The present research aims at exploring the effectiveness of spiral bianshi mathematics curriculum on the teaching of speed and circumference to Primary 6 students in Hong Kong. Cognitive and affective learning outcomes, together with students’ beliefs are investigated. Teaching materials of these two topics are designed basing on the framework of spiral bianshi mathematics curriculum and were implemented in three primary schools in Hong Kong. The effectiveness of the curriculum was investigated with a pre-test/post-test, experimental/control group design. Preliminary analyses of the cognitive learning outcomes revealed that the students using the bianshi curriculum and teaching materials performed better than their counterparts. The experimental group also showed more positive attitude in some of the affective variables, though such changes did not happen in all the affective components. The experimental group also showed more positive attitude in some of the affective components. Further statistical analyses could be performed to see why the improvement was not as prominent as expected. A possible further analysis could be, by separating those who had sizable improvement with those who had not, we may attempt to identify the characteristics of students, to see who benefit most (in the affective domain) from the bianshi curriculum. It is hoped that these qualitative data would help unveil the secret of the learning process that leads to the desirable learning results.
[Copyright © 2010 Anna Mei-Yan Chan, Ngai-Ying Wong & Chi-Chung Lam.]

Our research is to compare students’ ability of presenting counter examples between Korean students and Hong Kong students and prospective teachers’ ability of treating counter examples between Korean prospective teachers and Hong Kong prospective teachers. Our analysis suggests the methodological implication for mathematics education of two countries on how to improve teaching methodology dealing with counter examples in classrooms through investigating students’ and prospective teachers’ ability on applying counter-examples.
[Copyright © 2010 Issic K. C. Leung, Hee-Chan Lew & Tae Soen Cheon.]

Chinese pre-school children perform well in learning mathematics compared with English-speaking children. This study investigates the scenes behind Chinese pre-school Children's mathematics performance using teacher questionnaires and interviews. Results indicated that the Chinese number system appeared to afford advantages to Chinese children in learning individual mathematics concepts but this was not enough to explain why children perform well in other areas. Frequent practice and exposure to mathematics in pre-schools, together with parental support at home might explain why children performed well in mathematics learning. Study results also revealed that although the underpinning philosophy of pre-school curriculum planning in Hong Kong might be similar to some pre-schools in other parts of the world, such as the adoption of integrated curriculum and unstructured play, contradictory practice might also be incorporated. Mathematics teaching in Hong Kong pre-schools mirrors the Chinese cultural aspiration towards learning, and both teachers and parents play an active role in pursuing academic success for each child.
[Copyright © University of Exeter. Centre for Innovation in Mathematics Teaching].

The paper reports about a study on the knowledge of prospective mathematics teachers from China (Hong Kong and Mainland China) with regard to argumentation and proof as well as beliefs about using preformal and formal proofs in lessons based on a study design developed by Schwarz (2013). The study pointed out that the prospective teachers were generally strong in algebraic reflections and operations, but they lacked reflections on mathematical argumentation and proofs and their adequate teaching, for example, how to provide adequate feedback about proving approaches. Furthermore, differences concerning the acceptance of preformal proofs between prospective teachers from Hong Kong and Mainland China were found out in this study, which may be related to differences in the mathematics curriculum in these two regions. Implications for teaching proofs in geometry and algebra are discussed.
[Copyright © Association of Mathematics Educators].

Attention to details is one of the most important specific features of a mathematical way to thinking. When evaluating mathematical questions it is important to teach students to pay attention globally and locally, consider conditions, properties and relationships, since all of these aspects are as important to develop as mathematical techniques. To develop such skills in their students school teachers should have those skills themselves. In this study, we investigate the ability of school mathematics teachers to pay attention to details and use their mathematical knowledge. We are confident that the vast majority of teachers have excellent knowledge of mathematical techniques. Hence the question is whether this kind of knowledge might structure their attention in such a way that the emphasis on procedures deviates their attention from the essential details. Two groups of teachers from New Zealand and Hong Kong were given a mini-test containing seven simple mathematics questions. All questions in the test were provocative in the sense that they looked like routine questions but in fact they had some catch. The results from the test were startling – the vast majority of the teachers did not notice any catch and gave incorrect answers to most questions in the test. After the test the teachers were given a short questionnaire to reflect on their performance on the test. The teachers’ responses to the questionnaire are presented and analysed in the paper using theories on attention. Implementations of the results of the study in assessment and professional development are discussed.

In this chapter, we give an overview of the mathematics teacher education in Hong Kong. Against this background, the contents of the preparatory programme for pre-service and in-service mathematics teachers offered by the Faculty of Education at the University of Hong Kong are reviewed. Important stages of changes of the programme in the past decade are traced, and the content of the mathematics-related component is analyzed. Four issues on preparation of mathematics teachers are then discussed. They include: understanding of the mathematics curriculum, mastering of generic teaching skills and the teaching of specific topics, the development of basic needs for an era of information technology, and the development of teachers’ ability of self-reflection.
[Copyright © 2010 Sense Publishers. The publisher web site is located at https://www.sensepublishers.com]

實行校本評核是香港新高中學制改革的重要一環。雖然數學科校本評核的時間表至今還未落實，但已有不少本地研究結果顯示，數學科教師對校本評核的擬題及建議評核模式甚感徬徨和憂慮，亦懷疑其成效及公平性。在推行數學校本評核方面，英國和澳洲均有豐富經驗。香港建議的評估模式與英國曾使用的方式相近，而澳洲昆士蘭州的校本評核則建基於校本課程的推行，甚具特色。本文將透過分析英國 GCSE 數學科的學科作業和澳洲昆士蘭州校本評核的經驗得失，探討香港數學科校本評核未來的發展方向，以期為有關當局構想的校本評核模式提供改進建議。
[Copyright © 香港中文大學，2012.]