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ENQUIRE PROJECT DETAILS BY GENERAL PUBLIC |
| Project Details |
| Funding Scheme : | Early Career Scheme | ||||||||||||||||||||||||||||||||||||||||
| Project Number : | 24615919 | ||||||||||||||||||||||||||||||||||||||||
| Project Title(English) : | The effects of implementing a ‘learning as Making’ pedagogy on school mathematics learning: Primary students’ inquiry-based Making with 3D Printing Pens | ||||||||||||||||||||||||||||||||||||||||
| Project Title(Chinese) : | 「造中學」: 利用3D打印科技增進數學學習的設計本位研究 | ||||||||||||||||||||||||||||||||||||||||
| 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 : | 2019 / 20 | ||||||||||||||||||||||||||||||||||||||||
| Fund Approved : | 449,381 | ||||||||||||||||||||||||||||||||||||||||
| Project Status : | Completed | ||||||||||||||||||||||||||||||||||||||||
| Completion Date : | 14-8-2021 | ||||||||||||||||||||||||||||||||||||||||
| Project Objectives : |
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| Abstract as per original application (English/Chinese): |
Competence in early mathematics is crucial for later school success. Although research indicates that a spatial and hands-on approach to learning improves student engagement and mathematics skills for young learners, such approach has been difficult to implement in mathematics education, especially in Hong Kong, partly due to the culture of drilling and recalling procedures by manipulation of abstract symbols on paper. In contrast, Making draws upon the innately human desire to make things with our hands. One important application of Making in education is a spatial and hands-on approach to learning which also has implications for meeting the global needs for expertise in the Science-Technology-Engineering-Mathematics (STEM) disciplines. Despite its significance, few research has examined the effects of Making in education, including how Making may effectively support technology-enhanced mathematics and/or STEM learning.
This study builds on the PI’s previously developed notion of ‘learning as Making’ (LaM) to examine mathematics learning in a highly transformative and technological Making environment; it involves the use of 3D Printing Pens which enables 3D models to be created instantly via one’s moving hand. Within this particular LaM environment, students are engaged in inquiry-based learning through hands-on production of 3D-printed artefacts, which serve as both diagrams (processes) and products of learning. LaM aligns with emerging theoretical developments on gestures, embodiment and materialist perspectives of thinking and learning. The PI has conducted relevant empirical studies, pointing towards the rich mathematics learning with LaM in primary schools.
This design-based research explores the effect of a LaM pedagogy in mathematics education through designing and implementing twelve teaching experiments in six Hong Kong primary schools. In this mix-method study, (1) students’ development of visualisation, generalisation, and problem solving in mathematics will be analysed statistically using pre- and post-test measures, and (2) students’ inquiry-based Making during the lessons and post-lesson interviews will be captured via video-recording, after which discourse and micro-genetic analyses will examine students’ learning and sense-making processes with 3D Printing Pens.
This study fills the research gap with regard to the changing nature of knowledge, learning and pedagogy in the digital age, in that it will advance the educational potential of 3D printing technology and LaM in school mathematics in particular and STEM education in general. Its findings will contribute to teaching and learning abstract mathematical and/or STEM concepts in hands-on, technological, and innovation-oriented environments. More broadly, it will contribute to speculation on the future potential of emergent technologies in education and LaM curricula.
早期數學基礎對於成就以後學習至關重要。儘管研究指出，空間感訓練以及實踐式學習有助於年幼學生的數學參與度和數學技能的培養，但這些學習方法在數學教育中很難實施，特別是在香港。部分原因在於香港數學教育文化偏向重視以抽象化的數學符號進行反覆練習和運算。相比之下，「造」則迎合人類以雙手創新的天性和對製造的好奇。尤其在教學中，「造」強調空間感訓練以及實踐式學習，這同時迎合到國際間對科學（Science）、技術（Technology）、工程（Engineering）及數學（簡稱STEM）學科專業知識的需求。儘管其意義重大，但少有研究考察過「造」對教育的影響，例如「造」能如何有效支援數學及STEM的科技增進學習。 是次研究建基於研究員先前研發的「造中學」（Learning as Making）概念，以探討在創新、製造、和技術化的環境中學習數學。這其中涉及3D打印筆的應用，讓參與者能即時創建3D模型並進行探究式學習。「造中學」與手勢學、具身化認知、新物質主義等新興理論保持一致。研究員曾進行相關的實驗研究，顯示「造中學」能豐富小學數學學習。 此設計本位研究將在香港六所小學中設計並實行十二個教學實驗，從而探討「造中學」教學法對數學教育的影響。本次的混合研究中，數據的收集和分析包括：學生在數學中形象化、歸納和解難方面的發展，學生在課堂中探究「造」的過程，以及課後訪談，並從對話及微觀發生法的分析中探討學生用3D打印筆時的學習和意義建構過程。 這項研究增加了對數碼時代中日新月異的知識、學習和教學的研究，從而提升3D打印技術和「造中學」兩者在學校中，特別是數學，以至是STEM教育中的教育潛力。其研究結果將有助於在實踐式學習、技術和創新導向的環境中數學及STEM相關概念的教育和學習。更廣泛而論，研究結果將有助預測未來新興科技在教學和「造中學」課程中的潛力。 |
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| Realisation of objectives: | Overall, the study has fully met the project objectives set out as planned. The four project objectives were realized in the form of 9 research outputs (7 published journal articles and 2 accepted book chapters). In what follows, the PI provides a summary of project objectives achieved, followed by a more specific account of how each objective was achieved. Upon completion of the project, the research team has gathered quantitative evidence (Project Objective 1) and qualitative evidence (Project Objectives 2 and 3) of the effect of implementing a "Learning as Making (LaM) pedagogy" through inquiry-based Making with 3D Printing Pens, on primary students' geometry learning. Also under Research Objective 2, the research team generated findings regarding primary school teachers’ professional development by investigating their discourse change during and after Maker-centered mathematics lessons for inquiry-based geometry teaching. Regarding the fourth objective, the research team developed empirically-grounded theoretical accounts about LaM pedagogy and designed technology-enhanced learning tasks that promote productive mathematics/STEM learning, as well as engaging the PI’s research findings with the academic and professional communities to increase the research and social impact of this project. For example, a list of seven research outputs in the form of research and professional seminars have been generated as a result of the project (see Part C, Section 12). Research Objective 1. This objective was achieved and documented in Ng et al. (2021) and Ng and Ye (2022). In particular, Ng et al. (2021) reports 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. A pretest-posttest-delayed posttest design was used 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. Among the results, it was observed that students with the aid of 3D Pens demonstrated better retention of the properties of 3D solids than their dynamic geometry counterparts. Namely, the results from the ANCOVA suggest that the retention effect was more significant with 3D Pens. This study has established evidence that the digital instructions produced strong but relatively temporary geometry learning outcomes, while 3D Pen instructions as a form of embodied learning can help solidify that knowledge. Likewise, Ng and Ye (2022) used a mixed-methods design, with quantitative results showing that the designed learning activities with 3D Printing Pens greatly supported student learning on all questions related to working with vertices (0D), edges (1D), and faces (2D). The results of these studies 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. Research Objective 2. The PI achieved this dual objective of observing teachers’ and students’ mathematical discourse in the following studies: Ng & Ye (2022); Ng & Chan (2021); Ng & Park (2021); and Ng et al. (accepted). For example, in Ng and Ye (accepted), the researchers 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. In this study, two significant findings were reported. First, constructions with 3D Pens supported students’ composition of 3D solids by their 0D, 1D, and 2D parts, as well as improved students’ visualization of the relationships of these parts in embodied ways. Second, constructions with 3D Pens gave rise to gestures conducive to learning the properties of 3D solids. 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). In Ng and Park (2021) as well as Ng and Chan (2021), the researchers focused on in-service and pre-service teachers’ discourse respectively when learning to use the technology of 3D Pens in classroom teaching. For the former study, it was observed that pre-service teachers developed expertise by reflecting on the coordination of using 3D Pens towards achieving curricular goals. Importantly, their discourse showed that they did not only realize the impact of 3D Pen instruction but also compared it with the use of traditional teaching aids to enhance student learning. In Ng and Chan (2021), the researchers analyzed four in-service mathematics teachers’ noticing upon watching video episodes showing an actual mathematics lesson that implemented 3D Printing Pens for teaching and learning shape and space. Analysis included what the teachers identified as important or noteworthy in the video, and thematically accounting for the teachers’ interpretations and decisions in relation to using 3D Pens for teaching and learning mathematics. Findings suggest that the teachers underwent a discourse change by realizing the affordances of 3D printing as novel-to-them technologies. Research Objective 3. This objective was exemplified in Ng and Ye (accepted), in which the researchers adopted the theoretical approach of inclusive materialism, which sheds light on the ontologies of the body and mathematics in the teaching and learning activities with 3D printing technologies. Based on the linguistic expressions and gestures of students using 3D Pens for inquiry-based learning, the authors conclude that 3D Pens can support students’ understanding and construction of 3D solids. Theoretically, the adoption of a materialist perspective was helpful for exploring the unique prospect of using 3D Pens in mathematical activities, as embodied diagramming/gesturing during material creation which engenders new possibilities for encounters with mathematical concepts. Research Objective 4. The PI achieved this objective by providing an empirically grounded account of student learning and teacher professional development throughout the project, through actively engaging in classroom-based interventions with school mathematics teachers to develop a technology-enhanced constructionist pedagogy, termed ‘learning as making’. In Ng (2020), the PI shares one of these experiences of working with teachers on developing constructionist learning activities with 3D Pens, in particular, providing an account of collaborating with local primary school teachers on planning a lesson for properties of triangles. In Ng and Tsang (2020), the researchers further developed a three-fold characterization of constructionist learning in mathematics education, drawing upon examples from the project and the innate human desire to make things with our hands. The authors argued that 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, the authors discuss how constructionist learning can play an important role in teaching and learning school mathematics via a transdisciplinary STEM education. 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 played an active role in the construction of artifact (physically) and mathematical meaning (cognitively). | ||||||||||||||||||||||||||||||||||||||||
| Summary of objectives addressed: |
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| Research Outcome | |||||||||||||||||||||||||||||||||||||||||
| Major findings and research outcome: | The project’s major findings are four-fold. 1. There exists significant retention effect of 3D Pen instruction for geometry learning. It was observed that students with the aid of 3D Pens demonstrated strong retention of the properties of 3D solids. Namely, the results from the ANCOVA suggest that the retention effect was significant with 3D Pens. Moreover, the project has established evidence that the digital instructions produced strong but relatively temporary geometry learning outcomes, while 3D Pen instructions as a form of embodied learning can help solidify that knowledge. 2. Students’ cognition in the dimension of measure, shape and space benefitted from constructionist and inquiry-based learning with 3D Printing technology. As revealed in the students’ discourse (verbal and gestural), 3D Printing Pens played an active role in the students’ construction of artifact (physically) and mathematical meaning (cognitively). Specifically, constructions with 3D Pens supported students’ composition of 3D solids by their 0D, 1D, and 2D parts, as well as improved students’ visualization of the relationships of these parts in embodied ways. Finally, constructions with 3D Pens gave rise to gestures conducive to learning the properties of 3D solids. 3. Teachers developed expertise in lesson design and technology-rich pedagogy with 3D printing over the course of the study. The teacher participants used the videos collected in this study to anticipate their future teaching in 3D Pen-rich mathematics classrooms. Their discourse was multimodal, as they often re-enacted their imagined drawing process with 3D Pens, either through gesturing or diagramming on paper. Moreover, they attended to students’ nuanced actions of 3D drawing, which ranged from the hand movements with 3D Pens to the size and orientation of the final product. Methodologically, the video episodes captured the dynamic processes of students’ constructionist practices with 3D Pens rather than merely their final products statically–this facilitated the teachers’ reflections about the evolution of students’ mathematical thinking. 4. Development of design-based constructionist learning trajectory and pedagogical principles with 3D Pens The findings characterized constructionist mathematics learning as hands-on and goal-oriented, allowing learners to construct knowledge actively rather than receive information passively; it aligns with transdisciplinary STEM learning because the 3D, tangible, and technologically enhanced nature of artifact constructions makes them applicable to real-world problems and projects, thereby helping to shape the learning experience of STE(A)M. Finally, low-floor, high-ceiling learning opportunities are afforded for students to engage with mathematical ideas and invent new ways to do mathematics without the constraints of paper-and-pencil. | ||||||||||||||||||||||||||||||||||||||||
| Potential for further development of the research and the proposed course of action: |
This project's future extensions include conceptualizing constructionist learning with 3D printing from the perspective of realistic mathematics education, which views learning mathematics as a human activity connected to the reality. As argued by realistic mathematics education, much opportunities should be given to children to reinvent mathematics through hands-on and informal experiences, which is in line with our developed conception of 'learning as making'. Therefore, future research may consider how students make connections and reinvent meanings of 3D-printed (mathematical) object, such as a 3D printed triangle, in real-world contexts, and how their mathematical discourse evolve before and after their creation and interactions with the 3D printed models. These research directions should contribute toward providing a basis for further research into the role of 3D materiality in mathematical cognition. Regarding the results shedding light on what teachers identified as important and noteworthy in a 3D Pen-enabled lesson and how they realized certain pedagogical affordances of the 3D Pens through video-aided reflections, the PI plans to examine the use of videos as a boundary object, serving purposes from the perspectives of both school teachers and researchers for pedagogical and curricular design with new forms of technology, including but not limited to 3D printing. | ||||||||||||||||||||||||||||||||||||||||
| Layman's Summary of Completion Report: | In recent years, a body of research has addressed mathematical cognition as situated not only in mental processes but also in physical actions, where providing rich perceptual, tactile, and kinesthetic experiences can greatly support learning mathematical concepts. In this connection, this study has been one of the first attempts to examine the relationship among gestures, embodiment, and mathematical thinking by highlighting the role of 3D printing in mathematics education. The empirical investigations point to the potential changes in thinking, learning, and doing that may result from the use of 3D printing technology, which enable mathematics to be performed in the third dimension and thereby helping to make certain mathematical concepts tangible through touch and moving one's hands. Specifically, by comparing pre- and post-test results, as well as examining students' linguistic expressions and hand movements during classroom-based interventions, this study reveals that 3D printing supported students' investigations, visualizations, and learning about geometric relationships in significant ways. Furthermore, through pedagogical reasoning in the context of video-aided reflections, this study conclude that teachers can learn to be responsive to students' diverse ways of construction with 3D Printing Pens and to facilitate meaningful classroom conversations with students in their classrooms. | ||||||||||||||||||||||||||||||||||||||||
| 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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| Realisation of the education plan: | |||||||||||||||||||||||||||||||||||||||||
| SCREEN ID: SCRRM00542 |