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.

This study involved 34 female adolescent students attending mathematics classes in a girls' hostel in Hong Kong. The subjects' ages ranged from 12 to 18 years. All students exhibited varying degrees of emotional and behavioural problems, and all experienced learning difficulties in mathematics. The study aimed to discover whether the use of a simple token reward system would increase the students' work output, participation rate, accuracy, and neatness of bookwork during mathematics lessons, and whether the system would also have a positive influence on the girls' attitude toward mathematics. The four-week intervention programme involved the provision of token rewards during lesson time to every girl who showed any improvement in any of the four aspects of learning. Baseline measures were taken over a two-week period before the intervention commenced, and regular measurements were taken during and immediately after the programme. The same measures were taken again four weeks after the reinforcement programme had ended to check for maintenance. The results showed that the use of tokens did lead to significant improvements (in most cases p <.01 or better) in work output, participation rate, accuracy and neatness while the programme was in operation. Performance declined, however, in all but neatness once the tokens were no longer in use. The decline in scores did not regress to the baseline level, but most differences were no longer statistically significant. Very minor attitudinal changes in a positive direction were noted; but only in one case did these reach statistical significance.
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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

With the economic and technological developments of Asian countries in the last two decades, nurturing individuals' capabilities for logical thinking and problem solving have become one of the major foci of secondary education. Being a core subject for developing the fundamental ability of high school students towards systematic and organized ways of thinking, mathematics is no longer a requirement only for students who are going to study science or engineering majors in university but has become a common core subject for whole-person education. In this chapter, we shall investigate the recent development of high school mathematics curricula in Hong Kong, South Korea and Singapore, in coping with the change. Copyright © 2018 selection and editorial matter, Kerry J. Kennedy and John Chi-Kin Lee; individual chapters, the contributors.

This study investigates how teacher background, subject knowledge and pedagogic efficacy affect Grade 4 children's (aged 9-10) mathematical achievement in 10 primary schools in Hong Kong. Mathematics teachers were selected for their strong commitment to teaching mathematics and their pupils' consistently high international mathematics performance. Teacher measures (i.e. level of mathematics education, teaching experience, mathematics subject knowledge, performance in mathematical operations and pedagogic efficacy) were checked for factor consistency and assessed against age-appropriate pupil mathematical achievement. The results showed that teachers were secure in their subject knowledge, and that such knowledge was related to their performance of mathematical operations, but it was high levels of pedagogic efficacy and the ability to perform age-appropriate mathematics operations (rather than subject knowledge) that positively affected their pupils' achievement. These findings contradict ongoing international calls for the enhancement of primary school teachers' mathematical subject knowledge, as they show pedagogic efficacy to be more strongly associated with pupil achievement.
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What is learning and how could the learning in mathematics be enhanced has fallen into debate for many years. Singapore rank number one in both TIMSS and PISA in 2015. What are the insights we could earned from such competition? Regarding to the facts that Singapore is one of the first countries in implementing the metacognition into their mathematics curriculum in 1990s (Chan & Leung, 2013), metacognition may possible be the answer we are searching for. There is no doubt that textbooks take a very important role in this. White & Mesa (2014) indicated that lecturer rely highly on textbook in their teaching especially the tasks assigned. However, researches with textbooks related to mathematical content and researches on their potential in developing metacognitive knowledge are limited (Mesa, 2004; Mesa, 2010). Especially, comparisons between metacognitive strategies among textbooks in different countries are very limited. Thus the following questions are proposed to be investigated. 1. Does mathematics textbook emphasis enough metacognitive strategies in enhancing students' metacognition? 2. Does the pattern of using metacognitive strategies in mathematics textbooks different among countries/cities? The assessment is divided as seven categories: think aloud, questioning, self-questioning, error detection, group activity, alternative strategies and reflection. It is identical to those suggested by Chan and Leung (2013). Result shows that think aloud is the most popular strategy used in textbooks among Singapore, British and Hong Kong. However, other strategies weight about only 20% in total. It is suggested that more metacognitive ingredients could be added in textbooks in enhancing students' metacognition.