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  1. ; ( , Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education)
    Ayalon, M ; Koichu, B ; Leikin, R ; Rubel, L ; Tabach, M (Ed.)
    This study presents how the commognitive-based Opportunities for Reasoning and Proving (ORP) Framework, developed for research purposes to analyze mathematical tasks, was applied as a learning tool for teachers. Seven novice secondary teachers, who participated in a professional learning community around integrating reasoning and proving, were introduced to the ORP Framework and engaged in a sorting tasks activity. We show how the ORP Framework helped teachers to focus on the ORP embedded in tasks, to attend to student mathematical work, and to communicate about ORP coherently and unambiguously. We discuss the affordances of using a framework, which relies on the operationalized discursive language of commognition, to promote teachers’ communication around reasoning and proving. 
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    Accepted Manuscript Full Text Available
  2. ; ( , Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education)
    Ayalon, M ; Koichu, B ; Leikin, R ; Rubel, L ; Tabach, M (Ed.)
    We follow a beginning mathematics teacher, Olive, from the university-based course Mathematical Reasoning and Proving for Secondary Teachers through the supervised internship where Olive taught in her cooperating teacher’s classroom. By drawing upon Activity Theory, we compare her teaching within the two teaching settings, and we examine the opportunities for reasoning and proving she provided to her students in each teaching setting. As a prospective teacher, Olive provided her students opportunities for reasoning and proving. During the internship, these opportunities initially diminished due to institutional and contextual constraints. However, Olive gradually carved out unique paths to engage students with reasoning and proving as her teaching independence increased. 
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  3. ; ; ; ( , Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education)
    Ayalon, M. ; Koichu, B. ; Leikin, R. ; Rubel, L. ; Tabach, M. (Ed.)
    The topic of study in this report is student focusing and noticing. Specifically, we examined a teacher’s goals for student focusing and noticing and the student outcomes for focusing and noticing. The mathematics context for this research was quadratic functions and covariational reasoning. Two whole-class discussion episodes were analyzed. Results showed ways that the teacher’s goals and student outcomes were aligned and three ways that they were misaligned. These results could inform how quadratic functions are taught and how teachers can improve the alignment between their goals for student focusing and noticing and student outcomes for focusing and noticing. 
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    Accepted Manuscript Full Text Available
  4. ; ; ( , Note technique Centre scientifique et technique de lindustrie textile belge)
    Ayalon, M ; Koichu, B ; Leikin, R ; Rubel, L ; Tabach, M (Ed.)
    Building on student work (SW) in mathematics classroom discussion requires complex decision-making from mathematics teachers. Previous literature on problem-based lessons recommends selecting and sequencing pieces of SW in a way that creates a mathematical storyline, but there is rarely any empirical evidence on how mathematics teachers can master such practices. We use the case of StoryCircles, a lesson-based professional development program, to show how iterative processes in which teachers were engaging with SW assisted them in developing heuristics for a careful selection and sequencing of SW. The results show that these processes involved 1) the teachers’ emerging awareness of features of SW; and 2) an evolving capacity to relate these features to the lesson goal. We discuss design features that fostered these changes. 
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    Accepted Manuscript Full Text Available
  5. ; ( , International Group for the Psychology of Mathematics Education)
    Ayalon, M ; Koichu, B ; Leikin, R ; Rubel, L ; Tabach, M (Ed.)
    We used videotaped enactments of high cognitive demand tasks to investigate whether teachers who were engaged in the teaching practice of building—and thus were focused on having the class collaboratively make sense of their peers’ high-leverage mathematical contributions—provided scaffolding that supported the maintenance of high cognitive demand tasks. Attempting to build on high-leverage student thinking seemed to mitigate the teachers’ tendencies to provide inappropriate amounts of scaffolding because they: (1) believed the building practice required them to refrain from showing the students how to solve the task; (2) wanted to elicit student reasoning about their peer’s contribution for the building practice to utilize; and (3) saw the benefits of their students being able to engage in the mathematical thinking themselves. 
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    Accepted Manuscript Full Text Available