Topic Study Group No. 13: Teaching and Learning of Geometry—Secondary Level

Cheah, Ui Hock; Herbst, Patricio; Ludwig, Matthias; Richard, Philippe; Scaglia, Sara

doi:10.1007/978-3-319-62597-3_40

Cited by 4 publications

(2 citation statements)

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“…Professional analysis of many publications [19][20][21][22] allows to assert the need for a certain rethinking by teachers of the goals and objectives of teaching geometry at school, and, as a consequence, a certain restructuring of the methodological activities of a teacher of mathematics in teaching geometry to students. Understanding the modern role and place of geometry in the formation and development of the student's personality, readiness and ability to provide appropriate conditions in the learning process of geometry are crucial for the teacher's choice of strategy and tactics of methodological activities [23].…”

Section: Discussionmentioning

confidence: 99%

Opportunities for Method Competence Development of Mathematics Teachers: The Role of Participation in Competitions with Colleagues

Матяш¹,

Mykhailenko²

2020

ujer

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The article contains explanations of the importance of developing the competence of teachers with teaching mathematics and introduces the idea of constructive approximation of the methodical activity of school teachers and lecturers of pedagogical universities. It describes certain features of the Ukrainian system of methodical training of future mathematics teachers at pedagogical universities. The objective of the study is to experimentally discover the influence of teachersp articipation in special geometry teaching competitions on the methodological development of practicing and future mathematics teachers. For the purposes of the study, the Vinnytsia State Pedagogical University hosted a competition of geometry teaching methodological findings for practicing teachers and a methodological skills contest for future math teachers in 2017, 2018, and 2019. We surveyed 32 participants of the above competitions. Practicing math teachers have laid stress upon the high quality of discussions on current problems of teaching geometry, new opportunities to share the experience gained, the high level of expertise and recognition of their own ideas about teaching geometry within the cooperation with the Pedagogical University organized by us. Future mathematics teachers have indicated the growing interest in future methodical activities at school, decided upon their own own aspirations for methodological development. The main conclusions: the educational environment for training the future mathematics teachers at the university should promptly respond to the new requirements for methodical performance of a teacher of the modern school; future math teachers have more opportunities for methodological development in specially created conditions of communication with experienced practicing teachers; practicing math teachers have more opportunities for methodological self-development in the process of active discussion of methodological issues with future teachers, lecturers of pedagogical universities, and scientists in the field of mathematics teaching methodology. We bring your attention to topicality of the problem of math teachers' creative approach to teaching, their willingness to comprehend, analyze and adopt innovations.

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Section: Discussionmentioning

confidence: 99%

Opportunities for Method Competence Development of Mathematics Teachers: The Role of Participation in Competitions with Colleagues

Матяш¹,

Mykhailenko²

2020

ujer

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“…In Krutetskii's studies with 34 mathematically talented students, 23 exhibited harmonic reasoning. In geometric instruction, teaching practice associated with argumentation encourages connections with other branches of mathematics and coordinates perceptual with numerical or symbolic skills [1,45,54,55]. Research has nonetheless revealed student preference for logical-verbal over visual processing [53], which is observed in fewer students [56].…”

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confidence: 99%

Reasoning, Representing, and Generalizing in Geometric Proof Problems among 8th Grade Talented Students

Uclés

Ruiz-Hidalgo

2022

Mathematics

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Proof, a key topic in advanced mathematics, also forms an essential part of the formal learning experience at all levels of education. The reason is that the argumentation involved calls for pondering ideas in depth, organizing knowledge, and comparing different points of view. Geometry, characterized by the interaction between the visual appearance of geometric elements and the conceptual understanding of their meaning required to generate precise explanations, is one of the foremost areas for research on proof and argumentation. In this qualitative analysis of the arguments formulated by participants in an extracurricular mathematics stimulus program, we categorized students’ replies on the grounds of reasoning styles, representations used, and levels of generality. The problems were proposed in a lesson on a quotient set based on the similarity among triangles created with Geogebra and the responses were gathered through a Google form. By means a content analysis, the results inform about the reasoning style, the scope of the argumentation, and the representation used. The findings show that neither reasoning styles nor the representations used conditioned the level of generality, although higher levels of argumentation were favored by harmonic and analytical reasoning and the use of algebraic representations.

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Structures and representations used by 6th graders when working with quadratic functions

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Cañadas

Damián

2022

ZDM Mathematics Education

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This study lies within the field of early-age algebraic thinking and focuses on describing the functional thinking exhibited by six sixth-graders (11- to 12-year-olds) enrolled in a curricular enhancement program. To accomplish the goals of this research, the structures the students established and the representations they used to express the generalization of the functional relationship were analyzed. A questionnaire was designed with three geometric tasks involving the use of continuous variables in quadratic functions. The students were asked to calculate the areas of certain figures for which some data were known, and subsequently to formulate the general rule. The results show that the participating students had difficulties expressing structures involving quadratic functions. However, they displayed the potential to use different types of representations to establish the functional relationship. The originality of this study lies in the differences observed in the process of generalization with discrete variables, since, in the case of continuous variables, students could recognize the general expression from analyzing the set of values that can be attributed to the variables in an interval.

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Topic Study Group No. 13: Teaching and Learning of Geometry—Secondary Level

Cited by 4 publications

References 0 publications

Opportunities for Method Competence Development of Mathematics Teachers: The Role of Participation in Competitions with Colleagues

Opportunities for Method Competence Development of Mathematics Teachers: The Role of Participation in Competitions with Colleagues

Reasoning, Representing, and Generalizing in Geometric Proof Problems among 8th Grade Talented Students

Structures and representations used by 6th graders when working with quadratic functions

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