According to the Programme for International Student Assessment, functions constitute an important part of mathematical literacy. In Japan, students start learning about bivariate relationships in the fourth grade (at the age of 9). However, reports suggest that elementary school students and lower-level secondary school (junior high) students…

It has become increasingly clear that the early use of decomposition for addition is associated with later mathematical achievement. This study examined how younger children execute a base-10 decomposition strategy to solve complex arithmetic (e.g. two-digit addition). 24 addition problems in two modalities (WA: Written Arithmetic; OA: Oral…

Recently a team of third- and fourth-grade teachers tested instructional ideas on the topic of division with remainders (DWR) using lesson study. The Common Core State Standards for Mathematics give little attention to the concept of the remainder, specifying only that students are to solve problems for which remainders must be interpreted (NGA…

On the basis of the construct of "discursive focus" by Sfard (2000), this study explores how students' attention is brought to new mathematical content in whole-class interaction between the teacher and the children. In a sixth-grade lesson introducing the concept of constancy of proportion, we analyzed the progression of social…

This paper describes a pedagogical framework that teachers can use to support students who are engaged in solving open-ended problems, by explaining how two Japanese expert teachers successfully apply open-ended problems in their mathematics class. The Open-Ended Approach (OPA) framework consists of two main sections: Understanding Mathematical…

This study examined how types of tasks influenced student activities/thinking and defined the role of Seatwork in mathematics lessons. It used 60 lessons from the TIMSS videotaped Study. These data indicated that practice was the most prevalent form of tasks in the U.S. In Germany, students completed mathematical calculations after a complex…

Background: Educators, researchers and policy-makers worldwide continue to struggle to understand the changes needed for improving educational outcomes and attainment for students, particularly in content areas such as mathematics and science that are essential for developing a highly skilled workforce. Given the continuing emphasis on linking…