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.

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.

比較臺灣、內地和香港三地2000年前後進行的建構主義數學新課程改革的期望課程和實施課程，發現有很多因素限制建構主義課程的實施，如政治因素、考試文化、社會參與、教科書編寫和教師培訓等，而系統的課程評價模式的引入、師範教育的改革以及鼓勵更廣泛的社會參與等是促進課程改革成功的有效策略。
[Copyright © 2011 北京教育科學研究院; 北京廣播電視大學.]

The paper focuses on the evaluation of the present curriculum in Hong Kong. It discusses the analysis of questionnaires collected from 130 primary schools in Hong Kong. Findings regarding the views of mathematics teachers on the goals of curriculum, teaching content and assessment methods are also presented. Besides the paper discusses the learning and teaching strategies in the mathematics classroom, small class teaching (SCT) has been adopted by most of the schools in the first three years of primary education for about ten years. A lot of research has been conducted to study the efficacy of SCT. Most of the studies confirmed the benefits of SCT. The author made a study of this in 4 primary schools. There were classroom observations for 10 lessons. Whether their teaching can enhance children^ higher order thinking skills will also be investigated. In Hong Kong, the Territory-wide System Assessment (TSA) is an assessment administered at the territory level. It facilitates assessment for learning by providing schools with objective data on students' performances at the end of Key Stages 1-3. This paper examines its efficacy and discusses the public view on it. Teachers are interviewed regarding their views on the mathematics curriculum and their experiences. Children are also interviewed to investigate their interest in mathematics learning. The paper continues to discuss the mathematics curriculum in 3 different countries namely, the United States, the United Kingdom and Mainland China. A brief comparison is made regarding the content of their primary mathematics curricula, the learning and teaching strategies, children^ interest in mathematics learning and the cultural impact on their learning. Moreover, analysis of the cultural differences and contextual factors such as high expectation of parents, keen competition in education may shed light on the design of the mathematics curriculum. Research into comparative studies of the mathematics curricula of major Asian

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.

Background: This study was part of a large-scale quasi-experiment on the causal relations among feedback, self-directed learning, and mathematics achievement of primary students in Hong Kong. The larger study was sponsored by a General Research Grant awarded by Research Grants Council of UGC, Hong Kong (Project Number 844011). Aims and Keywords: The study aimed to develop and validate, using a Rasch approach, of an instrument for measuring mathematics achievement of Primary five students. Sample: The sample comprised 1,368 Primary 5 students from 16 Hong Kong schools who participated voluntarily. Methods: A pre-test/post-test design was used for the larger study. Data for this study were collected at the pre-test in form of a mathematics test completed during class-time. A 35-item mathematics test was developed after careful analysis of the local curriculum, and in consultation with teachers on the suitability of the test for students by the end of Semester One of Primary 5. Rasch analysis with the Winsteps software (version 3.70) was then used to validate the instrument. Results: The results showed that: (1) item-fit was between 0.5 and 1.5 for all items except one; (2) Eigen value of the first contrast of the Rasch PCA of Residuals was below 2.0; (3) Rasch person and item reliabilities were 0.80 and 1.00 respectively; (4) there was good alignment between item difficulty and student ability; (5) no gender-DIF was found in the items. Conclusions: Measurement validity is one of the most crucial factors for the overall validity of any research study. This study developed a valid and reliable instrument for measuring mathematics achievement of Primary 5 students.

在2012及2015年學生能力國際評估計劃（PISA）考試中，亞洲地區包括上海、香港、新加坡及台灣的學生（平均15歲）的數學能力名列首五名，美國、英格蘭等歐美國家則處於中游位置。從這項考試數據顯示，美、英兩地學生的數學能力不及亞洲地方。硏究顯示，不同地方學生的數學運用差異與身處的學習環境有一定關係；此外，他們如何學習數學、應用數學邏輯亦會影響評估表現（OECD, 2012）。課堂上，教科書是輔助老師教學的主要工具。Nciol & Crepo（2006）指出，教科書對學生數學學習表現有重要影響，亦在教師教授數學時扮演關鍵角色。Stein、Remillard與Smith（2007）研究進一步發現，教科書内容中的排序、組織、焦點會影響數學老師的教學及學生如何學習數學。 因此，本文對照香港、新加坡、美國及英格蘭的初中數學教科書，探討當中異同。透過20多篇探討四地初中數學教科書的文章，檢視學生數學成績差異與教科書編撰的關係。全文將從教科書的課程目的、課題內容、練習題目及使用等四方面分析問題。