Geometric Construction Problem Solving in Computer-Aided Learning

Schreck, Pascal; Mathis, Pascal; Narboux, Julien

doi:10.1109/ictai.2012.162

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…Moreover, it was seen that the statements coded as challenger were checked in a quicker manner in GeoGebra groups compared to compass-straightedge groups. Different settings, which emerge as a result of challenger, can be tried quickly by means of the movement of a free object belonging to the geometric figure (Schreck et al, 2012). In other words, the dragging feature of GeoGebra might facilitate the examination process of the applications of different cases and help the groups to come up with some generalizations and properties regarding the challenger (Stupel et al, 2018).…”

Section: Discussionmentioning

confidence: 99%

Components of collective argumentation in geometric construction tasks

Demiray

Işıksal-Bostan

Saygı

2023

Turkish Journal of Education

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This study aims to examine the components of collective argumentation of pre-service middle school mathematics teachers during geometric construction activities. To scrutinize this issue, case study research was utilized. The participants were 14 pre-service middle school mathematics teachers who worked collectively by forming four groups. During the data collection process, the groups worked on four geometric construction tasks by using compass-straightedge or GeoGebra. The findings presented that the collective argumentation processes were depicted by means of eleven components. In more detail, the six components of Toulmin’s argument model which are data, warrant, claim, backing, rebuttal, and qualifier were insufficient to represent collective argumentation. Instead of claim, the term conclusion was used in this study since the associated data and warrant were provided in the argumentation. The collective argumentation processes of the groups involved not only the mentioned six components but also the five additional components, which were named conclusion/data, target conclusion, guidance, challenger, and objection. The new components might be used while investigating the argumentation process in other disciplines.

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Section: Discussionmentioning

confidence: 99%

Components of collective argumentation in geometric construction tasks

Demiray

Işıksal-Bostan

Saygı

2023

Turkish Journal of Education

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“…Second, this construction does not take degenerate cases into account -here when points M a , M b and M c are collinear. Actually, this is a simplified RC-construction: when all the possible cases are considered, the formal language used to express RC-construction must contain conditional structures (Marinković et al, 2014;Schreck et al, 2012). Detecting degenerate cases and tacking them into account has been accurately described in (Chou, 1988).…”

Section: Rc-constructibilitymentioning

confidence: 99%

Using jointly geometry and algebra to determine RC-constructibility

Schreck

Mathis

2019

Journal of Symbolic Computation

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In most cases in geometry, applying analytic or algebraic tools on coordinates helps to solve some difficult problems. For instance, proving that a geometrical construction problem is solvable using ruler and compass is often impossible within a synthetic geometry framework. But in an analytic geometry framework, it is a direct application of Galois theory after performing triangularizations. However, these algebraic tools lead to a large amount of computation. Their implementation in modern Computer Algebra Systems (CAS) are still too time consuming to provide an answer in a reasonable time. In addition, they require a lot of memory space which can grow exponentially with the size of the problem. Fortunately, some geometrical properties can be used to setup the algebraic systems so that they can be more efficiently computed. These properties turn polynomials into new ones so as to reduce both the degrees and the number of monomials. The present paper promotes this approach by considering two corpora of geometric construction problems, namely Wernick's and Connely's lists. These lists contain about 280 problems. The purpose is to determine their status i.e. whether they are constructible or not with ruler and compass. Some of these problems had unknown status that will be settled in this paper. More generally, the status of all problems of these corpora are fully automatically given by an approach combining geometry and algebra.

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Geometric Construction Problem Solving in Computer-Aided Learning

Cited by 2 publications

References 15 publications

Components of collective argumentation in geometric construction tasks

Components of collective argumentation in geometric construction tasks

Using jointly geometry and algebra to determine RC-constructibility

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