Teachers and students have experienced an unusual year in 2020 because of the COVID-19 pandemic. To minimize the risk of the epidemic spreading, face-to-face lecturing hours have been reduced, resulting in a substantial need for online instruction. Our project thus aims to develop open access flipped learning resources (e.g. dynamic courseware and instructional videos) for secondary school mathematics teachers and students in Hong Kong. The overarching goal of this study is to make theoretically and empirically supported suggestions for developing the resources. Experiential learning theory was used as the theoretical foundation for developing the resources. A three-cycle recursive instructional design approach involving 34 mathematics educators was used to develop and improve materials that better meet the needs of frontline teachers. Both the qualitative (semi-structured interviews and written feedback) and quantitative (evaluative survey) data collection methods were conducted. The findings of this study reveal the concerns of and requests from our teacher participants, such as providing more detailed guidelines, advanced questions, and interactive quizzes. The findings also reflect the substantial need for open access flipped learning resources in secondary schools. Based on the lessons learned, suggestions are made to inform future development of resources (e.g. inviting retired teachers for assistance). Copyright © 2021 Informa UK Limited, trading as Taylor & Francis Group.

Although mathematical modeling plays an important role in many curricula worldwide, significant discrepancies persist in the importance of mathematical modeling in ordinary mathematics classrooms and teacher education. This paper compares pre-service mathematics teachers' professional mathematical modeling competencies in three different regions—Germany, Mainland China, and Hong Kong—where educational and cultural traditions differ, including the role of mathematical modeling. In total, 232 pre-service mathematics teachers from the three regions completed a modeling task covering mathematics content knowledge (MCK) of modeling and mathematical pedagogical content knowledge (MPCK) of modeling. The results show that pre-service teachers from Germany demonstrated the strongest MCK and MPCK of mathematical modeling; by contrast, pre-service mathematics teachers from Mainland China and Hong Kong demonstrated relatively weaker MCK and MPCK of mathematical modeling. MCK and MPCK of mathematical modeling were also found to be unevenly developed at different competence levels for the three regions. These differences may be attributed to the history of mathematical modeling in mathematics curricula, teacher education, and teaching culture in these three regions. Copyright © 2021 The Author(s).

This paper presents a Learning Study case on the topic of weight in the subject of Mathematics in a Hong Kong school of students with mild intellectual disabilities. The research team, composed of teachers from four Special Education schools, academic staff from a University and officials from the Education Bureau. The three parties worked as a learning community to design and implement a research lesson on the concept of weight.In Special Education Schools, the most common tool for teaching the topic of weight is a set of balance scale to compare the weight of two different objects. Through the demonstration of comparing two different objects, the lower side of the balance scale indicates the heavier weight. The findings of the pre-lesson student interviews show that the students only memorized the visual image of the lower or higher level of the balance scale without understanding what makes the difference in the height level of the balance scale. After identifying the learning difficulties of the students, the teachers realized that the conceptual understanding of weight is far more important than utterance of the observable phenomenon of the balance scale.The lesson adopted a communicative approach using the Variation Theory as a pedagogical tool and integrating the STEM elements in designing the learning activities to help students discern the critical features of the object of learning, as well as explore the concept of weight comprehensively through observation and inquiry. Students were encouraged to use their innate ability to estimate the weight of some objects in their daily life even without a balance scale in hand.This Learning Study case reports the implementation process with the support of video clips of student interviews and the research lesson. It is hoped that this presentation will open up the discussion about teaching the topic of weight in the field of special education. Copyright © 2018 WALS.

Background: Dot enumeration is the basic mathematics competency in young children and a significant indicator of later mathematics achievement. Aim: The present study focused on (1) how children's dot enumeration ability changed as they progressed from late kindergarten years (K3) to the second year of primary school in Hong Kong (P2), and (2) the extent to which such changes are associated with students' mathematics outcomes assessed at the fourth grade, including standardized mathematics achievement, whole number magnitude understanding, and rational number concept. Sample(s): Two hundred and eleven Hong Kong kindergarteners were recruited. Methods: The participants' dot enumeration was assessed from K3 to P2. Their mathematics outcomes were assessed at P4, including standardized mathematics achievement, whole number magnitude understanding, and rational number concept. Results: The changes in their dot enumeration speed reflected a linear growth pattern. Further, both the initial level and growth rate of dot enumeration predicted standardized mathematics achievement and whole number magnitude understanding 2 years later while only the latter predicted rational number concept. Conclusions: The results indicate the importance of focusing on children's growth in a specific mathematics skill, in addition to their status at one single time point. Practical implications are discussed in this article. Copyright ©John Wiley & Sons Ltd.

It has been well documented that active learning (AL) improves student learning outcomes in education. This quasi-experimental study explores the effect of active learning on students' knowledge of calculus concepts, in the form of the Calculus Concept Inventory (CCI), regular assignment scores, and test scores, during an 8-week calculus tutorial program. The active pedagogies used were cooperative problem-based learning and peer assessment, implemented using an interactive online whiteboard (IOWB) called RealtimeBoard. This study reveals statistically significant evidence that active learning increases students' conceptual understanding and graded assignment performance in a first-year calculus class in Hong Kong. Furthermore, this study contributes towards a better understanding of how active learning can be implemented effectively in Asian tertiary mathematics education. Copyright © Springer.

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

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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Constructivist theory of learning is employed in delivering mathematics methodology modules in the Two-year Full-time Certificate in Education (Secondary) Programme in the Hong Kong Institute of Education, where I am working. This paper aims to determine second year student mathematics teachers’ teaching strategies which they acquired after attending a Methods I module in their first year of study, and changes in their practices after attending a second methodology module (Methods II) in their second year. In their first year of study, Chinese student mathematics teachers had been taught in Methods I the various teaching models, for example, specific methods in concept and skill teaching, and the general discovery and expository strategies. Discussion and application of the models were further enhanced in the Methods II module in the second year of study. On the basis of these teaching models, a questionnaire of 64 items of specific teacher activities was designed. It was administered to the class of students at the start of the first semester in their second year of study. Students were asked to indicate the frequency of using each stated teacher activity on a 5-point frequency scale (from “almost never” to “almost always”). Methods II was then offered to these students. At the end of the module, the same questionnaire was administered again. A focus group meeting was also held at the same time. Results showed that student teachers very often tested their pupils’ prior knowledge at the start of the lesson, and they became more aware of building mathematics learning on pupils’ prior experience. Exposition of mathematics content was still preferred; some time was set aside during the lesson to offer guidance to their pupils. Nevertheless, they provided little opportunities for pupils to express themselves and to explore mathematics (e.g., in small-group discussion, in playing mathematical games, and in computer-assisted learning). In the focus group meeting, student teachers