Teaching Multiplication: An Analysis of Elementary School Mathematics Teachers' Manuals from Japan and the United States
Abstract
Teachers' manuals accompanying commonly used textbook series, 2 from Japan and 2 from the United States, were analyzed for their initial treatment of the multiplication operation. The 2 U.S. series included in this study were Investigations in Number, Data, and Space and Math in My World. The 2 Japanese series included were Shintei sansuu (Elementary School Mathematics) and Shinhen atarashli Sansuu (New Elementary School Mathematics). I examined the manuals for grades 2 and 3 in the Japanese series and Math in My World, and grade 3 in Investigations. The findings suggested that although there were a number of common features, such as use of the equal set context in the introduction of the operation and an emphasis on strategies to help students master basic facts, the Japanese series' treatment of multiplication was much different from both U.S. series. These differences included the Japanese emphasis on the multiplier and multiplicand distinction, the delayed treatment of 1 and 0 as factors, and the strict use of horizontal notation during the introductory discussion of the operation. These findings raise a number of questions about the treatment of multiplication in the U.S. textbooks.