematics) specialised in algebra. Therefore, this project wishes to analyse the theory of equations in tongsan with the perspective of mathematics education, instead of only that of historiography, and to look for revelations for modern mathematics learning and teaching. This study is a two-year project. Main tasks for the first year are: (1) Starting with Sfard’s duality and Tall’s ‘procept’ theories, to do literature review about theories of algebra teaching and learning; (2) to go to Kyujanggak Institute of Korean Studies in Seoul National University to collect Korean and Chinese texts, and collaborate with scholars in SNU for text interpretations; (3) to present preliminary results in an HPM conference. Tasks for the second year are: (1) to analyse Korean mathematics texts with theories of algebra teaching and learning; (2) to present full results in an international conference of history of science or mathematics education; (3) to publish one paper in a journal in Taiwan, one in top-class SCI journal Archive for History of Exact Sciences, and possibly one article in a non-academic magazine for practical purposes of algebra teaching.