The topic of similarity plays an essential role in developing students’ deductive reasoning. However, knowing how to teach similarity and understanding how to incorporate deductive reasoning and proof along with plane geometry remain a challenge to both school curriculum creators and teachers. This study identified the problems and characteristics regarding how similarity is treated in secondary mathematics textbooks in Hong Kong in the past half century. The content analysis method was used to analyze six secondary mathematics textbook series published in different periods. From the epistemological perspective of the textbook contents, our analysis shows the historical context and learning trajectories of how similarity was treated in school curriculum. The natural axiomatic geometry paradigm is not emphasized too much at different stages and most of the textbooks did not provide formal proofs of similarity. The intuitive idea was gradually con-solidated into a formal definition of similarity. Furthermore, the way that rigorous geometric de-duction can be performed from intuitive concepts and experimental geometry to the idea of proofs and formal proofs is also discussed. Copyright © 2021 by the authors.

Values, as a culturally specific notion, have a vital role to play in classroom mathematics learning. In this chapter, we argue that valuing, especially from the student's perspective, serves as a lens for us to better understand how they perform in mathematics learning. To develop such a lens, we investigated the componential structure of Hong Kong mathematics students by utilising a values questionnaire as a lens to better understand what the students find important in mathematics learning. A principal component analysis has been used in this study with the objective to interrogate the data. The analysis of the data led to the identification of nine components valued by Hong Kong students in their mathematics learning. We discuss the findings in terms of the Hong Kong culture and context and the value categories and we suggest implications for future research studies. Copyright © 2018 Springer Nature Switzerland AG.

Mathematics has be stereotyped as a male-dominated subject, and there is considerable evidence to support this belief. There has been much research in the past three decades on gender-related differences in elementary and secondary school mathematics. The research found that teachers possess different beliefs about male and female students that influence their teaching behaviour, which then directly or indirectly impact their students' behaviours, beliefs, and achievements in mathematics. Based on data collected from teacher questionnaire surveys in the Chinese Mainland and Hong Kong, this study examines teachers' beliefs about the achievements of boys and girls in mathematics. The study also compares the findings in the two regions surveyed. Results showed that teachers gave more attention to boys than girls, regardless of the teacher's gender. Not only are teachers more likely to recall more boys than girls, but also more boys than girls with average academic standards. Copyright © 2013 Korean Society of Mathematical Education.

It has become increasingly recognized that what teachers and students value affect teaching and learning in general and in the area of mathematics in particular. Yet, the extent to which this is so varies across cultural regions. In recent years, how the ethnic Chinese teach and learn mathematics has attracted much attention worldwide. It is precisely the purpose of the present study to investigate the value structures of three Chinese regions. Using a recently developed and validated questionnaire, students’ values in mathematics learning in the Chinese Mainland, Hong Kong and Taiwan are delineated. In the first place, the results reveal that there are six dimensions in the students’ value structure, namely achievement, relevance, practice, communication, information and communications technology as well as feedback. However, in each of the six value components derived from the principal components analysis, statistically significant differences between the regions were found. Copyright © 2015 Springer Science + Business Media B.V.

This study is the part of a larger study on investigating Hong Kong (HK) prospective teachers’ (PTs) Subject Matter Knowledge (SMK) and Pedagogical Content Knowledge (PCK). In this paper, five HK PTs’ SMK and PCK on teaching one topic regarding square root were investigated. The results suggest that insufficient understanding on the concept of algebraic operation is the major obstacle to limit those student teachers from teaching students with mathematical understanding. The results further echo with the viewpoint that SMK and PCK are two interrelated constructs and rich SMK leads to high quality of PCK.

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.]

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].

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.]