The purpose of this study is to compare the differences of four essential aspects (i.e., representational forms, contextual features, cognitive demand levels, and response types) embedded in mathematical problems within the topics of numbers and operations in mathematics textbooks used in Finland, Indonesia, Malaysia, Singapore, and Taiwan. This…

This study analysed the designs of algebraic problems in elementary mathematics textbooks used in Finland, Indonesia, Malaysia, Singapore, and Taiwan. This study employed a content-analysis method that focused on four dimensions: representational forms, cognitive demand levels (CDLs), contextual features, and types of responses. The result of the…

This study investigated the performance of 790 fourth graders from Taiwan for judging the reasonableness of a computational result by using corresponding methods pertaining to whole numbers. A number-sense web-based two-tier diagnostic test was used to assess the number-sense performance of the fourth graders who participated in this study. The…

This study analyzed geometry problems in four middle-grade mathematics textbook series from Taiwan, Singapore, Finland, and the United States, while exploring the expectations for students' learning experiences with these problems. An analytical framework developed for mathematics textbook problem analysis had three dimensions: representation…

A web-based two-tier test (WTTT-NS) which combined the advantages of traditional written tests and interviews in assessing number sense was developed and applied to assess students' answers and reasons for the questions. In addition, students' major misconceptions can be detected. A total of 1,248 sixth graders in Taiwan were selected to…

The purpose of this study was to examine the differences between Finnish and Taiwanese textbooks for grades 7 to 9 on the topic of solving systems of linear equations (simultaneous equations). The specific textbooks examined were TK in Taiwan and FL in Finland. The content analysis method was used to examine (a) the teaching sequence, (b)…

The key purpose of this study was how we taught the use of benchmark strategy when comparing fraction for fifth-graders in Taiwan. 26 fifth graders from a public elementary in south Taiwan were selected to join this study. Results of this case study showed that students had a much progress on the use of benchmark strategy when comparing fraction…

Two 12-question estimation instruments were designed to compare the differences of estimating strategies used by the 8th-graders when solving contextual and numerical problems. Both instruments are parallel, meaning that the numbers used in both instruments are the same; however, they were presented differently. One hundred and ninety-eight…

The purpose of this study was to examine the relative effectiveness of two different learning modes; namely, a computer animation self-directed learning approach and a paper version of the self-directed learning approach, to 5th-graders' number sense development. Two 5th-grade classes, 30 students each, were selected from a public elementary…

This study examined the strategies used by pre-service teachers when responding to number sense related questions. 15 pre-service teachers from one University in Southern Taiwan were interviewed. Results indicated that about one-third of these pre-service teachers were able to use number sense strategies (such as understanding the meaning of…