In this study, we examined aspects relating to the impact of integrating question-asking activiti... 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...
The spread of the Covid-19 pandemic shed light on the role of social media as a platform that fac... 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.
In this study, we examined aspects relating to the impact of integrating question-asking activiti... 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...
The spread of the Covid-19 pandemic shed light on the role of social media as a platform that fac... 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.
The 40th International Conference on the Psychology of Mathematics Education (PME), 2017
The increasing interest in STEM education raised awareness of issues related to interdisciplinary... 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.
EduLearn 18 10th annual International Conference on Education and New Learning Technologies, 2018
Many students experience difficulties and failures in mathematics already in elementary school. O... 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.
The 7th International Conference on Teacher Education: The Story of Innovation in Teacher Education , 2019
During the last decade, the flipped-class learning (FCL) method is increasingly being integrated ... 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.
The 7th International Conference on Teacher Education: The Story of Innovation in Teacher Education , 2019
In the Northern District of Israel there is a shortage of teachers who can teach high level mathe... 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.
The 7th International Conference on Teacher Education: The Story of Innovation in Teacher Education , 2019
Recognition of the central role of the educational system in maximizing students’ potential and p... 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.
The 7th International Conference on Teacher Education: The Story of Innovation in Teacher Education , 2019
In this paper, we describe the experience of eighteen elementary school mathematics teachers who ... 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.
This paper describes a study that followed the experience of 12 mathematics teachers in primary s... 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.
The study described in this paper examined mathematics teachers’ (inservice and preservice) knowl... 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 Multifaceted Nature of Creativity in the Teaching of Geometry, 2020
Geometry is one of the most ancient branches of mathematics. In order to ‘understand geometry’, l... 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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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.
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.