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…

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…

The topic of fractions is an important concept in elementary school mathematics. The study of fractions not only enables students to perform computations but also provides a foundation for later work with rates, percents, slope, and other topics in secondary school mathematics. However, research has long reported that many students and even adults…

In the study reported here, the authors examined the LEs (learning expectations) related to Grades 1 to 8 number and quantity in mathematics across several US states and high performing TIMSS (Third International Mathematics and Science Study) Asian countries, including Singapore, Taiwan and Japan. The general strategy used is based on the topic…

This study analyzes the learning expectations related to grades 1-8 algebra across several U.S. states and high performing TIMSS Asian countries and regions, including Singapore, Taiwan and Japan. In order to narrow and focus the investigation, only one topic within the strand is carefully reported. Based on the official curriculum documents,…

Using cognitive ethnography as a guiding framework, we investigated US and Japanese fourth-grade teachers' domain knowledge of key fraction representations in individual interviews. The framework focused on revealing cultural trends in participants' organization of knowledge and their interpretations of that organization. Our analyses of the…

Presents 3 examples for setting teacher's aims in Japanese and American mathematics classrooms. Provides 10 guidelines for teachers who would like to include more mathematical dialogue and encourage the expression of conceptual splatter in their classrooms. (YP)

Documented differences in frequency and type of mathematical explanations during lessons in U.S., Taiwanese, and Japanese first- and fifth-grade classrooms. Found that explanations occurred more frequently in Japanese and Taiwanese classrooms than in U.S. classrooms. Typical explanations in Asian classrooms were more substantive than in U.S.…

U.S. (n=150) and Japanese (n=200) fourth graders generated multiple solutions with explanations for a simple mathematical task. U.S. responses revealed gender differences (girls averaged more responses), and comparison by nation revealed similarity of strategy frequencies, but Japanese students used more formal language and mathematical ideas. (13…

A two part examination of the evidence concerning one possible basis for the poor mathematical performance of United States students, the content of the textbooks used in their classes, is presented. The results of a detailed analysis of Japanese and U.S. mathematics textbooks for grades 1 through 12 are reported. Two international studies (1964…

Types of questions asked in first-grade mathematics classes in Japan, Taiwan, and the United States were investigated. Observations of 311 lessons by 16 Japanese, 20 Taiwanese, and 33 U.S. teachers suggest that the kinds of questions asked in Taiwan and Japan contribute to more sophisticated mathematical knowledge. (SLD)