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。

The present research aims at exploring the effectiveness of spiral bianshi mathematics curriculum on the teaching of speed and circumference to Primary 6 students in Hong Kong. Cognitive and affective learning outcomes, together with students’ beliefs are investigated. Teaching materials of these two topics are designed basing on the framework of spiral bianshi mathematics curriculum and were implemented in three primary schools in Hong Kong. The effectiveness of the curriculum was investigated with a pre-test/post-test, experimental/control group design. Preliminary analyses of the cognitive learning outcomes revealed that the students using the bianshi curriculum and teaching materials performed better than their counterparts. The experimental group also showed more positive attitude in some of the affective variables, though such changes did not happen in all the affective components. The experimental group also showed more positive attitude in some of the affective components. Further statistical analyses could be performed to see why the improvement was not as prominent as expected. A possible further analysis could be, by separating those who had sizable improvement with those who had not, we may attempt to identify the characteristics of students, to see who benefit most (in the affective domain) from the bianshi curriculum. It is hoped that these qualitative data would help unveil the secret of the learning process that leads to the desirable learning results.
[Copyright © 2010 Anna Mei-Yan Chan, Ngai-Ying Wong & Chi-Chung Lam.]

Attention to details is one of the most important specific features of a mathematical way to thinking. When evaluating mathematical questions it is important to teach students to pay attention globally and locally, consider conditions, properties and relationships, since all of these aspects are as important to develop as mathematical techniques. To develop such skills in their students school teachers should have those skills themselves. In this study, we investigate the ability of school mathematics teachers to pay attention to details and use their mathematical knowledge. We are confident that the vast majority of teachers have excellent knowledge of mathematical techniques. Hence the question is whether this kind of knowledge might structure their attention in such a way that the emphasis on procedures deviates their attention from the essential details. Two groups of teachers from New Zealand and Hong Kong were given a mini-test containing seven simple mathematics questions. All questions in the test were provocative in the sense that they looked like routine questions but in fact they had some catch. The results from the test were startling – the vast majority of the teachers did not notice any catch and gave incorrect answers to most questions in the test. After the test the teachers were given a short questionnaire to reflect on their performance on the test. The teachers’ responses to the questionnaire are presented and analysed in the paper using theories on attention. Implementations of the results of the study in assessment and professional development are discussed.

實行校本評核是香港新高中學制改革的重要一環。雖然數學科校本評核的時間表至今還未落實，但已有不少本地研究結果顯示，數學科教師對校本評核的擬題及建議評核模式甚感徬徨和憂慮，亦懷疑其成效及公平性。在推行數學校本評核方面，英國和澳洲均有豐富經驗。香港建議的評估模式與英國曾使用的方式相近，而澳洲昆士蘭州的校本評核則建基於校本課程的推行，甚具特色。本文將透過分析英國 GCSE 數學科的學科作業和澳洲昆士蘭州校本評核的經驗得失，探討香港數學科校本評核未來的發展方向，以期為有關當局構想的校本評核模式提供改進建議。
[Copyright © 香港中文大學，2012.]