Flipping the classroom is a current pedagogical innovation in many schools and universities. Although interest in flipped classroom (or Inverted Classroom) continues to grow, its implementation so far has been driven more by teachers' intuitive beliefs, rather than empirically-based principles. Many studies merely replace in-class instructions with videos and use class time for group discussions. But what instructional design framework should we use in planning the overall flipped classroom approach? This paper attempts to answer this question through two exploratory studies conducted in a Hong Kong secondary school. In Study 1, a flipped classroom Mathematics remedial approach was offered for underperforming students (n = 13) in Form 6 (Grade 12). In Study 2, high ability students (n = 24) in Form 6 participated in another flipped classroom Mathematics training approach. Both flipped classroom approaches utilized the First Principles of Instruction design theory. Paired t-test results indicated significant learning gains in both groups of students. Based on the suggestions of students and teacher as well as the existing literature, several recommendations for course planning, out-of-class learning, and in-class learning of flipped classroom are proposed.

The Hong Kong Education Bureau recommends that primary school pupils' mathematical achievement be enhanced via collaborative discussions engendered by group work. This pedagogic change may be hindered by Confucian heritage classroom practices and Western-dominated group work approaches that predominate in Hong Kong. To overcome these obstacles, we introduced a relational approach to group work in a quasi-experimental study. Our sample included 20 teachers randomly allocated to experimental (12) and control (8) conditions and their 504 mathematics pupils (aged 9-10). The relational approach focused on the development of peer relationships in a culturally appropriate manner and was implemented over 7 months. Pupils were pre-/post-tested for mathematical achievement and systematically observed, and the teachers were assessed for subject knowledge and pre-/post-tested for pedagogic efficacy. Analysis of covariance (ANCOVA) and hierarchical linear modeling (HLM) results show enhanced mathematical achievement, supported by improved peer-based communication skills and time-on-task for the experimental pupils. Experimental teachers raised their pedagogic efficacy. Results indicate the potential of the relational approach for boosting academic achievement via enhanced child-peer-teacher interaction and the need to reassess the role of peer-based latent collectivist learning in Confucian heritage classrooms.

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。

本文旨在匯報在香港中學數學科創新教學法的探索性研究結果。“翻轉課堂”，即學生在家中觀看相關概念視頻資料後，然後在課堂上解題，可以讓學生提高學習解決問題的能力和相關知識；而創新教學法與“翻轉課堂”的方式恰恰相反，學生首先在課堂中盡力解決問題並分享結果，再通過家中觀看相關概念與步驟的視頻來鞏固概念和解題步驟。同時整個教，學過程利用移動裝置支援學生學習。這種創新教學方法名為“流動翻轉課堂”。中學一年級的兩個班級參與了本次兩個星期的研究，其中一個使用“翻轉課堂”而另一個使用“移動翻轉課堂”。研究結果表明儘管兩個班級學習成績均取得提高，但使用翻轉課堂的班級有更好的表現。但是，在解決問題技巧方面，學生使用新的教學方式展示出更好的結果。這表明新的教學方式有助於提升學生解決問題的能力。

The dominance of Asian communities in international league tables such as those produced by The Program for International Student Assessment, which monitors competence in literacy and numeracy, has resulted in a policy discourse from the English government of failing schools, deficit curricular and ineffective teachers. This in turn has led to a re-defining of the National Curriculum framework for pupils educated in England with greater focus given in the Early Years curriculum to Mathematical functions particularly those associated with skills in counting; understanding and using number; calculating simple addition and subtraction problems and the understanding of shape, space and measure. Drawing on research carried out in Hong Kong and England this article offers a cross-cultural comparison of the expectations of Early Years Teachers in terms of the capabilities of early learners in achieving elements of number competency. The study of teachers’ expectation is a neglected field in research when applied to compare intercultural achievement. In identifying divergent national expectations, the current panic over what constitutes an appropriate maths curriculum is critiqued and recommendations made for further exploration into teachers’ expectations as to the age and stage at which elements of the maths curriculum are introduced in English schools.
[Copyright © 2016 ASPE.]

The DG has prepared a questionnaire to collect data of teachers' practise in China, Taiwan, Hong Kong, and Korea. The results, together with the literature search in theory and practice in mathematics education was prepared into a booklet of 90 pages for discussion during the ICME-12. There were two sessions of discussion during the ICME-12 and the following is a report of work and discussion of the DG during the ICME-12.

The adoption of educational technology in teaching depends on how well a teacher accepts it. This paper draws on a technology acceptance survey of pre-service primary mathematics teachers in Hong Kong to study the factors influencing their technology acceptance. This work adopted a mixed method approach, in which quantitative data were collected through questionnaire survey from 234 pre-service teachers, where the data were analysed using structural equation modelling with a customised technology acceptance model. The qualitative data were also collected from 14 of these pre-service teachers through interviews, and analysed using the iterative coding process. The results show an overall positive attitude towards the use of educational technology, while perceived usefulness is more influential than perceived ease of use. Perceived ease of use is found to rely heavily on facilitating conditions rather than computer self-efficacy. We also found that subjective norms have an indirect influence on the usage and adoption in our context. Explanations for these findings are discussed, together with implications of the results. Our findings are intended to provide insights to policy makers about how to design teacher education programmes that address the demands of learning and teaching with educational technologies in Hong Kong and related contexts.
[Copyright © 2015 Australasian Journal of Educational Technology.]