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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]

There has been a renewed interest in creativity as a twenty-first century skill in K-12 mathematics education. However, previous research has paid less attention to creative actions than to other learning outcomes, which are often product- instead of process-based, especially in a programming context. Thus, situated in the context of mathematical learning in a block-based programming environment, Scratch, this study seeks to investigate how in-service mathematics teachers develop mathematical concepts and programming skills to demonstrate their creative actions as a form of professional development. By conducting task-based interviews and thematic analysis, we found that testing and iterative practices of reusing and remixing are two important kinds of creative actions inspired by the programming environment, which give rise to new possibilities for doing mathematics in terms of generating new ways to engage in mathematical processes and to understand mathematics from a computational perspective. Our findings will inform teacher education and professional development programs addressing creativity in technology-enhanced mathematics classrooms, with particular attention to the role of mathematics, programming, and their interplay in inspiring teachers' (and students') creative actions and new possibilities for doing mathematics. [ABSTRACT FROM AUTHOR]

Programming is an interdisciplinary practice with applications in both mathematics and computer science. Mathematics concerns rigor, abstraction, and generalization. Computer science predominantly concerns efficiency, concreteness, and physicality. This makes programming a medium for problem solving that mediates between mathematics and computer science in intriguing ways. Behind programming practices is computational thinking (CT), a mode of thinking involved in formulating and solving problems so that the solutions could be represented and carried out by computing means. In this paper, CT is seen as a boundary object connecting mathematics and computer science in a school problem-solving context. In particular, we examine and analyse middle school students' work upon engaging in mathematical problem solving-in a programming environment, taking CT as a boundary object embedded in the block-based programming environment, Scratch. The analysis is guided by observing boundary crossing features of CT in the students' artefacts produced in Scratch while solving mathematical problems related to symmetry and arithmetic sequence. The findings of this study open up new dimensions to explore CT as a boundary object in integrated STEM pedagogy. [ABSTRACT FROM AUTHOR]

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]

There has been substantial research undertaken on the integration of computational thinking (CT) in K-12 mathematics education in recent years, particularly since 2018 when relevant systematic reviews were conducted on the topic. Many empirical studies in this area have yet to elaborate clearly and explicitly on how CT may support mathematics learning, or otherwise, in CT-based mathematics activities. Addressing this research gap, we conducted a systematic review on the integration of CT in K-12 mathematics education with a focus on CT-based mathematics instruction and students learning under such instruction. The Web of Science database was searched for in terms of studies published from 2006 to 2021, from which 24 articles were selected to provide illustrations of CT-based mathematics instruction and related student learning, and they were further analyzed according to education levels and contexts, programming tools, learning outcomes in CT and mathematics, and the mutual relationship between CT and mathematics learning. Among the results, this review found that geometrized programming and student-centered instructional approaches were facilitators of productive learning in CT and mathematics. Moreover, CT-based mathematics learning entails an interactive and cyclical process of reasoning mathematically and reasoning computationally, which can occur when: (1) applying mathematics to construct CT artefacts; (2) applying mathematics to anticipate and interpret CT outputs; and (3) generating new mathematical knowledge in parallel with the development of CT. The findings contribute to an in-depth understanding of what, and how, CT-based mathematics instruction impacts student learning in K-12 contexts. [ABSTRACT FROM AUTHOR]

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]

This paper reports on a mixed-methods, design-based study conducted with five classes of Primary 6 (age 11–12 years) students learning the properties of 3D solids. The researcher and participating teachers designed mathematics lessons that integrated the hands-on construction of artifacts (i.e., making) with a class set of 3D printing pens to introduce various properties of prisms and pyramids in two primary schools in Hong Kong. Quantitative results show that the designed learning activities with 3D printing technology greatly supported student learning on all questions related to working with vertices (0D), edges (1D), and faces (2D). Qualitatively, one researcher observed that the students produced hand movements and language that were conducive to learning the properties of 3D solids while they interacted with 3D printing pens. This study draws attention to the unity of mind–body and body–tool interactions in the act of making something (i.e., mathematics learning as embodied making). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper reports on a design-based study within the context of a 3-day digital making (DM) summer camp attended by a group of students (aged 11–13) in grades 5 and 6. During the camp, students were presented with a set of mathematical problems to solve in a block-based programming environment, which was connected to various physical input sensors and output devices (e.g., push buttons, LED lights, number displays, etc.). Students' code files, and screen captures of their computer work, were analyzed in terms of their developed computational problem-solving practices and any computational concepts that emerged during the problem-based DM. The results suggested that the designed tasks consistently supported the students' modeling and algorithmic thinking, while also occasioning their testing and debugging practices; moreover, the students utilized computational abstractions in the form of variables, and employed different approaches, to formulate mathematical models in a programming context. This study contributes to the 'big picture' of how using computers might fundamentally change mathematics learning, with an emphasis on mathematical problem-solving. It also provides empirically grounded evidence to enhance the potential of computational thinking as a new literacy, and problem-solving as a global competence, in formal school settings. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we build on a previously developed notion of 'learning as Making' to examine mathematics thinking and learning in a highly transformative and technological Making environment: one that involves a handheld 3D printing technology which enables 3D models to be created instantly via one's moving hand. In particular, we present two examples of Maker-centred lessons for teaching and learning of primary mathematics. In these lessons, the students actively constructed artefacts with 3D Printing Pens while engaging in inquiry-based learning activities, where the target concepts were properties of prisms and cross-sections at the primary 5 (age 10–11) and primary 6 (age 11–12) levels respectively. We use diffractive analysis to capture the fine details in students' body-material interactions while engaging in the tasks with or without the 3D Printing Pens during the lessons. Through the lens of Making as a material act of creation and seeking to update Papert's constructionist view of learning, we propose to rethink Making in school mathematics according to a four-fold characterisation: Making is co-constructing meanings, Making is mathematising, Making is assembling with technology and Making is inventing. We discuss our contribution towards advancing a materialist perspective of learning mathematics and implications for a 'learning as Making' pedagogy and curriculum. [ABSTRACT FROM AUTHOR]

In this paper, I introduce Sfard's discursive framework to examine secondary-school calculus students' communication during exploratory activities mediated by the use of touchscreen dynamic geometry environments (DGEs). Six pairs of secondary-school students participated in an open-ended task to explore calculus relationships using touchscreen-DGEs. Qualitative data capturing the students' linguistic communication (speech) and hand movements (gestures and dragging) were analysed when the students interacted with the touchscreen-DGEs used during the task. Findings suggest that new forms of communication were mobilised through the act of dragging on a touchscreen-DGE. In particular, routines for comparing, reasoning, conjecturing and verifying emerged within the use of the haptic DGE interface. In this paper, potentials of the touchscreen-DGEs in facilitating new forms of gestural thinking, as well as theoretical and methodological considerations that recognise the changing ways in which the hand and media interact, are discussed. [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 paper, we investigate children's learning of reflectional symmetry in a dynamic geometry environment. Through a classroom-based intervention involving two 1-h lessons, we analyse the changes in the children's thinking about reflectional symmetry: first, they developed dynamic and embodied ways of thinking about symmetry after working with a pre-constructed sketch called the 'symmetry machine'. Secondly, they moved from distinguishing symmetrical and asymmetrical figures statically to generalising about properties of symmetry. This was evident in the way children expressed symmetric movement through words, gestures and diagrams during the computer-based lessons as well as in the follow-up paper-and-pencil tasks. We highlight the specific roles of the teacher and of the digital technology in supporting the process of semiotic mediation through which the children learned symmetry. [ABSTRACT FROM AUTHOR]

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]

Background: This paper compares the effects of two classroom-based technology-enhanced teaching interventions, conducted in two schools in sixth (age 11–12) grade. In one school, the intervention involves the use of a class set of 3D Printing Pens, and in another school the use of dynamic geometry environments, for inquiry-based learning of the relations among the number of vertices, edges, and faces of prisms and pyramids. An instrument was designed as guided by the van Hiele model of geometric thinking and administered to the two groups in the form of pretests, posttests, and delayed posttests to assess students' prior knowledge before the intervention started, the learning outcomes obtained immediately after intervention, and the retention of knowledge after the interventions had been completed for a sustained period of time. The purpose of this study is to explore differences in geometry learning outcomes in two technology-enhanced environments, one that involves dynamic, visual representations of geometry and another that involves embodied actions of constructing physical 3D solids. Results: The results show that students using dynamic geometry improved at a higher rate than those using 3D Pens. On the other hand, students with the aid of 3D Pens demonstrated better retention of the properties of 3D solids than their dynamic geometry counterparts. Namely, the posttest results show that the dynamic geometry environment (DGE) group generally outperformed the 3D Pen group across categories. The observed outperformance by the DGE group on "advanced" implies that the DGE technology had a stronger effect on higher levels of geometric learning. However, the results from the ANCOVA suggest that the retention effect was more significant with 3D Pens. Conclusions: This study has established evidence that the DGE instructions produced strong but relatively temporary geometry learning outcomes, while 3D Pen instructions can help solidify that knowledge. The results of this study further shed light on the effect of visual and sensory-motor experiences on school mathematics learning and corroborate previous work showing that the effects of gesture are particularly good at promoting long-lasting learning. [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]