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.]

This study investigates the relationship between subject matter knowledge (SMK) for mathematics teaching and self-reported non-cognitive factors among 201 prospective mathematics teachers (PMTs) in Hong Kong. Participants completed a survey adopted from Fennema and Sherman [19] were assessed their confidence in learning mathematics (CLM), attitude towards success in mathematics (ASM), mathematics anxiety (MA), effectance motivation in learning mathematics (EMM), while 73 of them were assessed in a written test on their knowledge. The regression analysis suggests that CLM is the main predictor of the performance in SMK compared to MA and EMM. Findings also show that there were statistically significant effects of both gender and program of studies on their performance on MA, EMM and CLM. The results suggest a further investigation of the relationship between beliefs and SMK among PMTs in other contexts. Implications for the current teacher education system in Hong Kong are also discussed.
[Copyright © 2015 Pushpa Publishing House.]

This study examines the differences and similarities of mathematics teachers’ subject matter knowledge among England, the Chinese mainland and Hong Kong. Data were collected from a ten-item test in the SKIMA subject matter audit instrument [Rowland, T.; Martyn, S.; Barber, P. & Heal, C. (2000). Primary teacher trainees’ mathematics subject knowledge and classroom performance. In: T. Rowland & C. Morgan (eds.), Research in Mathematics Education, Volume 2 (pp. 3–18). ME 2000e.03066] from over 500 participants. Results showed that participants from England performed consistently better, with those from Hong Kong being next and then followed by those from the Chinese mainland. The qualitative data revealed that participants from Hong Kong and the Chinese mainland were fluent in applying routines to solve problems, but had some difficulties in offering explanations or justifications.
[Copyright © 2010 Korean Society of Mathematical Education.]