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There were statistically significant differences in teachers' perceptions of less successful PD between teachers with different lengths of teaching experience and genders. The authors" careful operationalization of the two mismatches reveals how and why teachers selectively implemented aspects of the program that they felt comfortable with (category 1 - I will to change i ), and that a likely reason for this were the challenges in the I ambitious instruction i that IBL presents and how teachers' I sense-making i of ambitious instruction differed from the PD designers' intention (categories 2 and 5). Keywords: What went wrong; Professional development for mathematics teachers; Less successful PD programs; Challenges of PD innovations; Researchers' reflection EN What went wrong Professional development for mathematics teachers Less successful PD programs Challenges of PD innovations Researchers' reflection 573 580 8 09/01/23 20231001 NES 231001 Researching less successful PD programs: a missing link in the literature A famous quote, attributed to John Dewey at around 1933, maintains that "failure is not mere failure. [Extracted from the article]

Facilitators of professional development (PD) for mathematics teachers currently gain increasing attention, as their practices are crucial for the success of spreading mathematics educational ideas and innovations into schools and strengthening the professional expertise of teachers. So far, mainly two components of facilitation have been empirically researched: facilitators' knowledge resources and facilitation moves. In this paper, we propose to develop a more comprehensive conceptual framework in order to explain facilitators' practices and underlying decisions. For this purpose, we lift Schoenfeld's ROG framework for teachers' decision-making (comprising resources, orientations, and goals) to the facilitator level, and add identity as a fourth component to obtain what we call the ROGI framework. We draw on data collected simultaneously in two PD projects for mathematics teachers in Germany and in Israel. Through three cases of facilitation, we illustrate how the adapted ROGI framework helps to understand processes of decision-making made by facilitators during mathematics professional development sessions. [ABSTRACT FROM AUTHOR]

Professional development (PD) courses are the main context for mathematics teachers' lifelong learning. Leaders with expertise are needed to facilitate these courses; thus, there is a growing interest in understanding the nature of this profession, its core practices, and the challenges it entails. This paper focuses on a specific group of facilitators: experienced mathematics teachers who have just begun facilitating PD courses in addition to their classroom teaching. To better understand these novice facilitators' practices, a commognitive approach was implemented to examine how they draw on their mathematics teaching experience when leading PD courses. In commognitive terms, these practitioners draw on multiple professional discourses, but mostly on the discourses of teaching and facilitation. The analysis of the challenges and affordances associated with participating in these two professional discourses showed that novice facilitators bring into play their teaching practices in four distinct ways: enacting a familiar practice, negating a familiar practice, questioning the relevance of a familiar practice, and generating a new practice based on their teaching experience. We claim that novice facilitators' well-established identity as teachers is both a challenge and an asset in grounding successful facilitation practices. Overall, facilitators modify their teaching experience through the adoption, adaptation, and retraction of their teaching practices. Implications for the preparation and support of facilitators, within processes of upscaling PD programs, are discussed. [ABSTRACT FROM AUTHOR]

In this paper I explore the question of what counts as successful implementation of a mathematics professional development (PD) project at scale. Two kinds of upscale are presented and differentiated from one another: upscale of settings and upscale of values, and the link between this differentiation and how success may be defined is discussed. As part of the discussion, three models of taking a PD project to scale are described, namely replication, adaptation and reproduction, and these are tied to the degree of professional autonomy of teachers within the PD. The examination of these ideas draws on data from two PD projects for secondary mathematics teachers in Israel, that are now years after their pilot phase and still being implemented. The first project is aimed at supporting mathematics teachers in teaching mathematically at-risk students and in helping these students to succeed in high-stakes exams. The second project is aimed at enhancing mathematics teachers' reflection on their teaching practices, using classroom video as a tool. Both projects were implemented at scale across Israel, and reviewing results from these implementations enables some general insights to be gained regarding the success of scaled-up PD projects. The crucial role of PD facilitators in successful implementations is highlighted. [ABSTRACT FROM AUTHOR]

This paper reports on a study conducted within VIDEO-LM (Viewing, Investigating and Discussing Environments of Learning Mathematics), a video-based professional development project for secondary mathematics teachers that aims to enhance reflection on practice. The study explored VIDEO-LM sessions where Israeli teachers watched an 8th grade geometry lesson from Japan. We analyzed teachers' discussions around this lesson and characterized main themes and reflection types. Findings suggest that watching the Japanese lesson, using the VIDEO-LM framework, led to productive discussions among teachers. The fact that the videotaped lesson was culturally "far" from the teachers' reality provoked them to re-see everyday aspects of their practice, revealing some dissonances which promoted reflective thoughts and actions. [ABSTRACT FROM AUTHOR]

Is it possible that a meeting of mathematicians and primary school teachers will be productive? This question became intriguing when one professor of mathematics initiated a professional development course for practicing primary school teachers, which he taught alongside a group of mathematics Ph.D. students. This report scrutinizes the uncommon meeting of these two communities, who have very different perspectives on mathematics and its teaching. The instructors had no experience in primary school teaching, and their professed goal was to deepen the teachers’ understanding of the mathematics they teach, while teachers were expecting the course to be pedagogically relevant for their teaching. Surprisingly, despite this mismatch in expectations, the course was considered a success by teachers and instructors alike. In our study, we analyzed a lesson on division with remainder for teachers of grades 3-6, taught by the professor. The framework used for the data analysis was mathematical discourse for teaching, a discursive adaptation of the well-known mathematical knowledge for teaching framework. Our analysis focuses on the nature of the interactions between the parties and the learning opportunities they afforded. We show how different concerns, which might have hindered communication, in fact fueled discussions, leading to understandings of the topic and its teaching that were new to all the parties involved. The findings point to a feasible model for professional development where mathematicians may contribute to the education of practicing teachers, while they are gaining new insights themselves. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the authors discuss various reports within the issue including video as a catalyst for mathematics teachers' professional development, the selection of classroom video and the ways to create and use videos for teacher learning.

The VIDEO-LM project (Viewing, Investigating and Discussing Environments of Learning Mathematics) is aimed at enhancing mathematics teachers' reflection on their professional practice, through watching and discussing videotaped lessons of unknown teachers. The discussions are guided by the use of an analytic framework, comprised of six detailed 'viewing lenses.' In this article, we first provide a brief historical context of practicing teacher education, followed by the description of the framework we developed. We then present selected data from 17 implementation sites that illustrate the impact of VIDEO-LM courses on the professional growth of participants. Findings show that using the six-lens framework in video-based peer conversations supports the development of a reflective language, with which mathematics teachers engage in deep discussions about core issues of their profession. [ABSTRACT FROM AUTHOR]

The collective case study described herein explores solution approaches to a task requiring visual reasoning by students and teachers unfamiliar with such tasks. The context of this study is the teaching and learning of calculus in the Palestinian educational system. In the Palestinian mathematics curriculum the roles of visual displays rarely go beyond the illustrative and supplementary, while tasks which demand visual reasoning are absent. In the study, ten teachers and twelve secondary and first year university students were presented with a calculus problem, selected in an attempt to explore visual reasoning on the notions of function and its derivative and how it interrelates with conceptual reasoning. A construct named 'visual inferential conceptual reasoning' was developed and implemented in order to analyze the responses. In addition, subjects' reflections on the task, as well as their attitudes about possible uses of visual reasoning tasks in general, were collected and analyzed. Most participants faced initial difficulties of different kinds while solving the problem; however, in their solution processes various approaches were developed. Reflecting on these processes, subjects tended to agree that such tasks can promote and enhance conceptual understanding, and thus their incorporation in the curriculum would be beneficial. [ABSTRACT FROM AUTHOR]

This article discusses the possibility of using nonprofessional tutoring as means for advancing low achievers in secondary school mathematics. In comparison with professional, paraprofessional, and peer tutoring, nonprofessional tutoring may seem less beneficial and, at first glance, inadequate. The described case study shows that nonprofessional tutors may contribute to students' understanding and achievements, and thus, they can serve as an important assisting resource for mathematics teachers, especially in disadvantaged communities. In the study, young adults volunteered to tutor low-achieving students in an urban secondary school. Results showed a considerable mean gain in students' grades. It is suggested that affective factors, as well as the instruction given to tutors by a specialized counselor, have played a major role in maintaining successful tutoring. [ABSTRACT FROM AUTHOR]

Investigates adults' long-term memory of mathematics learned in high school. Theories of recall; Long-term maintenance of knowledge learned in school; Graphical descriptions of simple linear functions.