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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. [ABSTRACT FROM AUTHOR]

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 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. [ABSTRACT FROM AUTHOR]

In this paper, I discuss the potential transformations to teach K-12 geometry topics with the technology of 3D Pens, which enabled 3D models to be created instantly via one's moving hands. I draw on an example of using constructionist learning activities with 3D Pens to teach young children, 'how tall is the triangle?' [ABSTRACT FROM AUTHOR]

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. [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]

This paper reports a design and implementation of a STEM enrichment programme infused with affective elements designed for Hong Kong students. Specifically, it features a design-thinking approach to develop solutions to a self-selected problem addressing the United Nations Sustainable Development Goals. Around 30 upper primary school (grades 5 to 6) and 20 lower secondary students (grades 7 to 10) enrolled in the study. Considering empathy as a core value of the design-thinking process and aligned with affective dimensions of thinking and learning, we investigate students’ design-thinking development and STEM learning processes while highlighting empathy map as a pedagogical tool. We discuss the implications and insights of offering humanistic perspectives on STEM curricular design, especially for K-12 students. Our results showed that students at different age range were able to use empathy maps to devise designs effectively, despite their varying degrees of empathy. Furthermore, we conceptualize empathy maps as a pedagogical tool that creates physical boundaries in design thinking, making students’ mental transitions across design stages more explicit. This study contributes to a better understanding of the educational potentials of design-thinking enhanced classrooms, with the results informing theoretical and practical advice on the integration of the empathy map in innovation-oriented projects. [ABSTRACT FROM AUTHOR]

Touchscreen devices have become prominent in a variety of educational contexts due to their use of hands-on and interactive learning styles, and particularly for their direct engagement, rapid orientation, and multi-touch affordances, which textbooks and oral instruction may not always provide. As such, over the past decade, both the number of touchscreen applications for mathematics learning and the body of research examining their efficacy have increased. Yet, there are still few existing systematic reviews of how these touchscreen-based mathematics applications promote K-12 student learning. In response, this paper provides an in-depth examination of extant studies which adopt practices that utilize touchscreen technology for K-12 mathematics teaching and learning. The Web of Science database was searched for research published between 2010 and 2023, and 34 papers were chosen to review the empirical bases of touchscreen-based mathematics learning. These articles were analyzed based on the educational contexts found, touchscreen actions prompted, and the mathematical meanings elicited from these actions. Most significantly, we propose a touchscreen action matrix that characterizes the actions performed on the touchscreen platform and presents the mathematical meanings derived from these action categories. We hope that this review and characterization provide guidance for researchers, designers, and educators in eliciting mathematical knowing with action-based design in touchscreen medium. • 34 studies of touchscreen-based mathematics applications are systematically reviewed. • Most apps target number concepts via gamified environments at the early primary level. • We proposed a 2 × 2 touchscreen action matrix to characterize actions on touchscreens. • Number of Input, Temporality, Spatiality & Speed are the four dimensions of interest. • We present findings of how mathematical meanings are elicited from touch taxonomies. [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]

Video-based learning (VBL) has received increasing attention from researchers and educators in facilitating professional development (PD) for pre-service teachers (PSTs) in technology-enhanced ways. While a variety of VBL activities have been incorporated to address PSTs' reflective learning, a paucity of research concerns the effects of VBL activities on developing PSTs' professional competencies. Using a systematic literature review and meta-analysis, this research first identifies knowledge and competencies learning outcomes, followed by examining the overall effects of VBL activities on PSTs' development of content knowledge (CK), pedagogical knowledge (PK), psychological characteristics, and generic competencies. A total of 30 empirical studies that have reported available statistics to compute effect size were identified, involving 2161 PSTs, which allowed for comparisons of 74 effect sizes. There was a medium effect size in favor of VBL on PSTs' CK, with Hedges's g = 0.53 (p <.01) in random effects model; a small to medium effect size on PK, with Hedges's g = 0.38 (p <.001) in fixed effect model; and a medium effect size on psychological characteristics, with Hedges's g = 0.50 (p <.001) in random effects model. Our analysis of categorical moderators revealed the moderating effects of collaboration mode, video content, and video length simultaneously occur. These findings suggested a competency model through the analysis of the synthesized literature on VBL learning outcomes. The model provides insights into how VBL activities should be designed and assessed for PSTs' PD. • There was a medium effect size of VBL on PSTs' content knowledge. • There was a small to medium effect size of VBL on PSTs' pedagogical knowledge. • There was a medium effect size of VBL on PSTs' psychological characteristics. • The impacts of VBL on PSTs' generic competencies are under-researched. • Collaboration mode, video content, and video length moderate the effects of VBL. [ABSTRACT FROM AUTHOR]

This paper discusses the importance of considering bilingual learners' non-linguistic forms of communication for understanding their mathematical thinking. In particular, I provide a detailed analysis of communication involving a pair of high school bilingual learners during an exploratory activity where a touchscreen-based dynamic geometry environment (DGE) was used. The paper focuses on the word-use, gestures and dragging actions in student-pair communication about calculus concepts as they interacted with a touchscreen-based DGE. Findings suggest that the students relied on gestures and dragging as non-linguistic features of the mathematical discourse to communicate dynamic aspects of calculus. Moreover, by examining the interplay between language, gestures, dragging and diagrams, it was possible to identify bilingual learners' competence in mathematical communications. This paper raises questions about new forms of communication mobilised in dynamic, touchscreen environments, particularly for bilingual learners. [ABSTRACT FROM AUTHOR]

In this article, we review the publications served by theCanadian Journal of Science, Mathematics and Technology Educationin the past 15 years, specific to the field of mathematics education, and make connections with development of the field. In particular, we adopt current Editor-in-Chief John Wallace's (2009) approach of “looking back, looking forward,” to reflect on the journal's development both qualitatively, by recapping significant moments of the journal and highlighting recurrent themes, and quantitatively, by reviewing the number of contributions in terms of country, language, and genre. In looking forward, we inform a discussion of future directions of the journal. [ABSTRACT FROM PUBLISHER]

In this article, we report on two lessons aimed at introducing junior high school students to the idea of shearing in a touchscreen dynamic geometry environment. By using shearing, we hoped to shift students’ attention away from a formula-driven, computational conception of area toward a more geometric one. We found that the students were able to solve several problems involving the comparison of polygons based on verbal and diagrammatic explanations. We describe the features of the touchscreen dynamic geometry technology that supported their learning, as well as the specific role that the teacher played in modeling students’ reasoning about area. [ABSTRACT FROM PUBLISHER]

Amid the maker movement, educators are proposing various making activities with programmable artifacts to prepare students for coping with the challenges in the twenty-first century. Today, the "4C" skills—critical thinking, creativity, communication, and collaboration—are regarded as significant learning outcomes in Science, Technology, Engineering, and Mathematics education; however, few researchers have investigated the adoption of problem-based learning in K-12 programming education for developing students' 4C skills. A case study was conducted in a "digital making" camp in which 54 upper elementary and lower secondary school students (10–14 years old) were engaged in harnessing a block-based programming tool, Scratch, to conduct various problem-solving tasks. Through triangulating multiple sources of qualitative data (including lesson plans, classroom field notes, videotaped lesson records, student solutions/artifacts, and post-intervention interviews), together with the microgenetic learning analysis, this study characterizes students' 4C skills development in the process of problem-based digital making. We found that the problem-based digital making environment supported the students' development of (a) critical thinking in the form of critical modeling and critical data handling; (b) creativity in the form of creative explorations, creative solutions, and creative expressions; and (c) communication and collaboration in the form of communicative scaffolding and collaborative debugging. Complementary evidence-based suggestions for scaffolding problem-based digital making activities are suggested. [ABSTRACT FROM AUTHOR]

Educators and researchers are becoming interested in cultivating computational thinking (CT). However, in the Hong Kong context, CT-related studies regarding young children are rarely found. The present study aimed to use an unplugged digital arts activity to examine the CT concepts that children performed and document their CT developmental trajectories. Constructionism theory highlights the importance of children engaging in hands-on activities and developing independent thinking skills. Meanwhile, social constructivism theory emphasizes the role of teachers as scaffolders, supporting children in their learning processes. A sample of children (N = 27, aged 3–6) was recruited from a nursery school in Hong Kong to participate in an animation art workshop. A total of 540 min of video data was recorded and collected for content analysis. The teaching team (N = 4) for this workshop were invited to write up their reflective journals, capturing their observations of the scaffolding strategies employed and their perspectives on how children at various levels demonstrated their understanding of CT concepts throughout the entire process. Within an analytical framework based on powerful ideas, the findings from the observations and field notes revealed that the children’s CT concepts and practices could be linked with the CT conceptual framework. In this study, older children showed a sophisticated competency and a more complicated mind structure in terms of the CT concept. Our findings highlight the importance of designing an age-appropriate curriculum for nurturing the computational thinking of young children through animation art. [ABSTRACT FROM AUTHOR]

This article explores the complex relational landscape of international partnerships where local and transnational education objectives are entangled. We present a methodological practice for experimenting with diagrams and maps. Our emphasis on spatial rendering of local/global relationality is intended to invite discussion about the postcolonial context of international education work and the geopolitics of transnational curriculum. We pursue a diagrammatic and archipelagic form of creative abstraction, which we present as a posthuman cartographic practice. To illustrate this practice, we focus on a specific international curriculum development project funded by the World Universities Network. [ABSTRACT FROM AUTHOR]

• The intervention aimed at developing teachers' conceptual and practical tools to engage students. • The intervention teachers reduced the discourse behavior to evaluate a student's response. • Their discourse behaviors increased to prompt students to engage with others' ideas. • Students responded to the changes by showing increased amount of classroom contribution. The present study investigated the efficacy of an intervention program to assist teachers in the development of conceptual and practical tools for engaging students in dialogic classroom discourse. Sixteen fourth-grade mathematics teachers received 28 h of the intervention over a semester of 4 ½ months. Compared to the nonintervention group, the intervention teachers showed a reduced tendency to evaluate student responses and were more likely to promote students to engage with others' ideas. Students of the intervention group responded to the teachers' changes by demonstrating increased amount of contributions in classroom discussion. The results indicate that increasing awareness on dialogic classroom discourse provides an encouraging platform for teacher professional development to improve the quality of disciplinary teaching and learning. [ABSTRACT FROM AUTHOR]