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"Geometry Computer-assisted instruction."
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Interactions on digital tablets in the context of 3D geometry learning: contributions and assessments
Over the last few years, multi-touch mobile devices have become increasingly common. However, very few applications in the context of 3D geometry learning can be found in app stores. Manipulating a 3D scene with a 2D device is the main difficulty of such applications. Throughout this book, the author focuses on allowing young students to manipulate, observe and modify 3D scenes using new technologies brought about by digital tablets. Through a user-centered approach, the author proposes a grammar of interactions adapted to young learners, and then evaluates acceptability, ease of use and ease of learning of the interactions proposed. Finally, the author studies in situ the pedagogic benefits of the use of tablets with an app based on the suggested grammar. The results show that students are able to manipulate, observe and modify 3D scenes using an adapted set of interactions. Moreover, in the context of 3D geometry learning, a significant contribution has been observed in two classes when students use such an application. The approach here focuses on interactions with digital tablets to increase learning rather than on technology. First, defining which interactions allow pupils to realize tasks needed in the learning process, then, evaluating the impact of these interactions on the learning process. This is the first time that both interactions and the learning process have been taken into account at the same time.
eBook
Visualizing mathematics with 3D printing
The first book to explain mathematics using 3D printed models.
Winner of the Technical Text of the Washington Publishers
Wouldn't it be great to experience three-dimensional ideas in three dimensions? In this book—the first of its kind—mathematician and mathematical artist Henry Segerman takes readers on a fascinating tour of two-, three-, and four-dimensional mathematics, exploring Euclidean and non-Euclidean geometries, symmetry, knots, tilings, and soap films. Visualizing Mathematics with 3D Printing includes more than 100 color photographs of 3D printed models. Readers can take the book's insights to a new level by visiting its sister website, 3dprintmath.com, which features virtual three-dimensional versions of the models for readers to explore. These models can also be ordered online or downloaded to print on a 3D printer.
Combining the strengths of book and website, this volume pulls higher geometry and topology out of the realm of the abstract and puts it into the hands of anyone fascinated by mathematical relationships of shape. With the book in one hand and a 3D printed model in the other, readers can find deeper meaning while holding a hyperbolic honeycomb, touching the twists of a torus knot, or caressing the curves of a Klein quartic.
eBook
Interactions on Digital Tablets in the Context of 3D Geometry Learning
Over the last few years, multi-touch mobile devices have become increasingly common. However, very few applications in the context of 3D geometry learning can be found in app stores. Manipulating a 3D scene with a 2D device is the main difficulty of such applications.
Throughout this book, the author focuses on allowing young students to manipulate, observe and modify 3D scenes using new technologies brought about by digital tablets. Through a user-centered approach, the author proposes a grammar of interactions adapted to young learners, and then evaluates acceptability, ease of use and ease of learning of the interactions proposed.
Finally, the author studies in situ the pedagogic benefits of the use of tablets with an app based on the suggested grammar. The results show that students are able to manipulate, observe and modify 3D scenes using an adapted set of interactions. Moreover, in the context of 3D geometry learning, a significant contribution has been observed in two classes when students use such an application.
The approach here focuses on interactions with digital tablets to increase learning rather than on technology. First, defining which interactions allow pupils to realize tasks needed in the learning process, then, evaluating the impact of these interactions on the learning process. This is the first time that both interactions and the learning process have been taken into account at the same time.
eBook
Towards an ecological-dynamics design framework for embodied-interaction conceptual learning
Designers of educational modules for conceptual learning often rely on procedural frameworks to chart out interaction mechanics through which users will develop target understandings. To date, however, there has been no systematic comparative evaluation of such frameworks in terms of their consequences for learning. This lack of empirical evaluation, we submit, is due to the intellectual challenge of pinning down in what fundamental sense these various frameworks differ and, therefore, along which parameters to conduct controlled comparative experimentation. Toward an empirical evaluation of educational-technology design frameworks, this conceptual paper considers the case of dynamic mathematics environments (DME), interactive modules for learning curricular content through manipulating virtual objects. We consider user activities in two paradigmatic DME genres that utilize similar HCI yet different mechanics. To compare these mechanics, we draw from complex dynamic systems theory a constraint-based model of embodied interaction. Task analyses suggest that whereas in one DME genre (GeoGebra) the interaction constraints are a priori inherent in the environment, in another DME genre (Mathematics Imagery Trainer) the constraints are ad hoc emergent in the task. We conjecture differential learning effects of these distinct constraint regimes, concluding that ad hoc emergent task constraints may better facilitate the naturalistic development of cognitive structures grounding targeted conceptual learning. We outline a future empirical research design to compare the pedagogical entailments of these two design frameworks.
Journal Article
Mobile computer-supported collaborative learning for mathematics: A scoping review
This study conducted a scoping review of publications in mobile Computer-Supported Collaborative Learning for mathematics. Papers published between 2007 and 2021 inclusive were retrieved from research databases to achieve this goal. Twenty-eight papers met the inclusion–exclusion criteria of the study. It was shown that two papers were published on average over the last 15 years. The majority of the papers were published in peer-reviewed journals. Intending to improve mathematics pedagogy, the two most popular math mCSCL contents were general elementary mathematics and geometry. The review also revealed that math mCSCL benefited elementary students the most. The majority of math mCSCL software was custom-built and designed for synchronous sharing. The research designs were consistent with the existing reviews. The effects on social and attitude skills, as well as mathematics competency, were the most frequently mentioned benefits of math mCSCL. Usability issues, device unfamiliarity, inability to track students' activities, synchronization, and coordination concerns were among the problems highlighted during the implementation of math mCSCL. The implications for future research are discussed.
Journal Article
Integrating CAD and Orthographic Projection in Descriptive Geometry Education: A Comparative Analysis with Monge’s System
Descriptive geometry plays a fundamental role in developing spatial reasoning and geometric problem-solving skills in engineering education. This study investigates the comparative effectiveness of two instructional methodologies—Monge’s traditional projection system and the CADOP method, which integrates computer-aided design tools with orthographic projection principles. A quasi-experimental design was implemented with 90 undergraduate engineering students randomly assigned to two groups. Both groups followed the same instructional sequence and were evaluated using baseline surveys, rubric-based performance assessments, and post-training reflections. Quantitative analysis included mean comparisons, t-tests, and effect sizes, while inter-rater reliability confirmed scoring consistency. The results showed that CADOP students significantly outperformed those taught with Monge’s method across all criteria—conceptual under-standing, graphical accuracy, procedural consistency, and spatial reasoning—with very large effect sizes. Qualitative data indicated that CADOP enhanced clarity, efficiency, and confidence, while Monge promoted conceptual rigor but higher cognitive effort. The findings confirm that CADOP effectively reduces procedural complexity and cognitive load, supporting deeper spatial comprehension. Integrating CADOP with selected manual practices offers a balanced pedagogical approach for modernizing descriptive geometry instruction in engineering education.
Journal Article
Design of Computer-Aided Instruction Model Based on Knowledge Graph Construction and Learning Path Recommendation
This paper proposes a computer-aided teaching model using knowledge graph construction and learning path recommendation. It first creates a multimodal knowledge graph to illustrate complex relationships among knowledge. Learning elements and sequences are then used to form time sequences stored as directed graphs, supporting flexible path recommendations. Learners select elements based on interests and learning bases, updating behavior data for precise path recommendations. The platform, employing distributed architecture, integrates data processing and teaching applications for comprehensive cycle management and assessment. Controlled experiments validate its efficacy in enhancing learning outcomes compared to traditional methods, catering to personalized learning needs and advancing intelligent teaching.
Journal Article
Exploring differences in primary students’ geometry learning outcomes in two technology-enhanced environments: dynamic geometry and 3D printing
BackgroundThis 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.ResultsThe 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.ConclusionsThis 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.
Journal Article
Evaluating Spatial Thinking Ability Using Item Response Theory
Science, Technology, Engineering, and Mathematics (STEM) education initiatives have placed pressure on teachers to bring technology tools into classroom, including three-dimensional (3D) printing. Yet, little research has examined what specific math skills are required for 3D printing technology. This article describes a follow-up analysis of findings from a quasi-experimental study that tested feasibility of 3D geometry instruction, Anchored Instruction with Technology Applications (AITA), designed to help students visualize and construct 3D models based on Enhanced Anchored Instruction. Although we found that AITA improved math outcomes of students with math learning disabilities (MLD) in the previous analysis, we only used composite scores encompassing a variety of math and spatial tasks. In this study, we employed item response theory and differential item functioning to examine the impacts of MLD on students’ spatial thinking skills, understand the types of items to assess the intended skills in a valid way, and provide a detailed information of whether student ability and MLD status have caused different results to assess students’ spatial thinking skills. Results showed that students with MLD struggle to learn spatial thinking skills, and AITA was a significant positive indicator to improve spatial thinking skills for both students with and without MLD.
Journal Article