Hands-on: A digital-embodied path to functional thinking
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| Názov: | Hands-on: A digital-embodied path to functional thinking |
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| Autori: | Wei, Hang |
| Informácie o vydavateľovi: | Utrecht University Library, 2025. |
| Rok vydania: | 2025 |
| Predmety: | Belichaamd ontwerp, Onderwijstechnologie, Parallelle assen representatie, Digitaal-belichaamd leren, Functioneel denken, Functional thinking, Covariational reasoning, Parallel axes representation, Mathematical abstraction, Nomogram, Klasimplementatie, Educational technology, Embodied design, Hand-tracking, Digital-embodied learning, Wiskundige abstractie, Covariationeel redeneren, Hand tracking, Classroom implementation |
| Popis: | Functional thinking (FT)—understanding relationships between variables through aspects such as input-output, covariation, and correspondence—is an important skill. However, students often struggle with its abstract nature. Traditional teaching, often relying on static pictures, does not effectively build dynamic reasoning about how variables change together. This thesis addresses the challenges through integrating digital technologies through the lens of embodied cognition. The main innovation is the use of nomograms. A nomogram is a visual tool that maps functional relationships through parallel axes and arrows. In this thesis, we reimagine digital nomograms as dynamic, interactive tools that connect students’ sensorimotor experiences with formal mathematics. The overarching question guiding the thesis is: How do nomogram tasks foster students’ FT development in a digital-embodied learning environment? The investigation begins in Chapter 2 with a systematic review, which identified that while dynamic software is common, the potential of continuous, real-time feedback and geometry-based approaches in embodied learning remains underutilized. These gaps motivated the design of a digital-embodied learning environment centered on nomograms. Chapter 3 details the design and pilot study of an embodied learning environment using nomograms. A key design feature is the use of bimanual movement tasks, which prompt students to physically coordinate two variables along the nomogram's input and output axes. Real-time color feedback guides students to adjust their hand positions. This tactile process was found to foster a rich sensorimotor experience of functional relationships. In Chapter 4, the research moves the refined intervention into authentic classroom conditions on a larger scale. Quantitative findings demonstrated significant improvements across all aspects of FT. Qualitative data clarified how key design features scaffolded the transition from concrete sensorimotor experiences to abstract mathematical reasoning. Chapter 5 delves deeper into the micro-processes by investigating how bimanual movements specifically support covariational reasoning. By analyzing hand-tracking data, this chapter links sensorimotor fluency with conceptual development. The analysis showed that students who made greater learning gains spent more time in fluency phases, suggesting that prolonged, embodied exploration can foster deeper reasoning. This methodological approach provided a "microlens" into the perception-action loops that underpin students' understanding of functional relationships. Finally, Chapter 6 synthesizes the findings: (1) Nomograms can be effective tools to foster input-output thinking, covariational reasoning, and representation conversion within correspondence thinking, especially when they are augmented with real-time feedback and bimanual tasks. (2) Embodied design features (particularly coordinated bimanual movements) create attentional anchors for abstract functional relationships, helping students “feel” how changes in one variable correspond to changes in another. (3) The design is practically feasible in regular classroom settings, with empirical evidence of learning gains and positive engagement. Theoretical implications include: students’ bimanual movement fluency develops concurrently with mathematical thinking. The findings indicate that body-artifact functional dynamic systems – involving bimanual coordination, real-time feedback, and interactive digital representations – facilitate the mathematization of functional relationships. Methodologically, this thesis offers a replicable framework for future design-based research in digital-embodied learning. Specifically, it combines systematic review, iterative environment design, classroom testing, and fine-grained sensor data (hand-tracking) to analyze students’ learning processes. |
| Druh dokumentu: | Doctoral thesis |
| DOI: | 10.33540/3107 |
| Prístupové číslo: | edsair.doi.dedup.....2c6514a1a4e2ad34949e4abaa55fcfb4 |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | Functional thinking (FT)—understanding relationships between variables through aspects such as input-output, covariation, and correspondence—is an important skill. However, students often struggle with its abstract nature. Traditional teaching, often relying on static pictures, does not effectively build dynamic reasoning about how variables change together. This thesis addresses the challenges through integrating digital technologies through the lens of embodied cognition. The main innovation is the use of nomograms. A nomogram is a visual tool that maps functional relationships through parallel axes and arrows. In this thesis, we reimagine digital nomograms as dynamic, interactive tools that connect students’ sensorimotor experiences with formal mathematics. The overarching question guiding the thesis is: How do nomogram tasks foster students’ FT development in a digital-embodied learning environment? The investigation begins in Chapter 2 with a systematic review, which identified that while dynamic software is common, the potential of continuous, real-time feedback and geometry-based approaches in embodied learning remains underutilized. These gaps motivated the design of a digital-embodied learning environment centered on nomograms. Chapter 3 details the design and pilot study of an embodied learning environment using nomograms. A key design feature is the use of bimanual movement tasks, which prompt students to physically coordinate two variables along the nomogram's input and output axes. Real-time color feedback guides students to adjust their hand positions. This tactile process was found to foster a rich sensorimotor experience of functional relationships. In Chapter 4, the research moves the refined intervention into authentic classroom conditions on a larger scale. Quantitative findings demonstrated significant improvements across all aspects of FT. Qualitative data clarified how key design features scaffolded the transition from concrete sensorimotor experiences to abstract mathematical reasoning. Chapter 5 delves deeper into the micro-processes by investigating how bimanual movements specifically support covariational reasoning. By analyzing hand-tracking data, this chapter links sensorimotor fluency with conceptual development. The analysis showed that students who made greater learning gains spent more time in fluency phases, suggesting that prolonged, embodied exploration can foster deeper reasoning. This methodological approach provided a "microlens" into the perception-action loops that underpin students' understanding of functional relationships. Finally, Chapter 6 synthesizes the findings: (1) Nomograms can be effective tools to foster input-output thinking, covariational reasoning, and representation conversion within correspondence thinking, especially when they are augmented with real-time feedback and bimanual tasks. (2) Embodied design features (particularly coordinated bimanual movements) create attentional anchors for abstract functional relationships, helping students “feel” how changes in one variable correspond to changes in another. (3) The design is practically feasible in regular classroom settings, with empirical evidence of learning gains and positive engagement. Theoretical implications include: students’ bimanual movement fluency develops concurrently with mathematical thinking. The findings indicate that body-artifact functional dynamic systems – involving bimanual coordination, real-time feedback, and interactive digital representations – facilitate the mathematization of functional relationships. Methodologically, this thesis offers a replicable framework for future design-based research in digital-embodied learning. Specifically, it combines systematic review, iterative environment design, classroom testing, and fine-grained sensor data (hand-tracking) to analyze students’ learning processes. |
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| DOI: | 10.33540/3107 |