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| Project Details |
| Funding Scheme : | General Research Fund | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Project Number : | 14603720 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Project Title(English) : | Mathematical Problem Solving through Digital Making: Envisioning a Computationally Enhanced Mathematics Curriculum in Hong Kong's Primary and Secondary Schools | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Project Title(Chinese) : | 數學解難中的「造中學」：預視香港中小學中融合計算思維的數學課程 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Principal Investigator(English) : | Prof NG , Oi Lam | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Principal Investigator(Chinese) : | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Department : | Dept of Curriculum & Instruction | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Institution : | The Chinese University of Hong Kong | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| E-mail Address : | oilamn@cuhk.edu.hk | ||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Co - Investigator(s) : |
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| Panel : | Humanities, Social Sciences | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Subject Area : | Education | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Exercise Year : | 2020 / 21 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Fund Approved : | 638,908 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Project Status : | Completed | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Completion Date : | 30-4-2024 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Project Objectives : |
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| Abstract as per original application (English/Chinese): |
Computational thinking (CT) is a powerful cognitive tool for solving problems, designing systems, and understanding human behaviour by drawing on concepts fundamental to computer science. It is helpful not only in maintaining competence in a technological society but also in supporting development in higher-order skills such as critical thinking, analysis, and scientific inquiry for the Science-Technology-Engineering-Mathematics (STEM) disciplines. Surrounding this, calls for incorporating CT into mathematics education are rapidly increasing. However, the mere presence of computers in the classroom does not ensure their effective use or quality education. Structural changes in the curriculum are needed to take full advantage of using CT to teach mathematics and problem solving.
This study builds on the PI’s previously developed conception of “learning as Making” to envision a computationally enhanced mathematics curriculum—one that supports mathematical problem solving through digital Making (dM). Digital Making involves students’ active creation of both digital and tangible artefacts through block-based programming with physical input sensors and output devices. It promotes active learning and transforms mathematical problem solving beyond merely using formulae and performing arithmetic calculations procedurally. Rather, CT concepts and practices such as sequences, variable-naming, abstraction, algorithmic thinking, decomposing, and iterating are highlighted during problem-based dM activities, through which scientific inquiry, mathematical thinking, and engineering design can also be exhibited as integrated STEM learning.
In this design-based study, a total of 20 lessons with problem-based dM tasks will be developed with content appropriate to senior primary and junior secondary mathematics curricula. These lessons will be implemented monthly to roughly 100 students in two primary and two secondary schools in Hong Kong longitudinally over two academic years. Data collection includes: (1) students’ digital artefacts and dM processes collected via code files and screen-capturing, (2) focus group interview and artefact-based interview data captured via video-recording. The study will adopt user analysis, thematic analysis, and case studies to delve into students’ acquired CT concepts, developed problem-solving practices, and formed computational perspectives in the course of the designed curriculum.
This study will inform the “big picture” of how using computers might fundamentally change mathematics learning, with an emphasis on mathematical problem solving (and more generally, STEM education). Findings will contribute to extending academic and professional knowledge about learning mathematics with computational tools, in response to CT and Making as a social movement. Ultimately, it will provide evidence-based directions of enhancing CT as a new literacy and problem solving as a global competence in school settings. 計算思維（Computational thinking）是一種通過運用計算機科學的基本概念以理解人類行為，設計系統並最終解決問題的強大認知工具。它是當今科技社會的基礎之一。在教育中，計算思維也有助於很多進階思維能力的發展，例如STEM學科中所需要的批判性思維、分析能力和科學探究能力。因此，將計算思維融入數學教育，是未來科技社會的趨勢與需要。但僅僅增加在課堂中使用電腦的次數並不代表能有效地利用計算思維。要充分挖掘以計算思維教授數學的潛力，改變課程結構這一步必不可少。 本研究建基於首席研究員先前提出的概念「造中學」（learning as Making），以探尋未來的數學課堂——一個以「造中學」協助數學解難的課堂的可行性。「造中學」，即提倡學生在動手製作中學習，其中一個例子是學生通過編寫積木式程式，並使用硬體感測器和顯示器，製作電子硬體成品。「造中學」可以促進主動學習，並令數學解難不再局限於運用公式和運算過程。不僅如此，透過「造中學」的解難活動還可以體現計算思維的概念和做法，例如數列、變數命名、演算與概括、分拆與重複步驟等。同時作為STEM的學習活動，亦可訓練參與者的數學思維、科學探究能力和工程設計能力。 在這項基於設計的研究中，制定共20節包含「造中學」任務，並適合高中和初中數學課程的課堂。這些課堂於每月在香港兩所小學和兩所中學中分別實施。共約100名學生參與，為期兩個學年。數據收集包括：（一）以編程檔和螢幕截圖形式收集學生的電子成品和「造中學」的過程；及（二）以視頻錄製形式收集焦點小組訪談和基於成品的訪談數據。研究將採用使用者分析、專題分析和案例研究，深入調查學生在預設課程中形成的計算思維概念、解難技巧、以及計算機科學觀點。 這項研究將探尋如何從根本上將計算思維融入數學解難，數學學習以及更宏觀的STEM教育。研究結果將有助於擴展以計算機科學作為工具來學習數學的相關學術和專業知識，並回應科技社會中的計算思維和「造」 （Making）的概念。最終為「在學校環境中的計算思維及解難能力將分別成為新的素質及世界性能力」一說，提供實證支持。 |
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| Realisation of objectives: | Realization of Research Objectives Objective 1: To study students’ development of computational concepts upon engaging in a series of problem-based digital making (dM) activities. This objective was thoroughly addressed through multiple studies: Cui & Ng (2021) explored the interplay between mathematical and computational thinking in primary students' problem-solving within a programming environment. Their findings highlighted how students developed computational concepts such as sequencing and abstraction through programming tasks. Weng et al. (2022) conducted a case study in a digital making camp, revealing that problem-based digital making environments supported students' development of critical thinking, creativity, communication, and collaboration skills. The study emphasized how these environments facilitated the acquisition of computational concepts. Ye et al. (2023) conceptualized flexibility in programming-based mathematical problem-solving, providing insights into how students adapt and apply computational concepts in varied contexts. These studies collectively demonstrate that engaging students in dM activities fosters the development of essential computational concepts, enhancing their problem-solving capabilities. Objective 2: To examine students’ computational problem-solving practices, mathematical thinking, and any CT- and mathematics-related challenges that emerge during problem-based dM activities. This objective was achieved through in-depth analyses: Ng, Liu, & Cui (2021) investigated students' in-moment challenges and the development of maker perspectives during problem-based digital making. The study identified specific hurdles students faced and how they navigated them, shedding light on their computational problem-solving practices. Weng et al. (2022) characterized students' 4C skills development during problem-based digital making, emphasizing how students engaged in critical modeling, creative explorations, and collaborative debugging. These practices illustrate the integration of computational thinking with mathematical reasoning. Ye, Ng, & Leung (2024) examined mathematics teachers' creative actions in programming-based mathematical activities, providing a perspective on how educators facilitate and observe students' computational and mathematical thinking processes. These findings offer a comprehensive understanding of the practices and challenges students encounter, informing strategies to support their learning effectively. Objective 3: To observe the impact of CT on students’ perspectives about themselves as computational thinkers and problem solvers, and about the role of computational tools in various facets of life. The impact of computational thinking on students' self-perception and their views on computational tools was explored: Ng, Liu, & Cui (2021) highlighted how students' engagement in digital making activities influenced their identities as makers and problem solvers, fostering a sense of agency and confidence in using computational tools. Weng et al. (2022) demonstrated that participation in problem-based digital making activities enhanced students' 4C skills, contributing to their self-efficacy and appreciation of computational tools in collaborative and creative contexts. These studies underscore the transformative effect of CT integration on students' self-concept and their recognition of the relevance of computational tools in various aspects of life. Objective 4: To develop evidence-based accounts of implementing a computationally enhanced mathematics curriculum in formal education settings and a possible learning trajectory. This objective was realized through both theoretical and practical contributions: Ng, Leung, & Ye (2023) explored computational thinking as a boundary object between mathematics and computer programming for STEM teaching and learning. Their work provides a conceptual framework for integrating CT into mathematics curricula. Ng et al. (2023) discussed the integration of programming, problem-solving, and recreational mathematics for a computationally enhanced mathematics education. This study offers practical insights into curriculum design and implementation strategies. Ng, Sinclair, Ferrara, & Liang (2023) examined how digital resources can transform arithmetic teaching and learning, emphasizing the role of tools like TouchCounts and Scratch in facilitating multimodal and embodied learning experiences. These contributions offer a comprehensive account of how computational thinking can be effectively embedded into mathematics education, outlining potential learning trajectories and instructional approaches. Summary Across all four objectives, the project has successfully advanced the understanding and practice of integrating computational thinking into mathematics education. The research outputs, including peer-reviewed journal articles and conference presentations, provide both theoretical frameworks and practical strategies for educators. The findings have implications for curriculum development, teacher training, and policy-making, contributing to the broader goal of preparing students for a computationally rich world. | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Summary of objectives addressed: |
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| Research Outcome | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Major findings and research outcome: | This project has generated significant insights into the integration of computational thinking (CT) into mathematics education through problem-based digital making (dM) activities. First, the research showed that engaging students in programming-based mathematical tasks helped them develop key computational concepts such as abstraction, sequencing, decomposition, and debugging. Studies such as Cui & Ng (2021) and Weng et al. (2022) demonstrated how these concepts emerged naturally through structured task design and hands-on engagement with tools like Scratch. Second, our findings revealed the complex interplay between computational problem-solving and mathematical reasoning. For example, students displayed flexibility in navigating between multiple solution paths (Ye, Ng, & Cui, 2023), and were able to apply mathematical structures to solve CT-based problems. These findings were elaborated through classroom studies and thematic analyses of students’ work and dialogues. Third, we observed how CT engagement influenced students’ perspectives on themselves as problem solvers. Students developed stronger identities as computational thinkers, and became more confident and motivated in tackling open-ended problems (Ng, Liu, & Cui, 2021; Weng et al., 2022). Finally, the project contributed to theorizing how CT can be embedded within a formal mathematics curriculum. Several publications (e.g., Ng, Leung, & Ye, 2023; Ng et al., 2023) provided conceptual models and implementation strategies that can guide educators and curriculum developers. The research identified features of effective task design and potential learning trajectories that connect CT with core mathematical concepts. Collectively, the outcomes have led to 10 (excluding 1 under review and 1 accepted) journal articles, several international conference presentations (e.g., ICME-15, ICCE), and contributions to edited volumes (e.g., Springer Handbook of Digital Curriculum Resources). These outputs have significantly advanced the scholarship on CT-mathematics integration and produced usable knowledge for curriculum and pedagogy design. | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Potential for further development of the research and the proposed course of action: |
Future work will focus on extending these findings to a broader range of topics and educational levels. We aim to co-develop a full-fledged CT-enhanced mathematics module with teachers and pilot it across multiple schools. Additionally, longitudinal studies will be conducted to trace students’ progression in computational and mathematical thinking over time. A key priority is capacity-building for teachers, including the development of a professional learning framework grounded in our research outcomes. We will also explore incorporating emerging technologies, such as AI tools, to further enrich CT integration in mathematics education. | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Layman's Summary of Completion Report: | This research project explored how students learn both computational thinking and mathematics by engaging in programming-based problem-solving activities. Using tools like Scratch programming, students created digital solutions to mathematical problems, helping them develop mathematical and logical thinking, creativity, and problem-solving skills. The study found that students not only learned key computing ideas like sequencing and debugging, but also developed mathematical concepts and confidence alongside tackling complex problems. In terms of changed perspectives, the designed CT-based mathematics instruction impacted the students' perception and self-efficacy about themselves as computational thinkers and problem solvers; meanwhile, they were more knowledgeable about the role of computational tools in various facets of life. Finally, the study suggested a learning progression for CT-based mathematics instruction through evidence-based accounts of implementation.. The design-based study highlighted researcher-teacher collaboration in playing a vital role of designing effective learning activities that blend computing and mathematics. The project produced new teaching strategies and curriculum ideas to better prepare students to solve problems with computational tools for a digital and AI-rich world. With this work, we have shown how digital making can make mathematics learning more personally meaningful and aligned with the technological world for students, while building essential skills for the future. | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Research Output | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Peer-reviewed journal publication(s) arising directly from this research project : (* denotes the corresponding author) |
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| Recognized international conference(s) in which paper(s) related to this research project was/were delivered : |
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| Other impact (e.g. award of patents or prizes, collaboration with other research institutions, technology transfer, etc.): |
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| SCREEN ID: SCRRM00542 |