- Israel
Atara Shriki
Seminar Hakibbutzim College, Mathematics Education, Faculty Member
- Oranim College of Education, Mathematics Education, Department Memberadd
- Mathematics Education, Teachers' professional development, Mathematical Logic, Dynamic Geometry Sofware, Problem Posing in Mathematics, Mathematical Creativity, and 20 moreE-learning, Educational Technology, Teacher Change/Professional Development, Problem posing and Problem solving, Analysis, Problem Solving, Problem posing, Inventing New Mathematical Concepts, Integrating Children Literature Into the Teaching of Mathematics, Ceva Theorem, Social Context of Teaching, Teachers Professional Needs, Prospective Teachers Mathematical Knowledge, "what If Not?" Strategy, Social Media, Leadership, Educational Leadership, History of Mathematics, Ancient Greek History, and Leadership Developmentedit
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Research Interests: Perception, Teaching and Learning, Mathematics Education, Faculty Development, Professional Development, and 8 moreTeacher Development, Curiosity, Student Learning, Questionnaires, Cognitively Guided Instruction in Math, Boolean Satisfiability, School of Education and Professional Development, and Teachers Professional Needs
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In this study, we examined aspects relating to the impact of integrating question-asking activities and providing answers to these questions while reading historical mathematical texts on prospective mathematics teachers’ self-reported... more
In this study, we examined aspects relating to the impact of integrating question-asking activities and providing answers to these questions while reading historical mathematical texts on prospective mathematics teachers’ self-reported cognitive load. The research design of the study was quasi-experimental. The study participants included two groups of 20 students each (experimental and control). The experimental group was instructed to ask questions while coping with the texts, whereas the control group received no special instructions. The experimental group participants were asked to think aloud while coping with the texts and audio record themselves. These records were transcribed into written protocols. Both groups had to respond to a self-esteem index questionnaire in which they had to report the level of difficulty they experienced during their attempts to cope with the texts, as an indicator of their sense of cognitive load. This process was repeated at three time points, re...
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The spread of the Covid-19 pandemic shed light on the role of social media as a platform that facilitates teacher professional development. This includes the Facebook network. Dedicated Facebook groups are perceived as a space that allows... more
The spread of the Covid-19 pandemic shed light on the role of social media as a platform that facilitates teacher professional development. This includes the Facebook network. Dedicated Facebook groups are perceived as a space that allows professional communities to collaborate and share resources and knowledge. By virtue of my role as a mathematics teacher educator, I was interested in examining the nature of interactions that took place in Israeli Facebook groups of mathematics teachers during the period of school closure that was imposed due to the pandemic. In this paper, I refer to the largest Facebook group of mathematics teachers in Israel, a group comprised of about 6,500 primary and secondary school teachers as well as prospective teachers. The analysis of the interactions related to three periods: (i) Pre-pandemic: The beginning of school year in September 2019 to the beginning of first school closure on March 13, 2020; (ii) the first closure of schools, that ended on May 2, 2020; and (iii) the gradual opening of schools until June 30, 2020, when summer vacation started. In period i, only about 250 members of the group were regularly active, most of them primary school mathematics teachers. Typical posts during this period referred to sharing learning materials developed by the teachers, requests for assistance in solving mathematical problems, and suggestions regarding didactic ideas and relevant Internet sites. As of February 2020, an average of 5 posts was published per day, with each post having, on average, 7 comments. In period II, three prominent phenomena were observed: a rapid increase in the active participation of middle and high school teachers; productive didactic discussions (particularly on topics related to remote teaching of mathematics); and an increase in the willingness of teachers to share learning materials they had developed (mostly ones that are suitable for teaching in Zoom). In addition, there was significant growth in the number of posts. On average, about 20 posts were published daily, with a wide range of responses to each post. In period iii, the nature of interaction changed again. At first, only 1 st-3 rd grade students returned to school, and teachers who had not previously taught mathematics at these age groups were required to do so since each class was separated into small capsules. These teachers asked for advice and appropriate teaching materials, and many group members happily uploaded worksheets, PowerPoint presentations, and references to sources, and even provided their phone number and suggested to contact them. However, the general didactic discussions faded. In conclusion, the Facebook group served as a space that responded to the ad hoc professional needs of its members. The fact that all teachers were required overnight to change teaching methods created solidarity among them, which contributed to the strengthening of the group as an independent and enterprising professional community. Given the potential of a social network such as Facebook to serve as a platform for mutual professional support of teachers, it is worth examining how this media can be leveraged to generate a secure and sustainable environment for continuous teacher professional development, not just in emergencies or crises. The paper includes examples of the types of interactions that took place during school closure and group members' viewpoints regarding the benefits of the collaborative generation of knowledge by teachers themselves over receiving a response from an outside institutional source.
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Abstract: Starting in a well known theorem concerning medians of triangle and using the ‘What If Not? ’ strategy, we describe an example of an activity in which some relations among segments and areas in triangle were revealed. Some of... more
Abstract: Starting in a well known theorem concerning medians of triangle and using the ‘What If Not? ’ strategy, we describe an example of an activity in which some relations among segments and areas in triangle were revealed. Some of the relations were proved by means of Affine Geometry.
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Research Interests: Psychology and Creativity
One aspect of professional development of mathematics teachers relates to the development of assessment skills. The aim of this study is to examine the effects of engaging prospective mathematics teachers in peer assessment, both as... more
One aspect of professional development of mathematics teachers relates to the development of assessment skills. The aim of this study is to examine the effects of engaging prospective mathematics teachers in peer assessment, both as assessors and assessees, on the development of their assessment skills in general and assessment of geometrical proofs in particular. The research was conducted within a Method course in which peer assessment activities were employed. Sixteen prospective mathematics teachers participated in the research and had to act both as assessors and assessees. Analysis of the research data reveals that during the various phases of the study the prospective teachers developed skills concerning the selection of categories and weights for the assessment of their peers' work. In the criteria set they selected for the peer assessment, they referred to meanings and roles of mathematical proof. In their reflections, the prospective mathematics teachers also referred ...
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Many students experience difficulties and failures in mathematics already in elementary school. Often, this has a negative impact on their mathematics self-efficacy as mathematics learners, and as a result, their motivation to study the... more
Many students experience difficulties and failures in mathematics already in elementary school. Often, this has a negative impact on their mathematics self-efficacy as mathematics learners, and as a result, their motivation to study the discipline decreases. These students might reach middle school with low confidence about their ability to study mathematics and may possibly avoid its learning.
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Engagement in problem posing activities is among the significant activities of teaching and learning mathematics. This engagement might become richer when technology is involved. In this paper, we describe the experience of teachers who... more
Engagement in problem posing activities is among the significant activities of teaching and learning mathematics. This engagement might become richer when technology is involved. In this paper, we describe the experience of teachers who were engaged in problem posing within a dynamic geometry environment, present some of their works, and discuss the prominent issues that emerged as a result of their experience.
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In Sanskrit, the ancient Hinduism language, ‘Vedas’ means ‘knowledge’. The Vedas are a corpus of more than 1,000,000 ancient philosophical writings divided into Sutras, some of which deal with mathematics. These mathematics Sutras, termed... more
In Sanskrit, the ancient Hinduism language, ‘Vedas’ means ‘knowledge’. The Vedas are a corpus of more than 1,000,000 ancient philosophical writings divided into Sutras, some of which deal with mathematics. These mathematics Sutras, termed ‘Vedic Mathematics’, concern various fields of mathematics. The Vedic methods are coherent, logical and simple, and students enjoy practicing them. Besides 'spicing up' the regular mathematics lessons by integrating some of the Vedic algorithms, engaging students in proving them supports the development of their insights regarding the rationale underlying the formal rules and algorithms included in the curriculum. In this workshop, we present some of the basic Vedic arithmetic and algebraic algorithms, involve the participants in proving the them and discuss the advantages and disadvantages of integrating Vedic mathematics into classes at different age groups and study levels.
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The recent reforms in mathematics education generate the necessity for teachers to attend professional development programs. In order to increase the teachers’ motivation to attend such programs it is essential to adjust their contents to... more
The recent reforms in mathematics education generate the necessity for teachers to attend professional development programs. In order to increase the teachers’ motivation to attend such programs it is essential to adjust their contents to the teachers’ needs. These needs are culturally and socially dependent; hence a certain program which is successful in one country might not be appropriate in another. While designing professional development programs it is important to consider the needs of the population to whom it is intended. The current study was designed in order to explore the needs of Israeli mathematics teachers for professional development, assuming that considering their urgent needs would help us in designing relevant programs.
The world of mathematics is constantly evolving. However, the mathematics included in school curricula seldom reflects this evolving nature of the discipline. Appreciating the importance of exposing students to contemporary mathematics,... more
The world of mathematics is constantly evolving. However, the mathematics included in school curricula seldom reflects this evolving nature of the discipline. Appreciating the importance of exposing students to contemporary mathematics, we identified fractal geometry as a topic that could meaningfully be integrated into the regular curriculum. In this article we briefly introduce the idea of fractals and demonstrate how they can be integrated into the teaching of infinite geometric series.
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Research Interests: Psychology and Creativity
In this paper, we focus on the multi-disciplinarity approach, in particular, the integration of music into mathematics lessons. The current study was conducted in the framework of a professional training program for teachers who were... more
In this paper, we focus on the multi-disciplinarity approach, in particular, the integration of music into mathematics lessons. The current study was conducted in the framework of a professional training program for teachers who were teaching mathematics in 4 th-6 th grades and were interested in learning about the principles of STEAM education and different ways of applying the approach in their classes. The program included four modules of multidisciplinary teaching units that integrate mathematics and arts: mathematics and music, mathematics and drawing, mathematics and photography, and mathematics and dance. In what follows, we relate to the first module-mathematics and music. Twenty-seven mathematics teachers (among them four with musical backgrounds) participated in an annual professional development program that took place fortnightly via the Zoom platform (due to the closure imposed by the Covid-19 pandemic). Before we have explicitly exposed the teachers to the rationale behind STEAM education, in general, and the multidisciplinary approach to the teaching of mathematics and music, in particular, the teachers were asked to design a lesson that integrates mathematics and music in the case of factions. To that end, they were allowed to choose any platform and rely on any source of information. We aimed to examine how teachers perceive the meaning of multi-disciplinarity of mathematics and music and how this perception is reflected in their products. The research data included transcripts of the whole class discussions in which the teachers presented the multidisciplinary lessons they had designed and described their underlying rationale; in-depth interviews via the Zoom platform with 15 of the participants following their presentations, aiming to learn more about the teachers' views regarding the integration of music and mathematics and the insights they gained during the process of designing the lessons; and the teachers' reflective journal in which they documented their thoughts, feelings, and deliberations while designing the integrative lesson and insights they gained. Results obtained point to the positive relationship between the teachers' professional knowledge and the level of integration implemented in their suggested learning activities. Moreover, teachers with broad professional knowledge and with musical knowledge developed activities with a high level of integration.
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Success in STEM fields depends largely on robust spatial skills, in particular on the ability to perform a mental rotation. Given that this ability can be nurtured, this article includes examples of diverse relevant tasks appropriate for... more
Success in STEM fields depends largely on robust spatial skills, in particular on the ability to perform a mental rotation. Given that this ability can be nurtured, this article includes examples of diverse relevant tasks appropriate for grades 6–8 students.
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Some twenty years ago, when I was a university student, one of my lecturers presented a problem that he called Treasure Island. At first glance, the problem appeared to be unsolvable. After students made some futile attempts, the lecturer... more
Some twenty years ago, when I was a university student, one of my lecturers presented a problem that he called Treasure Island. At first glance, the problem appeared to be unsolvable. After students made some futile attempts, the lecturer presented the surprising solution, without providing any explanation or even a hint. I spent the rest of the lecture thinking about the problem and trying to discover a solution.
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Geometry is one of the most ancient branches of mathematics. In order to ‘understand geometry’, learners should be able to infer in a deductive way as well as be endowed with enhanced visual competencies. These prerequisites render plane... more
Geometry is one of the most ancient branches of mathematics. In order to ‘understand geometry’, learners should be able to infer in a deductive way as well as be endowed with enhanced visual competencies. These prerequisites render plane geometry and solid geometry challenging for both teaching and learning. Hence, it is essential to consider creative ways for teaching the various branches of geometry in order to respond to the varied difficulties, while fostering deductive thinking and visual competencies. This book aims to provide readers with a broad knowledge of the various aspects of creativity and its assessment and to expose them to creative methods and approaches to the teaching of geometry. The content of the book is grounded in the research literature that engages in creativity in general and in creativity in teaching in particular. The chapters collected in the book present the multifaceted nature of geometry teaching in a creative-integrated way while exposing the readers to the beauty of geometry.
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This study explored Israeli elementary school mathematics teachers’ perceptions of their professional needs, with the purpose of developing in-service training courses which cater to these needs. Eighty-four teachers responded to the... more
This study explored Israeli elementary school mathematics teachers’ perceptions of their professional needs, with the purpose of developing in-service training courses which cater to these needs. Eighty-four teachers responded to the questionnaire and were interviewed. The results indicate that the respondents’ main needs are associated with strengthening their didactical knowledge capability of dealing with emotional aspects that relate to pupils’ learning of mathematics. Although most of the respondents lack formal mathematics education, they attribute less importance to their need to enhance knowledge in the field. In light of Israeli pupils’ relatively low attainments in mathematics, the authors believe that the education system should require teachers to expand their mathematics knowledge and that only teachers with appropriate knowledge will be permitted to teach the discipline.
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In this paper, we describe the process of students' self-assessment of their creativity and its development in the context of posing mathematical problems, presuming that such a process would support the development of their... more
In this paper, we describe the process of students' self-assessment of their creativity and its development in the context of posing mathematical problems, presuming that such a process would support the development of their creativity. Examination of two case studies reveals that self-assessment of creativity may support its development provided that one possesses specific personal recourses; however, this process might suppress the creativity of those lacking the needed resources. Therefore, we suggest that self-assessment of creativity cannot stand on its own, and should be supplemented by teachers' feedback or other environmental 'scaffolding'.
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In this paper we provide a partial description of certain facets and experiences that are central to the development of emotional knowledge from the retrospective perspectives of two highly experienced mathematics teachers in middle and... more
In this paper we provide a partial description of certain facets and experiences that are central to the development of emotional knowledge from the retrospective perspectives of two highly experienced mathematics teachers in middle and high school. One of the study participants refers to the emotional knowledge she developed over the years regarding her interactions with her students, while the second participant also refers to the emotional knowledge she developed regarding her interaction with the school principal. Both indicate the differences in their emotional reactions between the first practice years and the years after. The differences are seen primarily in the type and in the intensity of their emotions. While negative feelings mostly accompanied the first years, later years were accompanied by more positive emotions.
Research Interests: Psychology and Feeling
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The increasing interest in STEM education raised awareness of issues related to interdisciplinary approach to teaching. In secondary schools, such teaching is rare, mainly because teachers are often certified in one specific discipline.... more
The increasing interest in STEM education raised awareness of issues related to interdisciplinary approach to teaching. In secondary schools, such teaching is rare, mainly because teachers are often certified in one specific discipline. This implies that implementation of interdisciplinary approach to the teaching of mathematics and science necessitates the cooperation and collaboration of teachers from both disciplines in writing suitable learning materials. Our study aimed at examining the various aspects associated with such collaboration. The results indicate that mathematics teachers acknowledged the advantages of interdisciplinary teaching; however, they questioned the feasibility of the collaborative lesson planning and were concerned about their capability to implement the approach.
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Many students experience difficulties and failures in mathematics already in elementary school. Often, this has a negative impact on their mathematics self-efficacy as mathematics learners, and as a result, their motivation to study the... more
Many students experience difficulties and failures in mathematics already in elementary school. Often, this has a negative impact on their mathematics self-efficacy as mathematics learners, and as a result, their motivation to study the discipline decreases. These students might reach middle school with low confidence about their ability to study mathematics and may possibly avoid its learning.
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During the last decade, the flipped-class learning (FCL) method is increasingly being integrated into the education system, in general, and in mathematics education, in particular. The underlying assumption of the FCL method is that to... more
During the last decade, the flipped-class learning (FCL) method is increasingly being integrated into the education system, in general, and in mathematics education, in particular. The underlying assumption of the FCL method is that to some extent students ought to become responsible for their own learning. This assumption leads to a significant change in teachers’ role in the classroom: From the position of being responsible for the pace of learning and “providing knowledge” to providing one-to-one assistance to students who cope with specific difficulties in studying the learning materials. In addition, they have to initiate learning environments that encourage inquiry activities based on the materials learnt by the students and conclude the learning process by class discussion in which students have the opportunity to share insights with their classmates. In order to be able to adapt the changes described above, teachers need to experience this learning method as learners, either during their training period or in-service practice, in order to recognize its benefits and shortcomings. In this study, we explored pre-service mathematics teachers’ (PMT) perceptions regarding FCL as a result of their engagement in such learning as part of a mathematics course. Data was collected through the PMTs’ reflective journals and records of class discussions. The data analysis revealed that the PMTs went through the following phases: resistance and rejection, frustration, adjustment and acceptance. There were also a small group of PMTs who found no advantages to the study of mathematics via FCL.
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In the Northern District of Israel there is a shortage of teachers who can teach high level mathematics (“5-units”). To address this need, a three-year project (“Ramzor La’Zafon”) was initiated. As part of the project, teachers who were... more
In the Northern District of Israel there is a shortage of teachers who can teach high level mathematics (“5-units”). To address this need, a three-year project (“Ramzor La’Zafon”) was initiated. As part of the project, teachers who were highly experienced in teaching 5-units mathematics served as mentors for teachers who lacked such experience (hereinafter “mentor” and “mentee”, respectively). Both the mentor and the mentee were teaching at the same school. This type of mentoring relationship is considered a powerful tool for the professional development of teachers who are novices in a particular field, due to the mentor’s accessibility and relevant experience. The study examined mentees’ perceptions regarding the impact of the mentoring relationships on changes in their sense of self-efficacy (abbreviated SOSE) to teach 5-units mathematics. The results of the study indicate the presence of two main conditions, which, if exist simultaneously, have an impact on the success of mentoring relationships as well as on the increase in the mentees’ SOSE: A large gap between the mentor’s and mentee’s seniority (in favor of the mentor), and the availability and accessibility of the mentor: A large gap has implications for mentees’ readiness to recognize their mentors as authoritative figures in terms of mathematical and didactic knowledge and consider their advice; and the mentors’ availability and accessibility provide the mentees with a sense of a “safe environment”. Furthermore, a lack of availability of the mentor may harm mentees’ self-efficacy to teach 5-units mathematics, and consequently might undermine their willingness to persist in facing challenges.
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Recognition of the central role of the educational system in maximizing students’ potential and preparing for their future life, the design of the didactic tool “Correspondence with the Professor” was inspired by Paulo Freire’s ideas... more
Recognition of the central role of the educational system in maximizing students’ potential and preparing for their future life, the design of the didactic tool “Correspondence with the Professor” was inspired by Paulo Freire’s ideas regarding a humanizing pedagogy. As part of the implementation of the tool, students write a letter to an imaginary professor, describing their scholastic difficulties and the underlying reasons. Afterwards, they write themselves an answer letter on behalf of the professor, proposing ways for dealing with the difficulties. Each letter is accompanied by a students’ reflective writing.
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In this paper, we describe the experience of eighteen elementary school mathematics teachers who collaborated with their students in inquiring a mathematical topic that was unfamiliar to them. We termed this setting “Teacher-Students... more
In this paper, we describe the experience of eighteen elementary school mathematics teachers who collaborated with their students in inquiring a mathematical topic that was unfamiliar to them. We termed this setting “Teacher-Students Collaborative Inquiry Community” [TSCIC]. The study examined changes in participants’ perceptions of their role as mathematics teachers as a result of their involvement in TSCIC, acknowledging that such changes are indicators of professional development.
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This paper describes a study that followed the experience of 12 mathematics teachers in primary school while collaborating with their students in an inquiry of a mathematical topic they were unfamiliar with. The purpose of the study was... more
This paper describes a study that followed the experience of 12 mathematics teachers in primary school while collaborating with their students in an inquiry of a mathematical topic they were unfamiliar with. The purpose of the study was to identify various aspects related to this experience, as perceived by the teachers, and examine its implications on teachers' professional development in terms of changing their view of their role as mathematics teachers. The findings indicate that this experience, combined with carrying out an action research, had a positive effect on the professional development of the participants, and indeed modified their perceptions regarding their role as mathematics teachers. It also strengthened their sense of self-efficacy and professional image.
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The study described in this paper examined mathematics teachers’ (inservice and preservice) knowledge regarding the concept of parabola. The participants (33 preservice and 21 inservice) were asked to perform two tasks: in the first one,... more
The study described in this paper examined mathematics teachers’ (inservice and preservice) knowledge regarding the concept of parabola. The participants (33 preservice and 21 inservice) were asked to perform two tasks: in the first one, they were given four different verbal definitions of sets of curves, and for each definition they were asked to sketch a curve, which they believed, was compatible with the definition, and to describe its properties. In the second task, the participants were asked to sketch a Venn-Diagram in order to describe the logical connections between the four sets of curves, which were formed by the four definitions that appeared in the first task. All the definitions concerned the parabola.
The results show that only a few possess a full concept image concerning the parabola, and thus a few of them are capable of perceiving the parabola in its algebraic as well as geometrical contexts, or to identify links among them.
The results show that only a few possess a full concept image concerning the parabola, and thus a few of them are capable of perceiving the parabola in its algebraic as well as geometrical contexts, or to identify links among them.
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Geometry is one of the most ancient branches of mathematics. In order to ‘understand geometry’, learners should be able to infer in a deductive way as well as be endowed with enhanced visual competencies. These prerequisites render plane... more
Geometry is one of the most ancient branches of mathematics. In order to ‘understand geometry’, learners should be able to infer in a deductive way as well as be endowed with enhanced visual competencies. These prerequisites render plane geometry and solid geometry challenging for both teaching and learning.
Hence, it is essential to consider creative ways for teaching the various branches of geometry in order to respond to the varied difficulties, while fostering deductive thinking and visual competencies.
This book aims to provide readers with a broad knowledge of the various aspects of creativity and its assessment and to expose them to creative methods and approaches to the teaching of geometry. The content of the book is grounded in the research literature that engages in creativity in general and in creativity in teaching in particular.
The chapters collected in the book present the multifaceted nature of geometry teaching in a creative-integrated way while exposing the readers to the beauty of geometry.
Hence, it is essential to consider creative ways for teaching the various branches of geometry in order to respond to the varied difficulties, while fostering deductive thinking and visual competencies.
This book aims to provide readers with a broad knowledge of the various aspects of creativity and its assessment and to expose them to creative methods and approaches to the teaching of geometry. The content of the book is grounded in the research literature that engages in creativity in general and in creativity in teaching in particular.
The chapters collected in the book present the multifaceted nature of geometry teaching in a creative-integrated way while exposing the readers to the beauty of geometry.