Dynamic investigation of loci with surprising outcomes and their mathematical explanations

Segal, Ruti; Stupel, Moshe; Oxman, Victor

doi:10.1080/0020739x.2015.1075613

Cited by 8 publications

(7 citation statements)

References 3 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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“…Technology-based learning media have been widely used and utilized among educators in the learning process (Leung, 2017;Nisiyatussani, Ayuningtyas, Fathurrohman, & Anriani, 2018). Some of the technology-based media used are animated videos (Chasanah, 2021;Nisa' & Rofiki, 2022), Geogebra (Segal, Stupel, & Oxman, 2016;States & Odom, 2016) or mobilebased applications (Apsari & Rizki, 2018;Rahayu, Rinaldi, & Gunawan, 2021). Thus, one of the alternative learning resources that can be developed by teachers today is technology-assisted media.…”

Section: Introductionmentioning

confidence: 99%

Development of Almajriti (Aplikasi Matematika Jago Program Linier Interaktif) for Class Xi Students of Senior High School

Nisa'

Marhayati

Chandra

2022

jptk

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This research aims to develop a valid ALMAJRITI (Aplikasi Matematika Jago Program Linier Interaktif) learning media and to determine student responses. Student responses were obtained from questionnaires and tests (pre-test and post-test). The study conducted is in the form of R&D with ADDIE steps. Media, learning, material, IT (Information Technology), language, and practitioners experts validate the media. The validation results obtained from each validator sequentially are 100% (very valid), 85% (very valid), 84.62% (very valid), 70% (valid), 87.5% (very valid), 96 ,87% (very valid). The media is very valid if it gets 75% or more. Overall, the media obtained a very valid assessment result of 87.33%, so the media was feasible to use. Meanwhile, the test instrument was validated by a material expert. The media was tested in class XI IPA 3 MAN 1 Blitar. The use of media shows a positive student response. More than 65% of students gave a positive response based on the questionnaire results. In addition, the average pre-test was 17.07, the post-test was 77.5, and the percentage increase in student learning outcomes was 405%. Thus, there is an increase in student learning outcomes before and after using ALMAJRITI. This increase shows a positive response from students to the ALMAJRITI. Therefore, it can be concluded that the ALMAJRITI media is valid and feasible to be used as a learning resource for class XI students

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Dynamic investigation of loci with surprising outcomes and their mathematical explanations

Cited by 8 publications

References 3 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

Development of Almajriti (Aplikasi Matematika Jago Program Linier Interaktif) for Class Xi Students of Senior High School

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