The Teaching of Multidigit Multiplication in the Japanese Approach

Multidigit multiplication in vertical form uses the idea of the distributive law such as 27 × 3 = (20 + 7) × 3 = 20 × 3 + 7 × 3 for using a multiplication table under the base ten place value system. Multiplication in vertical form is not simply repeated addition such as 27 + 27 + 27. In this meaning, through the extension of multiplication from single digit to multidigit by use of vertical form with a multiplication table, students have to integrate their knowledge on the base ten system with the definition of multiplication by measurement (a group of groups; see Chaps. 3, 4, 5, and 6 of this book) and so on. How does the Japanese approach enable students to develop multiplication in vertical form by and for themselves based on their learned knowledge? This chapter illustrates this process as follows. Firstly, the diversity of multiplication in vertical form is explained in relation to the multiplier and multiplicand, and the Japanese approach in comparison with other countries such as Chile and the Netherlands is clearly illustrated. Secondly, how a Japanese teacher enables students to develop multiplication in vertical form beyond repeated addition is explained with an exemplar of lesson study. Thirdly, the exemplar illustrates a full-speck lesson plan under school-based lesson study which demonstrates how Japanese teachers try to develop students who learn mathematics by and for themselves including learning how to learn (see Chap. 1). Fourthly, it explains the process to extend multiplication in vertical form to multidigit numbers by referring to Gakko Tosho textbooks.