While Hong Kong students excel at international tests in mathematics, they do not display corresponding attitudes toward mathematics learning. This study examined 10 Hong Kong Secondary 6 students' perceptions of learning mathematics (experiential curriculum) and their perceived factors that limited the development of students' positive attitudes toward mathematics learning in the New Senior Secondary mathematics curriculum by content analysis of their responses in the interviews. Although the participants in this study expected to learn mathematics by "conceptual learning" and the authentic applications of mathematics, they experienced rote-and-drilling-dominated learning approaches in mathematics education, which had succeeded in developing their numerical senses and problem-solving skills but failed to develop their sense of creativity and positive attitudes toward mathematics. The practical mentality and the examination-oriented culture in Hong Kong were the perceived factors that caused such situations.香港學生於不同的國際數學評測中都表現優越，但他們對學習數學並未展現出相應的態度。本研究探討10名香港中六學生對學習數學的看法。研究員對學生的訪問回應進行了內容分析，從中了解阻礙學生發展出對學習高中數學課程的良好態度的因素。學生雖然期望能透過概念學習和應用數學於日常環境來學習數學，但他們總是經歷死記硬背及不斷操練的方式來學習。此方式或許能有效發展學生的數感和解難能力，但未能幫助他們建立創意和良好的數學態度。務實心態和應試文化是學生最重視的因素。 Copyright © 2022 香港中文大學香港教育研究所.

Subject-specific training in mathematics teaching for students with intellectual disabilities (IDs) has been little studied in the academic field and is uncommon in the practice of teacher education. Given that teachers face significant challenges in regard to teaching mathematics to ID students, it is necessary to know whether there is a need for subject-specific training. If yes, what kind of subject-specific training do teachers need? What kind of subject-specific knowledge should be covered? How can this kind of training contribute to improving mathematics teaching for ID students?To answer the above questions, this study focuses on one particular teacher professional development programme (BE MATHS programme) for mathematics teachers who teach ID students in special schools in Hong Kong. Programme effects and the contributing factors of the effects are examined to explore whether and how subjectspecific support can contribute to the profession of teaching mathematics to ID students.The study is conducted via a mixed-methods approach. First, it uses quantitative measures to examine teachers’ changes in mathematics teaching efficacy and students’ changes in their academic engaged time in mathematics classes. Second, a qualitative approach is used to explore the contributing factors of the changes.Quantitative results show that the programme has a significant positive effect on teachers’ mathematics teaching outcome expectancy and a conditional positive effect on teachers’ personal mathematics teaching efficacy. It is also found that the programme can improve teachers’ mathematics teaching by engaging more students in mathematics learning.The qualitative findings in this study show that the design of teaching and learning trajectories with subject experts is a substantial learning activity for teachers. During the design process, teachers and subject experts identified knowledge gaps within the mathematical content to be delivered to ID students and successfully inserted

In English-medium instruction (EMI), English-as-a-second-language students will learn all/some subjects through English. Although there are a considerable number of studies which explore classroom interaction in Hong Kong (HK) secondary EMI schools, few studies have investigated EMI lessons which involve South Asian ethnic minorised students. These students share different linguistic and cultural backgrounds and they may not share a common first language with the teacher and other classmates. This study conducts a multimodal conversation analysis of science and mathematics lessons at a HK EMI secondary school, triangulated with interview data, in order to explore how the EMI teacher mobilises various resources to make discipline-specific knowledge accessible and cater for the different needs of all students in the classroom. This study argues that the process of enacting inclusive practices is a process of translanguaging which requires the EMI teacher to mobilise various available multilingual and semiotic resources and draw on what students know collectively for transcending cultural boundaries from the students' everyday culture to cultures of school science and mathematics. Copyright ©2021 Springer.

Purpose:Amid rapid technological development in the Fourth Industrial Revolution, this article engages with an important question, especially in the context of science, technology, engineering, and mathematics (STEM) education: Can technology itself transform teaching and learning? Design/Approach/Methods:Constructionist learning responds to the current "maker movement," which draws upon the innate human desire to make things with our hands. Two important elements of constructionist learning-technology literacy and engineering design-have implications for meeting the global need for expertise in the STEM disciplines. To date, the practice of teaching and learning mathematics remains to be dominated by manipulation of symbols with the paper-and-pencil medium. In response, this article discusses how constructionist learning can play an important role in teaching and learning school mathematics via a transdisciplinary approach for STEM education.Findings:Two examples of the authors' empirical research on constructionist learning in school mathematics classrooms with 3D printing are illustrated. Findings suggest that the 3D Printing Pens played an active role in the construction of artifact (physically) and mathematical meaning (cognitively).Originality/Value:The empirical results as discussed in this article warrant more design-based classroom interventions to further investigate students' constructionist learning in technological, hands-on, and innovation-oriented environments. Copyright ©2021 SAGE Publications.

In this paper, we explore the challenges experienced by a group of Primary 5 to 6 (age 12-14) students as they engaged in a series of problem-solving tasks through block-based programming. The challenges were analysed according to a taxonomy focusing on the presence of computational thinking (CT) elements in mathematics contexts: preparing problems, programming, create computational abstractions, as well as troubleshooting and debugging. Our results suggested that the challenges experienced by students were compounded by both having to learn the CT-based environment as well as to apply mathematical concepts and problem solving in that environment. Possible explanations for the observed challenges stemming from differences between CT and mathematical thinking are discussed in detail, along with suggestions towards improving the effectiveness of integrating CT into mathematics learning. This study provides evidence-based directions towards enriching mathematics education with computation. Copyright ©2021 SAGE Publications.

Recent studies on English-Medium-Instruction (EMI) classroom interaction have begun to look at the role of translanguaging as a pedagogical practice in supporting participants to exploit multilingual and multimodal resources to facilitate content teaching and learning. The present study contributes to this growing body of literature by focusing on playful talk in multiple languages and modalities in EMI mathematics classrooms in a secondary school in Hong Kong. Based on the data collected from a linguistic ethnography, we analyze how the teacher constructs playful talk in order to achieve various pedagogical goals including building rapport, facilitating content explanation and promoting meaningful communication with students. The analysis demonstrates that translanguaging appears to be a critical resource and that several social factors, including the teacher's personal belief, history, sociocultural, and pedagogical knowledge, play a role in constructing playful talk. The playful talk transforms the classroom into a translanguaging space, which in turn allows the teacher and students to perform a range of creative acts and experiment with a variety of voices to facilitate the meaning making and knowledge construction processes. Copyright © 2021 Oxford University Press.

Recent studies on classroom discourse have challenged the traditional classroom role set and emphasised equal contributions from the participants and the emergence of knowledge through active participation. Co-learning emphasises the process in which teachers and students attempt to adapt to one another's behaviour and learn from each other in order to produce desirable learning outcomes. Current research has paid little attention to the ways in which content teachers and students jointly negotiate new knowledge in bi/multilingual classrooms. Based on data collected from a linguistic ethnography in Hong Kong English-Medium-Instruction secondary mathematics classrooms, this paper uses translanguaging as an analytical perspective to analyse how the EMI teacher and students co-learn in the classroom. The data are analysed using Multimodal Conversation Analysis and triangulated with the video-stimulated-recall-interviews which are analysed using Interpretative Phenomenological Analysis. The paper argues that translanguaging creates a safe space for co-learning that emphasises equity in knowledge construction and challenges the hierarchical relationship between the teacher and the learner. Copyright © 2021 Routledge.

This study examines how teachers' discourse moves influence patterns of authority in the mathematics classroom. We identify changes in authority structure in one classroom taught by a primary mathematics teacher in Hong Kong. This teacher participant was one of 32 who participated in a larger teacher-intervention study that aimed to help teachers orchestrate dialogic classroom discourse for rich learning opportunities in mathematics. Previous research has investigated teachers' discourse behaviors and authority structures in mathematics classrooms, but the connection between the two has yet to be addressed in extant studies. Our analysis shows that certain features and patterns embedded in classroom discourse can constrain or enable certain kinds of authority in the classroom. This study contributes to understanding the ways in which dialogic discourse may influence how authority is structured, including how mathematics teaching and learning are enacted through authority styles, and how the discipline of mathematics is positioned from an authority perspective. Copyright © 2021 Springer.

This paper documents the process and outcome of the development and validation of a coding scheme to analyse mathematics classroom discourse in the context of Hong Kong primary schools. The objective of this coding scheme was to systematically analyse teacher discourse behaviours before and after an intervention programme; the programme aimed to assist in-service teachers to develop conceptual and practical tools for engaging students in dialogical discourse in mathematics classrooms. This paper provides a detailed outline of what took place in designing and refining the coding scheme as well as improving its validity and reliability. The developed coding scheme can be effective for highlighting dialogic discourse, authority structures and student participation in mathematics classrooms and beyond. Consequently, it was possible to assess the efficacy of the teacher intervention programme. On the other hand, the developed coding scheme could be used to help teachers to gain a sense of efficacy over their instruction by giving them a roadmap for what they can do before and during instruction. Copyright © 2021 Routledge.

Given the relationship between teacher beliefs and practices, it is critical to understand how pre-service teachers' past school experiences impact on their beliefs about teaching. There is a growing recognition of the influence of preservice teachers' prior mathematical experiences on their beliefs regarding mathematics instruction in the primary school classroom. This qualitative study aimed to investigate Hong Kong primary pre-service teachers' past experiences in learning mathematics and their beliefs about the teaching of mathematics. Nineteen primary pre-service teachers who had selected mathematics as their major in a teacher training program participated in the study. Each participant was required to complete three beliefs tasks in the individual interview in order to recall the teaching of their best mathematics teachers, articulate their memories of learning mathematics, and uncover the kind of primary mathematics teacher they planned to be. The results provided a valuable insight into the effects of pre-service teachers' prior mathematics class incidents on their espoused pedagogical beliefs. While both positive and negative learning experiences of mathematics had a positive impact on interviewees' beliefs about mathematics teaching, most demonstrated their willingness to learn from the past and realised the need to establish better learning environments for their future primary school students. Copyright © 2021 International Journal of Instruction.