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.

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.