Dynamic investigation of triangles inscribed in a circle, which tend to an equilateral triangle

Stupel, Moshe; Oxman, Victor; Sigler, Avi

doi:10.1080/0020739x.2016.1206978

Cited by 3 publications

(3 citation statements)

References 5 publications

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“…Incorporating inquirybased tasks into geometry instruction almost inherently encourages the use of a dynamic geometry software (DGS) environment (Hölzl, 2001;Mariotti, 2002;Yerushalmy & Chazan, 1993). DGS provides convenient and often fascinating learning opportunities for investigating geometric properties and deepening understanding (De Villiers, 1998;Leikin, 2012;Leung & Lopez-Real, 2002;Oxman, Stupel, & Segal, 2016;Segal, Oxman, & Stupel, 2015;Stupel, Sigler, & Oxman, 2017). DGS gives learners a dynamic view of geometrical objects and an opportunity to explore and speculate about their properties, relationships, generalizations, and more.…”

Section: Integrating Inquiry-based Geometrical Tasks Into the Dynamic Geometry Environmentmentioning

confidence: 99%

“…GeoGebra) can improve their mathematical/geometrical knowledge and skills, and increased their understanding of the importance of formulating a conjecture based on a wide range of examples to provide a semi-proof (Stupel & Ben-Chaim, 2013) on the way to formulating a complete deductive proof. The students also gained a dynamic view of geometrical objects and an opportunity to explore and speculate about their properties, relationships, and generalizations (Oxman, Stupel, & Segal, 2016;Segal, Oxman, & Stupel, 2015;Stupel, Sigler, & Oxman, 2017).…”

Section: Technological Content Knowledge (Tck)mentioning

confidence: 99%

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Using Dynamic Geometry Software to Enhance Specialized Content Knowledge: Pre-Service Mathematics Teachers’ Perceptions

Segal¹,

Oxman²,

Stupel³

2021

INT ELECT J MATH ED

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The study aimed to expose how pre-service teachers perceived the value of an inquiry-based geometrical task with dynamic geometry software for increasing and deepening their understanding of the task itself, and for heightening their mathematical, pedagogical, and technological knowledge in the case of reflection and transformation. Twenty-seven pre-service teachers studying to become middle-school (junior high) mathematics teachers were assigned an inquiry-based geometrical task to explore -both by conventional, low-tech means (paper and pencil) and then in a dynamic geometry software (DGS) environment -the properties of objects formed by reflections in polygons (triangles and quadrilaterals) and to offer conjectures and proofs regarding the final polygon's shape and area concerning the original. The results show that the majority of participants indicated that DGS provided a valuable instrument for revising and expanding their knowledge, that the assignment demonstrated the value that technological tools have in teaching and learning processes, and the importance of adapting learning tasks in geometry to a dynamic geometry environment for expanding and deepening geometrical and pedagogical knowledge and reasoning skills.

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Section: Integrating Inquiry-based Geometrical Tasks Into the Dynamic Geometry Environmentmentioning

confidence: 99%

Section: Technological Content Knowledge (Tck)mentioning

confidence: 99%

Using Dynamic Geometry Software to Enhance Specialized Content Knowledge: Pre-Service Mathematics Teachers’ Perceptions

Segal¹,

Oxman²,

Stupel³

2021

INT ELECT J MATH ED

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“…In the previous paper [9], a complete proof was given to the property obtained in the following process:…”

Section: Introductionmentioning

confidence: 99%

Converging Polygons by a Dynamic Process to a Perfect Polygon

2016

Jour. Math. Sci. Adv. Appl.

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We give an interesting description of a dynamic process in which a polygon inscribed in a circle converges to a perfect polygon, and also of the convergence of a triangle where in a stage-by-stage manner one constructs a triangle, the length of whose sides are the averages of the side lengths of the previous triangle, which monotonically converges by a dynamic process to an equilateral triangle. Mathematical proofs are given to the convergence to a perfect polygon, and the stages are presented visually using computerized dynamic applets which one can reach by links that exist in the paper.

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The problem and geometric application of infinite sequences formed from three given numbers by calculating their pairwise means

Oxman

Stupel²

2022

International Journal of Mathematical Education in Science and

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Dynamic investigation of triangles inscribed in a circle, which tend to an equilateral triangle

Cited by 3 publications

References 5 publications

Using Dynamic Geometry Software to Enhance Specialized Content Knowledge: Pre-Service Mathematics Teachers’ Perceptions

Using Dynamic Geometry Software to Enhance Specialized Content Knowledge: Pre-Service Mathematics Teachers’ Perceptions

Converging Polygons by a Dynamic Process to a Perfect Polygon

The problem and geometric application of infinite sequences formed from three given numbers by calculating their pairwise means

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