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

Sinclair, Nathalie; Bartolini, Maria Giuseppina; Villiers, Michael De; Jones, Keith; Kortenkamp, Ulrich; Leung, Allen; Owens, Kay

doi:10.1007/978-3-319-62597-3_18

Cited by 22 publications

(15 citation statements)

References 36 publications

(31 reference statements)

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“…On the other hand, skills trained in abstract contexts can be applied in different practical contexts. This aim of geometry teaching was confirmed by many authors [23][24][25]. In addition, the authors of [25] also stressed the role of manipulation and the creation of geometrical images in developing the so-called spatial intuitive skills.…”

Section: Results Of the Pre-testmentioning

confidence: 79%

Using Tangram as a Manipulative Tool for Transition between 2D and 3D Perception in Geometry

Kmetova

Lehocká

2021

Mathematics

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Creating a mental image of our spatial environment is a key process for further abstract geometric thinking. Building a mental representation can be understood as a part of the process of visualisation. From the wide concept of visualisation, in this article, we will focus on the part where the mental representation of spatial relations, mental objects and mental constructions are created, and their manifestations as a 3D physical object and its plane representations arise. Our main goal is to follow the transition between 2D and 3D representations of physical objects and also to observe how and when such a transition happens in students’ thinking. For that purpose, we also use Tangram, because manipulation with the Tangram pieces in space and filling out planar figures by them indicates the transition between 3D and 2D. Our research, using an action research methodology, was conducted on the students of three 5th grade primary school classes as a part of a larger long-term project. We pointed out a relationship between spatial abilities and the perception of 2D–3D relationships in students’ mind.

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Section: Results Of the Pre-testmentioning

confidence: 79%

Using Tangram as a Manipulative Tool for Transition between 2D and 3D Perception in Geometry

Kmetova

Lehocká

2021

Mathematics

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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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“…In a recent review on geometry education in one of ICME-13 Monographs, Herbst and his colleagues found that there was attention to spatial thinking and to aspects of deductive reasoning from conjecturing to proving across different countries [5] (p. 3). New teaching approaches, such as tool-based task design, inquiry-based learning, and DGS dragging mode, have been applied to teaching secondary school geometry frequently [6]. Meanwhile, it is noted that the traditional Euclidean approaches still existed in the classroom.…”

Section: Introductionmentioning

confidence: 99%

The Learning Trajectories of Similarity in Mathematics Curriculum: An Epistemological Analysis of Hong Kong Secondary Mathematics Textbooks in the Past Half Century

Zhang

Wong

2021

Mathematics

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The topic of similarity plays an essential role in developing students’ deductive reasoning. However, knowing how to teach similarity and understanding how to incorporate deductive reasoning and proof along with plane geometry remain a challenge to both school curriculum creators and teachers. This study identified the problems and characteristics regarding how similarity is treated in secondary mathematics textbooks in Hong Kong in the past half century. The content analysis method was used to analyze six secondary mathematics textbook series published in different periods. From the epistemological perspective of the textbook contents, our analysis shows the historical context and learning trajectories of how similarity was treated in school curriculum. The natural axiomatic geometry paradigm is not emphasized too much at different stages and most of the textbooks did not provide formal proofs of similarity. The intuitive idea was gradually consolidated into a formal definition of similarity. Furthermore, the way that rigorous geometric deduction can be performed from intuitive concepts and experimental geometry to the idea of proofs and formal proofs is also discussed.

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

Cited by 22 publications

References 36 publications

Using Tangram as a Manipulative Tool for Transition between 2D and 3D Perception in Geometry

Using Tangram as a Manipulative Tool for Transition between 2D and 3D Perception in Geometry

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

The Learning Trajectories of Similarity in Mathematics Curriculum: An Epistemological Analysis of Hong Kong Secondary Mathematics Textbooks in the Past Half Century

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