Creativity, one of the cornerstones of students' 21st-century skills, is regarded as an important learning outcome of science, technology, engineering, arts, and mathematics (STEAM) education. Meanwhile, problem-based digital making (DM), which combines the child-friendly programming activities of DM with problem-solving elements, is an emerging instructional design to facilitate STEAM learning. This qualitative case study examines the implementation of a problem-based DM instructional program that used the block-based programming tool Scratch to cultivate the participants' creativity. Fifty-four middle school students (aged 10-14 years) in Hong Kong participated in the program, which totaled 10 contact hours over five consecutive weeks. Through triangulating students' DM artifacts, video recordings, field notes, and interviews, the researchers characterized the students' creative expression, examined the role of problem-based DM in encouraging creative work, and investigated the use of Scratch for mediating student creativity. The results showed that problem-based DM activities fostered students' creative expressions in the dimensions of novelty, utility, aesthetics, and authenticity. While Scratch mediated the way the students presented their solutions, it had limitations that hindered the students' digital artifact construction. The findings provide theoretical insights for framing creativity and offer practical implications for the implementation of problem-based DM in K-12 contexts. Copyright © 2023 SAGE Publications.

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. Copyright © 2022 Springer.

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. Copyright © 2022 Taylor & Francis.

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.

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. Copyright © 2021 International Forum of Educational Technology & Society (IFETS).

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.

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.