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
Co - Investigator(s) :
Dr LEUNG , Allen Yuk Lun
Dr Liang, Biyao
Prof Sinclair, Nathalie
Panel : Humanities, Social Sciences
Subject Area : Education
Exercise Year : 2020 / 21
Fund Approved : 638,908
Project Status : On-going
Completion Date : 30-4-2024
Abstract as per original application
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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