On teaching extrema triangle problems using dynamic investigation

Oxman, Victor; Stupel, Moshe; Segal, Ruti

doi:10.1080/0020739x.2016.1259514

Cited by 5 publications

(3 citation statements)

References 6 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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“…To improve the teaching and learning processes, it is important to expose teachers how to submit, to examine and to manage geometrical situations, analyze specific attributes, for propose a hypothesis, and write a proof (Oxman et al, 2016(Oxman et al, , 2018Segal et al, 2015Segal et al, , 2017. Overcoming the difficulties inherent in such a task often requires the instructor to offer a meaningful and supportive environment such as scaffolding to help and guide the students regarding what attributes are important and to refresh their memories with respect to knowledge that they may have (Cirillo & May, 2021;Dove & Hollenbrands, 2013;Tall, 1995).…”

Section: Introductionmentioning

confidence: 99%

Pre-service mathematics teachers investigating the attributes of inscribed circles by technological and theoretical scaffolding

Segal

Stupel²

2023

INT ELECT J MATH ED

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The benefits of technological and theoretical scaffolding were observed when pre-service teachers aiming to teach upper elementary grades were given three learning-based geometrical inquiry tasks involving inscribed circles. They were asked to collaboratively examine the accompanying geometrical illustration and data for some new or interesting feature and then propose a hypothesis resulting from their observations and prove them.<br /> Due to the difficulty generally involved in proposing and proving geometrical hypotheses, two forms of scaffolding were provided: theoretical scaffolding based on revising previous learning or specific attributes of the given data and technological scaffolding in the form of specifically designed GeoGebra applets that allowed dynamic observation of the attributes of the geometrical shapes and the changes they underwent during modification.<br /> We found that the two forms of scaffolding led to relatively pre-service teachers’ high levels of success. They exhibited high levels of interest and participation, were engaged in the tasks, and underwent high-quality learning processes. In follow-up interviews, they confirmed that the exercise improved their inquiry skills, and developed their pedagogical and technological knowledge.

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Some inequalities in a triangle in which the length of one side and the inradius are given

Oxman

2021

International Journal of Mathematical Education in Science and

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On teaching extrema triangle problems using dynamic investigation

Cited by 5 publications

References 6 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

Pre-service mathematics teachers investigating the attributes of inscribed circles by technological and theoretical scaffolding

Some inequalities in a triangle in which the length of one side and the inradius are given

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