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Felix Klein's notion of "double discontinuity" between university mathematics and secondary school mathematics has persisted in mathematics teacher education. Situating this study in Hong Kong, we investigated three prospective secondary teachers' experiences in higher education and secondary mathematics classrooms, including their figured worlds, identities, and mathematical knowledge constructed through those experiences. Our analysis revealed their contrasting experiences in these two contexts, adding to our understanding of the phenomenon of "double discontinuity" in terms of not only how it is relevant to Hong Kong but also how it may manifest in the specific cultural context. Moreover, we found coherency and continuity during the prospective teachers' secondary-tertiary transition; their learning experiences in both environments served as critical resources upon which they reflected to envision their future mathematics teaching. We conclude with implications and suggestions for mathematics teacher education to support prospective teachers' (and their future students') transitions between high school and university mathematics.

We report on an action research study conducted by two mathematics teacher educators in the United Kingdom and Hong Kong. The project consisted of three phases, the first two taking place in our respective teacher education courses and a final phase in which prospective mathematics teachers from both locations engaged in dialogue through a speculative fiction task. Our aim was to explore how our prospective mathematics teachers can be supported in becoming mathematics teachers for sustainable futures by innovating our own mathematics teacher education curricula. This study suggests that generative methods which support teachers in speculating on paths to potential futures as teachers of mathematics, can provide access to how prospective teachers negotiate issues in relation to the climate crisis and ways in which they conceive of related changes in their practices. By identifying the aspects of mathematics teaching that are viewed by the prospective teachers as contingent, and through offering tasks that support an expansion of this view, teacher educators are better placed to support the development of teaching practices needed for sustainable futures.

This paper reports on the design, implementation, and results of a video-based study that focused on supporting an individualized viewing experience, keeping a record of what was noticed, providing a degree of guiding framework, and facilitating a combination of individual and collaborative reflections in noticing activities for STEM professional development. A cohort of 20 prospective mathematics teachers at a public university in Hong Kong participated in the study. The participants engaged in a series of blended learning activities with a feature that allowed them to leave comments while viewing of a lesson video, which focused on technology integration in mathematics classrooms. The designed activities were helpful for the participants to document and reflect on their observations, while viewing videos outside the classroom allowed them to meaningfully engage with the course materials. Moreover, the use of videos supported the participants' broad but crucial STEM classroom practices that would help them prepare for future lessons.

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.

In this paper, we introduce a technology-enhanced pedagogical sequence for supporting lower secondary school students' sense-making of the concept of volume in a non-procedural and non-formula-driven way. Specifically, we illustrate a novel approach of using dynamic geometric environment (DGE) to introduce the meaning of volume and then deriving the volume of a hemisphere with minimal algebra but simple trigonometry. This method aims to support students' geometrical reasoning through comparing the volume of different three-dimensional shapes and analysing their cross sections two-dimensionally, thus drawing on the concept of area. We highlight the affordances of the designed DGE sketches for fostering a dynamic conception of volume. [ABSTRACT FROM AUTHOR]

We adopt five observation categories, namely classroom management, classroom environment, communication, mathematical content and tasks, to analyse four in‐service secondary mathematics teachers' noticing upon watching video episodes showing an actual mathematics lesson that implemented 3D Printing Pens for teaching and learning shape and space. We use coding to analyse what the participants generally identified as important or noteworthy in the video. Moreover, we employ thematic analysis to delve deeper into the participants' interpretations and decisions in relation to using 3D Pens for teaching and learning mathematics. Our findings have implications for teachers' professional development in the area of technology integration especially in terms of their realisation of the affordances of novel‐to‐them technologies. We also report methodological and conceptual contributions towards teacher noticing. Practitioner notesWhat is already known about this topic Various frameworks have been proposed for conceptualising teachers' expertise in technology‐rich pedagogies; however, few have addressed teachers' initial experience of adopting a novel‐to‐them technology in subject teaching.In teacher education, the method of video‐based noticing has been widely undertaken in the last two decades to help preservice and in‐service teachers visualise complex classroom situations and interpret classroom events.What this paper adds This study investigates what in‐service mathematics teachers find significant, the pedagogical considerations they make and their professional development in integrating technologies for teaching and learning mathematics.Particularly, video‐based noticing is used as a means for facilitating teachers' professional growth through realising the affordances of 3D Printing Pens in mathematics education.Implications for practice and/or policy This study provides qualitative evidence that video‐based noticing was productive in facilitating teachers' technological, pedagogical and content knowledge (TPACK), in particular, in realising the educational affordances of a novel‐to‐them technology.The videos captured the dynamic process of students' drawing with 3D Pens "in action" rather than merely capturing their final products in a static manner, which facilitated the teachers' reflections about the evolution of students' mathematical thinking. [ABSTRACT FROM AUTHOR]

The recent and popular "Maker" movement worldwide has revived conversations about creativity, hands‐on "Making," arts and design, humans with tools and digital experiences beyond the flat‐screen. However, such conversation mainly revolved outside the realm of formal education. This article presents two learning tasks, one in upper primary (age 10–11) and one in lower secondary (age 12–13), which integrate "Making" and 3D computer‐aided design (CAD), thereby facilitating Science, Technology, Engineering, and Mathematics (STEM) learning in mathematics classrooms. By adopting a design‐based research methodology, we examine students' mathematics learning with respect to dissecting and forming 2D shapes and volume of composite solids with the use of 3D CAD and the kinds of integrated STEM learning practices they demonstrated in the activities. Qualitative data were collected in the form of videos of the students' communication and screenshots of their initial and final designs as they engaged with the 3D CAD environment, as well as students' written reflections and teachers' lesson analysis. Results showed that the students used 3D CAD to develop spatial skills and to achieve mathematics learning far beyond using formulae and performing procedures. The learning activities also enabled an integrated STEM learning experience in productive and unobtrusive ways. [ABSTRACT FROM AUTHOR]