The instrumental deconstruction as a link between drawing and geometrical figure

Mithalal, Joris; Balacheff, Nicolas

doi:10.1007/s10649-018-9862-z

Cited by 11 publications

(3 citation statements)

References 12 publications

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“…The authors in [39] describe the potential of DGS for the process of reasoning after observing high school students when using GeoGebra in the context of minima and maxima geometric problems. The authors in [40] aim at a link between manipulation and deduction in 3D DGEs in the context of proof. As a basis, the authors refer to the former finding of a gap between students being able to formulate arguments from a drawing on the one hand and proving on the other.…”

Section: Dynamic Geometry Systemsmentioning

confidence: 99%

Teaching and Learning of Geometry—A Literature Review on Current Developments in Theory and Practice

Jablonski

Ludwig

2023

Education Sciences

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Geometry is part of the core of mathematics. It has been relevant ever since people have interacted with nature and its phenomena. Geometry’s relevance to the teaching and learning of mathematics can be emphasized, too. Nevertheless, a current potential shift in the topics of mathematics education to the detriment of geometry might be emerging. That is, other topics related to mathematics are seeming to grow in importance in comparison to geometry. Despite this, or perhaps because of it, geometry is an important component of current research in mathematics education. In the literature review, we elaborate relevant foci on the basis of current conference proceedings. By means of about 50 journal articles, five main topics are elaborated in more detail: geometric thinking and practices, geometric contents and topics, teacher education in geometry, argumentation and proof in geometry, as well as the use of digital tools for the teaching and learning of geometry. Conclusions and limitations for current and future research on geometry are formulated at the end of the article. In particular, the transfer to the practices of geometric teaching is explored on the basis of the elaborated research findings in order to combine both aspects of the teaching and learning of geometry.

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Section: Dynamic Geometry Systemsmentioning

confidence: 99%

Teaching and Learning of Geometry—A Literature Review on Current Developments in Theory and Practice

Jablonski

Ludwig

2023

Education Sciences

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“…Through analysis of successful student responses Healy and Hoyles (2002) showed how dynamic software tools can help students move from argumentation to logical deduction. Analyzing the process of instrumental deconstruction in the case of interactive diagram-based tasks, Mithalal and Balacheff (2019) argued that abstract reasoning involves a mix of observation and deduction (p. 162). Arzarello and Soldano (2019) introduced the notion of cognitive (dis)continuity between argumentation and proof, and discussed what they call "the basic gap" that can arise in the classroom.…”

Section: Connecting Examples and Universal Statements: The Interaction Between Proving And Exemplifyingmentioning

confidence: 99%

Online assessment of students’ reasoning when solving example-eliciting tasks: using conjunction and disjunction to increase the power of examples

Yerushalmy

Olsher

2020

ZDM Mathematics Education

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We argue that examples can do more than serve the purpose of illustrating the truth of an existential statement or disconfirming the truth of a universal statement. Our argument is relevant to the use of technology in classroom assessment. A central challenge of computer-assisted assessment is to develop ways of collecting rich and complex data that can nevertheless be analyzed automatically. We report here on a study concerning a dedicated design pattern of a special kind of task for assessing student's reasoning when establishing the validity of geometry statements that go beyond a single case, concerning the similarity of triangles. In each task students are given three relations that exist either in every triangle or in special types. Their task is to verify, by creating an example, claims that argue for logically compounded claims built out of the given relations. 50 students, aged 15-16, were asked to verify or disprove claims. Their submissions were automatically characterized along categories based on the correctness of the claims they chose and the examples they used to support the claims. We focus on characterizing the properties of the conjunction/disjunction design for automatically assessing conceptions related to examples generated by the learner with interactive diagrams. Our analysis shows that our automated scoring environment, which supports interactive example-eliciting-tasks, and the design principles of conjunction and disjunction of geometric relations, enable one to assess students' exploration of the logic of universal claims, characterize successful and partial answers, and differentiate between students according to their work.

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“…It is by no means trivial whether a drawing is well understood by the observer and if this is a correct drawing to provide the specific mathematic knowledge or artistic message [2][3][4]. This holds already in the case of a simple cube [5,6].…”

Section: Introductionmentioning

confidence: 99%

Is It a Cube? Common Visual Perception of Cuboid Drawings

Hoffmann

Németh

2021

Education Sciences

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A cube is one of the most fundamental shapes we can draw and can observe from a drawing. The two visualization methods most commonly applied in mathematics textbooks and education are the axonometric and the perspective representations. However, what we see in the drawing is really a cube or only a general cuboid (i.e., a polyhedron with different edge lengths). In this experimental study, 153 first-year ( 19–20-year-old) students, two-thirds of them being female, were asked to interactively adjust a cuboid figure until they believe what they see is really a cube. We were interested in how coherently people, who are actually students of arts studies and engineering with advanced spatial perception skills in most cases, evaluate these drawings. What we have experienced is that for most people there is a common visual understanding of seeing a cube (and not a general cuboid). Moreover, this common sense is surprisingly close to the conventions applied in axonometric drawings, and to the theoretical, geometric solution in the case of three-point perspective drawings, which is the most realistic visualization method.

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The instrumental deconstruction as a link between drawing and geometrical figure

Cited by 11 publications

References 12 publications

Teaching and Learning of Geometry—A Literature Review on Current Developments in Theory and Practice

Teaching and Learning of Geometry—A Literature Review on Current Developments in Theory and Practice

Online assessment of students’ reasoning when solving example-eliciting tasks: using conjunction and disjunction to increase the power of examples

Is It a Cube? Common Visual Perception of Cuboid Drawings

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