Although mathematical modeling plays an important role in many curricula worldwide, significant discrepancies persist in the importance of mathematical modeling in ordinary mathematics classrooms and teacher education. This paper compares pre-service mathematics teachers' professional mathematical modeling competencies in three different regions—Germany, Mainland China, and Hong Kong—where educational and cultural traditions differ, including the role of mathematical modeling. In total, 232 pre-service mathematics teachers from the three regions completed a modeling task covering mathematics content knowledge (MCK) of modeling and mathematical pedagogical content knowledge (MPCK) of modeling. The results show that pre-service teachers from Germany demonstrated the strongest MCK and MPCK of mathematical modeling; by contrast, pre-service mathematics teachers from Mainland China and Hong Kong demonstrated relatively weaker MCK and MPCK of mathematical modeling. MCK and MPCK of mathematical modeling were also found to be unevenly developed at different competence levels for the three regions. These differences may be attributed to the history of mathematical modeling in mathematics curricula, teacher education, and teaching culture in these three regions. Copyright © 2021 The Author(s).

By considering the example of proving the triangle postulate, this study aimed to explore Hong Kong preservice and novice teachers' knowledge competencies and their beliefs about preformal and formal proofs. The findings revealed that such teachers are not proficient in using preformal proofs and do not realize that preformal proofs are a useful tool for connecting abstract geometrical concepts with concrete meanings. We conclude by providing strategies for teachers to use preformal proofs effectively in their teaching of geometric propositions. Copyright © 2017 Mathematics Education Research Group of Australasia, Inc

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.

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.]

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 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.]

In this paper, qualitative results of a case study about the professional knowledge in the area of argumentation and proof of future teachers from universities in three countries are described. Based on results of open questionnaires, data about the competencies these future teachers have in the areas of mathematical knowledge and knowledge of mathematics pedagogy are presented. The study shows that the majority of the future teachers at the participating universities situated in Germany, Hong Kong and Australia, were not able to execute formal proofs, requiring only lower secondary mathematical content, in an adequate and mathematically correct way. In contrast, in all samples there was evidence of at least average competencies of pedagogical content reflection about formal and pre-formal proving in mathematics teaching. However, it appears that possessing a mathematical background as mandated for teaching and having a high affinity with proving in mathematics teaching at the lower secondary level are not a sufficient preparation for teaching proof.
[Copyright © FIZ Karlsruhe 2008.]

This study investigated the conceptual understanding of fraction division of 72 Hong Kong pre-service teachers by asking them to pose a real life story problem. Analyses of the problems posed show that many of these pre-service teachers had incorrectly interpreted the division concept in their problems as sharing rather than measurement. A short intervention shows significant improvement in posing problems in terms of mathematical correctness as related to real life situations. This study particularly shows an increase of the correct use of the measurement concept from the pre-test to the post-test. The study also shows that problem posing could be used to measure conceptual understanding. Additional studies should be conducted to show effects of different teaching interventions regarding improving the conceptual understanding of divisions of fractions.
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