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The purpose of this paper is to show the similarities as well as the differences of fundamental fraction knowledge owned by preservice elementary teachers from the United States ( N= 89) and Taiwan ( N= 85). To this end, we examined and compared their performance on an instrument including 15 multiple-choice test items. The items were categorized into four different types of fundamental fraction constructs, including part-whole relationship, quotient, equivalence, and meanings of operations. Each item was embedded in the area, linear, or set model except for the items constructed out of the meaning of operations. Several items were featured with a pictorial illustration. Quantitative analysis showed that U.S. preservice teachers were significantly outperformed by their Taiwanese counterparts overall. The difference between the two groups was statistically significant on 12 of 15 items. Findings suggest that preservice elementary teachers from both countries need to be better prepared in their understanding of the meaning of fraction multiplication or division operations. Findings also suggest that U.S. preservice elementary teachers need to be more knowledgeable in dealing with fraction problems embedded in a linear model. Further research is suggested to study the issues raised from the findings. [ABSTRACT FROM AUTHOR]

This paper reports selected findings from a study of number sense proficiency of students aged 8 to 14 years in Australia, Sweden, United States, and Taiwan. It comments on the meaning and importance of number sense, the development of the assessment instruments, and student responses to the items. Some implications for classrooms of the findings are then discussed. [ABSTRACT FROM AUTHOR]

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 recognizing the number size, using benchmarks, etc.) and the other two-thirds' relied heavily on written algorithms to solve problems. This is consistent with the findings of the earlier studies (Reys & Yang, 1998: Yang & Reys, 2002; Yang, 2003), which state that fifth, sixth and eighth graders in Taiwan rely heavily on the written method when responding to number sense related questions. This implies that the performance of pre-service elementary teachers on number sense is low. If we want to improve elementary students 'knowledge and use of number sense, then we should try to improve the ability of their future teachers 'number sense. This supports the statement of Ma (1999) which stated that "'to empower students with mathematical thinking, teachers should first be empowered (p. 105)." [ABSTRACT FROM AUTHOR]

To investigate the structure of number sense and then to assess its uses in fifth-grade children's number sense development, a computerized number sense scale was developed and evaluated. The findings of the study indicate that the newly developed scale, with four dominant factors identified and reconfirmed, is internally consistent and substantially valid. It can be reliably used as a screening measure for a quick check of students' number sense development via online self-assessment. Compared with our previous study, both qualitative and quantitative changes were detected in students' number sense development at different grades. The qualitative change in number sense development is manifested in different numbers of factor components produced at different grades. The quantitative change is manifested in different amounts of factor variance explained at different grades. Furthermore, among the four aspects of number sense, Taiwanese students perform best on recognizing the relative number size yet relatively worse on judging the reasonableness of computational results. [ABSTRACT FROM AUTHOR]

This research examined the presentation of fractions in textbooks used by fifth and sixth graders in Singapore, Taiwan, and the United States. The specific textbooks examined were My Pals Are Here! Maths (MPHM) in Singapore; Kung Hsung (KH) in Taiwan; and Mathematics in Context (MiC) in the USA. Results show the problems posed in MiC put more emphasis on real-life situations than KH textbooks in Taiwan and MPHM in Singapore. Designing materials that provide opportunities to connect mathematics content with applications in real life is consistent with recommendations from professional organizations. The activities in KH and MPHM tended to emphasize procedures, while the activities of MiC focused more on conceptual understanding and less on the development of procedures. An examination of the mathematics textbooks revealed that MPHM introduced and developed fractions the earliest among the three countries investigated and the content taught in MPHM was about one grade earlier than when the same content was experienced by students in KH and MiC. [ABSTRACT FROM AUTHOR]