Learners’ Understanding of the Definitions and Hierarchical Classification of Quadrilaterals: Towards a Theoretical Framing

Fujita, Taro; Jones, Keith

doi:10.1080/14794800008520167

Cited by 123 publications

(144 citation statements)

References 11 publications

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“…It should be stressed that a typical (prototype) example has been the key factor for the further use of the concept (Türnüklü et al 2013). It has been common for pre-service teachers to use their own image of figures to create their definition (Fujita and Jones 2007). Additionally, research results show that they have actually defined prototypical images (Ozdemir and Dur 2014).…”

Section: Teachers' Understanding Of Basic Geometric Conceptsmentioning

confidence: 89%

“…Some of studies have relied on examination of knowledge of basic definitions, such as the definitions of angle, polygon, triangle, rectangle, trapezoid, parallelogram, rhombus, oblong, square, deltoid, and circle. Very often the concept of trapezoid was examine (Fujita and Jones 2007;Usiskin and Griffin 2008;Türnüklü et al 2013;Ozdemir and Dur 2014;Brunheira and da Ponte 2015). This can be observed in regard to the formal definition of trapezoids and general mathematical assumptions (Fig.…”

Section: Teachers' Understanding Of Basic Geometric Conceptsmentioning

confidence: 99%

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Early Geometrical Thinking in the Environment of Patterns, Mosaics and Isometries

Swoboda

Vighi

2016

ICME-13 Topical Surveys

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This survey confirms that one of the research trends in early geometrical reasoning has been a focus on creating a theoretical basis for research in this area. The main reason for the work on the theoretical foundations has been the fact that building geometrical concepts proceeds according to other regularities more than it takes place while building arithmetic knowledge. In this way, a broad research area was outlined. The first theory was created by Dina and Pierre Van Hiele (the Netherlands), but many on-going studies are related to this issue and many have focused on analysing and further expanding this theory.In parallel, new conceptual approaches that capture the question of the theoretical basis in a different way have been created. They should be considered complementarily, as they repeatedly point to the other aspects of the geometrical knowledge. The examples discussed in this paper come from the circles of scholars gathered around Alain Kuzniak (France) and Milan Hejný (Czech Republic). A networking between Van Hiele's theory and the description of geometrical paradigms created by Kuzniak examine ways that children work at the lowest levels. This allows analysis of how they gain experience, which is the basis for the transition in the area of further paradigms. This is therefore a departure from the theories that have a linear structure and focus only on a successive development.Milan Hejný indicates new aspects for descriptions of understanding of geometrical concepts, but first and foremost, he connects his proposals with the concept of schema-oriented education, where creating skills and procedures should be seen from a long perspective. In his theoretical background, a relatively new trend concerning the development of geometric reasoning is a pro-ceptual approach to the concepts. The formation of geometrical concepts is related to the empirical

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Section: Teachers' Understanding Of Basic Geometric Conceptsmentioning

confidence: 89%

Section: Teachers' Understanding Of Basic Geometric Conceptsmentioning

confidence: 99%

Early Geometrical Thinking in the Environment of Patterns, Mosaics and Isometries

Swoboda

Vighi

2016

ICME-13 Topical Surveys

View full text Add to dashboard Cite

show abstract

“…Overall, the majority of studies have concentrated on descriptive (a posteriori) defining; for example, defining circles, triangles, quadrilaterals, and polyhedra after exploring their properties with the use of DGEs, paper-folding, and/or pencil-and-paper construction (c.f. Choi and Oh 2008;Fujita & Jones, 2007;Salinas, Lynch-Davis, Mawhinney, & Crocker, 2014;Usiskin, Griffin, Witonsky, & Willmore, 2008;Zandieh & Rasmussen, 2010). …”

Section: The Teaching and Learning Of Geometric Definitionsmentioning

confidence: 99%

Geometry Education, Including the Use of New Technologies: A Survey of Recent Research

et al. 2017

Self Cite

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This is a summary report of the ICME-13 survey on the theme of recent research in geometry education. Based on an analysis of the research literature published since 2008, the survey focuses on seven major research threads. These are the use of theories in geometry education research, the nature of visuospatial reasoning, the role of diagrams and gestures, the role of digital technologies, the teaching and learning of definitions, the teaching and learning of the proving process, and moves beyond traditional Euclidean approaches. Within each theme, there is commentary on promising future directions for research.

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“…It is known that the hierarchical nature of quadrilaterals is problematic for learners (Fujita and Jones 2007) and throughout this episode Karin focused attention not only on the conceptual basis of this hierarchy but also the logic underpinning it. In so doing she emphasised the important understanding that no one approach to defining quadrilaterals, whether by angle, diagonal or edge, is sufficient.…”

Section: Karin's Teaching Of Polygonsmentioning

confidence: 99%

Mathematics, PISA, and culture: An unpredictable relationship

Andrews

2015

J Educ Change

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Learners’ Understanding of the Definitions and Hierarchical Classification of Quadrilaterals: Towards a Theoretical Framing

Cited by 123 publications

References 11 publications

Early Geometrical Thinking in the Environment of Patterns, Mosaics and Isometries

Early Geometrical Thinking in the Environment of Patterns, Mosaics and Isometries

Geometry Education, Including the Use of New Technologies: A Survey of Recent Research

Mathematics, PISA, and culture: An unpredictable relationship

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