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.

Textbooks play an important part in teaching and learning mathematics. However, textbook research on spatial ability has so far received little attention. In this study, we investigated whether school mathematics textbooks provide enough opportunities for primary students to learn three-dimensional shapes and help them acquire spatial ability. Three mathematics textbook series used in Hong Kong were analysed through content analysis. Findings showed each series of textbooks contained five domains for introducing solid figures, which included real-life examples, understanding concepts, measurement, finding laws, and developing spatial ability. The development of spatial abilities was mainly shown in the production of three-dimensional graphics. What students experienced in the learning of 3-D shapes was relatively narrow. Geometric graphics were mainly limited to the conventional shapes at the early stage. Activities to explore three-dimensional graphics were insufficient. It was suggested that combining the surrounding world of children with geometry in the classroom was not just a criterion for textbooks but also the focus of classroom teaching. The flexibility of teachers’ adoptions of textbooks is also worthy of further investigation. Copyright © 2021 by the authors; licensee Modestum.

The success of East Asian school education in general, and in mathematics education in particular, has been an ongoing subject of research over the last few decades in the “West”, suggesting that no conclusive factor(s) underlying performance appears to have been identified yet. The phenomenon of the “paradox of the Chinese learner” remains, while OECD data indicates an absence of correlation between affective factors and performance. This paper reports on a research study that has been designed to explore the possible involvement — and significance — in student learning of the conative domain, since most if not all prior studies had focused only on the cognitive and affective domains. To this end, a validated questionnaire was administered to 1,505 students from primary and secondary schools in Hong Kong. The “What I Find Important (in My Mathematics Learning)” questionnaire collects data regarding student valuing in three ways: a 5-point Likert scale (64 items), semantic differential items (10 items), and an open-ended, scenario-stimulated response section (4 items). Principal component analysis and content analysis of collected questionnaire data suggest that Hong Kong students highly valued 11 attributes, namely word-problem skills, activities, practice, exploration, ICT, connections, process, feedback, explanation, control, and certainty. These values are interpreted from a sociocultural lens, with some of these associated with Confucian Heritage Culture values, but at the same time having interacted with cognitive and affective factors potentially to optimize student performance. Copyright © 2018 HKERA International Conference.

This chapter introduces the reader to the What I Find Important (in my mathematics learning) study (WIFI), conducted by a consortium of 21 research teams from 18 economies. It uses the same questionnaire to assess what students value in their respective mathematics education experiences. Two case economies, Hong Kong and Japan, provide the context for the discussion. This provides a reference point for analyzing four significant themes: the affordance to identify and define cultures and subcultures, the documenting and comparing of espoused and enacted valuing, the triangulation of survey responses, and the culturally situated labelling of values and valuing. Copyright © 2017 Springer International Publishing AG.

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.

Mathematical disagreements occur when students challenge each other’s ideas related to a mathematical concept. In this research, we examined Hong Kong and U.S. elementary teachers’ perceptions of mathematical disagreements and their resolutions using a video-stimulated survey. Participants were directed to give particular attention to the mathematics embedded within the disagreement and approaches for resolving the disagreement. Results revealed incomplete knowledge structures for the SELECTed mathematical topic for both Hong Kong and U.S. participants. Differences existed between the two groups regarding the resolution of the disagreement, as Hong Kong participants focused on the content within the resolution process while U.S. participants focused on the form of the resolution process. Both groups found value in mathematical disagreements but for different reasons. Hong Kong participants indicated that the mathematical disagreements supported them in identifying students’ misunderstandings. In contrast, U.S. participants reported that mathematical disagreements helped to identify areas in which students lacked prerequisite knowledge. Implications for future work are provided. Copyright © 2016 International Journal of Education in Mathematics, Science and Technology.