International Group for the Psychology of Mathematics Education, 2018
In this paper, we explore the ways in which learning more about research on students' experiences... more In this paper, we explore the ways in which learning more about research on students' experiences in mathematics classrooms has the potential to transform the work we do with teachers in teacher preparation, professional development, and research settings. We focus in particular on questions of student access to and participation in mathematics and highlight studies of the racialized and gendered experiences of students and the connections between these experiences and broader narratives about race, gender, and ability/disability. We conclude with questions and possibilities raised by these studies for our individual and collective efforts to support and understand teacher learning and changes in teacher practice.
Contents: Preface. Part I: Introduction. T.A. Romberg, T.P. Carpenter, J. Kwako, Standards-Based ... more Contents: Preface. Part I: Introduction. T.A. Romberg, T.P. Carpenter, J. Kwako, Standards-Based Reform and Teaching for Understanding. Part II: Learning With Understanding. R. Lehrer, L. Schauble, Developing Modeling and Argument in the Elementary Grades. A.S. Rosebery, B. Warren, C. Ballenger, A. Ogonowski, The Generative Potential of Students' Everyday Knowledge in Learning Science. T.P. Carpenter, L. Levi, P.W. Berman, M. Pligge, Developing Algebraic Reasoning in the Elementary School. J.J. Kaput, M.L. Blanton, A Teacher-Centered Approach to Algebrafying Elementary Mathematics. K. McCain, P. Cobb, K. Gravemeijer, Statistical Data Analysis: A Tool for Learning. J. Stewart, C. Passmore, J. Cartier, J. Rudolph, S. Donovan, Modeling for Understanding in Science Education. R. Nemirovsky, A. Barros, T. Noble, M. Schnepp, J. Solomon, Learning Mathematics in High School: Symbolic Places and Family Resemblances. Part III: Teaching for Understanding M. Franke, E. Kazemi, J. Shih, S. B...
International Group for the Psychology of Mathematics Education, 2018
In this paper, we explore the ways in which learning more about research on students' experiences... more In this paper, we explore the ways in which learning more about research on students' experiences in mathematics classrooms has the potential to transform the work we do with teachers in teacher preparation, professional development, and research settings. We focus in particular on questions of student access to and participation in mathematics and highlight studies of the racialized and gendered experiences of students and the connections between these experiences and broader narratives about race, gender, and ability/disability. We conclude with questions and possibilities raised by these studies for our individual and collective efforts to support and understand teacher learning and changes in teacher practice.
Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 2020
Language is a vital component in mathematics classrooms and researchers have thoroughly examined ... more Language is a vital component in mathematics classrooms and researchers have thoroughly examined how language functions in instruction. However, less is known about how teachers think about language enacted in their own classrooms. In this report, we describe how a teacher, Olivia, explicitly attended to language, particularly with emergent bilinguals. We describe affordances and tensions as she thought through language in the context of a professional development and in video- stimulated recall interviews.
Recent innovations in professional development are rife with a wide array of efforts focused on t... more Recent innovations in professional development are rife with a wide array of efforts focused on teacher collaboration. In this essay, we address some of the unexamined assumptions about the nature and significance of interactions in teacher professional collaboration, drawing on the concept of the “fourth wall” from theater and film studies. The fourth wall is a term used to describe the invisible wall that separates actors from their audience. We use this metaphor to interrogate the function of the fourth wall in professional learning and argue that it reflects a culture of professional learning that, despite innovations that tout teacher collaboration, upholds isolation in teaching and teacher learning and deep embedded norms of noninterference in one another’s practice. We also attend to the possibilities for supporting teacher learning that breaching the fourth wall affords when shared enactments of practice are used as a context for teachers’ sensemaking and collaboration.
Supporting teacher learning for normative change in classroom learning environments creates signi... more Supporting teacher learning for normative change in classroom learning environments creates significant demands on principal leadership. We offer an analytic framework that aims to understand principal practice for instructional transformation. The framework examines how the principal’s conception of teacher learning shapes practice in relation to particular contexts and support systems. We illustrate the explanatory power of this framework by using it to make sense of one elementary principal’s practice in leading her school for instructional transformation in mathematics. Our analysis contributes to how leadership efforts to transform instruction might be studied and ultimately supported.
Despite the complexity of facilitating professional development (PD) and growing attention to sup... more Despite the complexity of facilitating professional development (PD) and growing attention to supporting facilitators, few tools exist for facilitators to engage in ongoing inquiry into their practice. In this article, we offer a practical measure, the Collaborative Professional Development Survey (CPDS), designed to provide facilitators with information about teachers’ perceptions of aspects of the PD learning environment that research indicates matter for teachers’ opportunities to learn. We illustrate how facilitators used the CPDS to support their collective inquiry into facilitation. We also illustrate the social processes that appeared to enable facilitators’ productive use of the CPDS, including a routine to analyze the resulting data, and the orientations that underpinned their analysis. We discuss implications for facilitators’ use of the CPDS.
Filling the knowledge gap in the limited research on professional development leaders is an urgen... more Filling the knowledge gap in the limited research on professional development leaders is an urgent issue if teacher learning is to be improved. This research and development project is studying how leaders learn to cultivate mathematically rich professional development environments. The authors adapted two frameworks from classroom-based research—sociomathematical norms and practices for orchestrating productive discussion—to support leaders’ understanding of facilitation of mathematics professional development. In this article, the authors describe the use of these frameworks in their work and argue for a third framework—the mathematical knowledge for teaching. Based on the analysis of their work, they believe that mathematics professional development leaders need to cultivate particular sociomathematical norms for teacher explanation and employ practices for orchestrating discussions to achieve the purposeful development of teachers’ specialized knowledge of mathematics for teaching.
Currently, the field of teacher education is undergoing a major shift—a turn away from a predomin... more Currently, the field of teacher education is undergoing a major shift—a turn away from a predominant focus on specifying the necessary knowledge for teaching toward specifying teaching practices that entail knowledge and doing. In this article, the authors suggest that current work on K-12 core teaching practices has the potential to shift teacher education toward the practice of teaching. However, the authors argue that to realize this vision we must reimagine not only the curriculum for learning to teach but also the pedagogy of teacher education. We present one example of what we mean by reimagined teacher education pedagogy by offering a framework through which to conceptualize the preparation of teachers organized around core practices. From our perspectives, this framework could be the backbone of a larger research and development agenda aimed at engaging teachers and teacher educators in systematic knowledge generation regarding ambitious teaching and teacher education pedago...
We analyze a particular pedagogy for learning to interact productively with students and subject ... more We analyze a particular pedagogy for learning to interact productively with students and subject matter, which we call “rehearsal.” Our goal is to specify a way in which teacher educators (TEs) and novice teachers (NTs) can interact around teaching that is both embedded in practice and amenable to analysis. We address two main research questions: (a) What do TEs and NTs do together during the kind of rehearsals we have developed to prepare novices for the complex, interactive work of teaching? and (b) Where, in what they do, are there opportunities for NTs to learn to enact the principles, practices, and knowledge entailed in ambitious teaching? We detail what happens in rehearsals using quantitative and qualitative methods. We begin with the results of our quantitative analyses to characterize how typical rehearsals were structured and what was worked on. We then show how NTs and TEs worked together to enable novices to study principled practice through qualitative analyses of a pa...
The study describes teachers' collective work in which they developed deeper understanding of the... more The study describes teachers' collective work in which they developed deeper understanding of their own students' mathematical thinking. Teachers at one school met in monthly workgroups throughout the year. Prior to each workgroup, they posed a similar mathematical problem to their students. The workgroup discussions centered on the student work those problems generated. This study draws on a transformation of participation perspective to address the questions: What do teachers learn through collective examination of student work? How is teacher learning evident in shifts in participation in discussions centered on student work? The analyses account for the learning of the group by documenting key shifts in teachers' participation across the year. The first shift in participation occurred when teachers as a group learned to attend to the details of children's thinking. A second shift in participation occurred as teachers began to develop possible instructional trajectories in mathematics. We focus our discussion on the significance of the use of student work and a transformation of participation view in analyzing the learning trajectory of teachers as a group.
ABSTRACT We share insights from our work in a project investigating what leaders learn about cult... more ABSTRACT We share insights from our work in a project investigating what leaders learn about cultivating mathematically rich professional development environments for teachers. We discuss what leaders need to do when facilitating mathematical tasks with teachers if the goal is to develop teachers' specialized content knowledge (SCK) for teaching (Ball, Thames, & Phelps, 2008). SCK is the mathematical understandings and reasoning unique to teaching. With such a goal in mind, we argue for the importance of articulating the differences between doing mathematics in professional development and in the K-12 classroom. Developing teachers' SCK for teaching requires that leaders design and use tasks in ways that orient teachers to SCK, foster particular sociomathematical norms for explanation and representational use, and orchestrate discussions to make specialized knowledge explicit.
In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual ... more In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia (Vol. 1). Palmerston North, NZ: MERGA. ... Developing Pedagogies in Teacher Education to Support Novice
It is commonly argued that teachers need ongoing engagement with ideas about using student reason... more It is commonly argued that teachers need ongoing engagement with ideas about using student reasoning, pedagogy, and subject matter if they are to make sense of the complex demands of current reforms in mathematics education. Drawing on similar arguments about the potential benefits of using student work to organize professional development, this study charts the development of one teacher workgroup over a year. The analysis addresses two questions: (1) How did teachers' talk about student work develop? and (2) What kinds of mathematical and pedagogical issues were raised as a result of their ongoing and changing talk? The study locates teacher learning in their interactions with one another in the workgroup. In monthly cross-grade meetings, teachers brought and discussed student work that was generated by a similar mathematical problem posed to students in each of their classrooms. The paper documents the teachers' efforts to detail their students' reasoning and discuss how their engagement with mathematical and pedagogical concerns created opportunities for teacher learning.
This paper presents case studies of four students' experiences with writing in a fourth/fift... more This paper presents case studies of four students' experiences with writing in a fourth/fifth grade classroom. The paper focuses on the following questions: What is the relationship between children's social and intellectual identities and their successes or struggles in writing? How do ...
This paper presents a critical discourse analysis of a classroom event in which fourth and fifth ... more This paper presents a critical discourse analysis of a classroom event in which fourth and fifth grade students in a highly diverse urban school interpreted, discussed and responded to a district survey intended to illuminate the social climate of the city's schools, with a particular focus ...
The children in Ruth's fourth/fifth-grade classroom had been engaged for weeks in a literacy... more The children in Ruth's fourth/fifth-grade classroom had been engaged for weeks in a literacy project in which they researched and shared an aspect of their cultural background. The chil-dren interviewed their parents, ... The Aftermath of You're Only Half:
Instructional Explanations in the Disciplines, 2009
It has become commonplace among educational reformers to assert that all students should learn an... more It has become commonplace among educational reformers to assert that all students should learn and that learning should involve complex ideas and performances. In mathematics, the universal goal of education has been characterized as mathemat-ical proficiency in ...
International Group for the Psychology of Mathematics Education, 2018
In this paper, we explore the ways in which learning more about research on students' experiences... more In this paper, we explore the ways in which learning more about research on students' experiences in mathematics classrooms has the potential to transform the work we do with teachers in teacher preparation, professional development, and research settings. We focus in particular on questions of student access to and participation in mathematics and highlight studies of the racialized and gendered experiences of students and the connections between these experiences and broader narratives about race, gender, and ability/disability. We conclude with questions and possibilities raised by these studies for our individual and collective efforts to support and understand teacher learning and changes in teacher practice.
Contents: Preface. Part I: Introduction. T.A. Romberg, T.P. Carpenter, J. Kwako, Standards-Based ... more Contents: Preface. Part I: Introduction. T.A. Romberg, T.P. Carpenter, J. Kwako, Standards-Based Reform and Teaching for Understanding. Part II: Learning With Understanding. R. Lehrer, L. Schauble, Developing Modeling and Argument in the Elementary Grades. A.S. Rosebery, B. Warren, C. Ballenger, A. Ogonowski, The Generative Potential of Students' Everyday Knowledge in Learning Science. T.P. Carpenter, L. Levi, P.W. Berman, M. Pligge, Developing Algebraic Reasoning in the Elementary School. J.J. Kaput, M.L. Blanton, A Teacher-Centered Approach to Algebrafying Elementary Mathematics. K. McCain, P. Cobb, K. Gravemeijer, Statistical Data Analysis: A Tool for Learning. J. Stewart, C. Passmore, J. Cartier, J. Rudolph, S. Donovan, Modeling for Understanding in Science Education. R. Nemirovsky, A. Barros, T. Noble, M. Schnepp, J. Solomon, Learning Mathematics in High School: Symbolic Places and Family Resemblances. Part III: Teaching for Understanding M. Franke, E. Kazemi, J. Shih, S. B...
International Group for the Psychology of Mathematics Education, 2018
In this paper, we explore the ways in which learning more about research on students' experiences... more In this paper, we explore the ways in which learning more about research on students' experiences in mathematics classrooms has the potential to transform the work we do with teachers in teacher preparation, professional development, and research settings. We focus in particular on questions of student access to and participation in mathematics and highlight studies of the racialized and gendered experiences of students and the connections between these experiences and broader narratives about race, gender, and ability/disability. We conclude with questions and possibilities raised by these studies for our individual and collective efforts to support and understand teacher learning and changes in teacher practice.
Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 2020
Language is a vital component in mathematics classrooms and researchers have thoroughly examined ... more Language is a vital component in mathematics classrooms and researchers have thoroughly examined how language functions in instruction. However, less is known about how teachers think about language enacted in their own classrooms. In this report, we describe how a teacher, Olivia, explicitly attended to language, particularly with emergent bilinguals. We describe affordances and tensions as she thought through language in the context of a professional development and in video- stimulated recall interviews.
Recent innovations in professional development are rife with a wide array of efforts focused on t... more Recent innovations in professional development are rife with a wide array of efforts focused on teacher collaboration. In this essay, we address some of the unexamined assumptions about the nature and significance of interactions in teacher professional collaboration, drawing on the concept of the “fourth wall” from theater and film studies. The fourth wall is a term used to describe the invisible wall that separates actors from their audience. We use this metaphor to interrogate the function of the fourth wall in professional learning and argue that it reflects a culture of professional learning that, despite innovations that tout teacher collaboration, upholds isolation in teaching and teacher learning and deep embedded norms of noninterference in one another’s practice. We also attend to the possibilities for supporting teacher learning that breaching the fourth wall affords when shared enactments of practice are used as a context for teachers’ sensemaking and collaboration.
Supporting teacher learning for normative change in classroom learning environments creates signi... more Supporting teacher learning for normative change in classroom learning environments creates significant demands on principal leadership. We offer an analytic framework that aims to understand principal practice for instructional transformation. The framework examines how the principal’s conception of teacher learning shapes practice in relation to particular contexts and support systems. We illustrate the explanatory power of this framework by using it to make sense of one elementary principal’s practice in leading her school for instructional transformation in mathematics. Our analysis contributes to how leadership efforts to transform instruction might be studied and ultimately supported.
Despite the complexity of facilitating professional development (PD) and growing attention to sup... more Despite the complexity of facilitating professional development (PD) and growing attention to supporting facilitators, few tools exist for facilitators to engage in ongoing inquiry into their practice. In this article, we offer a practical measure, the Collaborative Professional Development Survey (CPDS), designed to provide facilitators with information about teachers’ perceptions of aspects of the PD learning environment that research indicates matter for teachers’ opportunities to learn. We illustrate how facilitators used the CPDS to support their collective inquiry into facilitation. We also illustrate the social processes that appeared to enable facilitators’ productive use of the CPDS, including a routine to analyze the resulting data, and the orientations that underpinned their analysis. We discuss implications for facilitators’ use of the CPDS.
Filling the knowledge gap in the limited research on professional development leaders is an urgen... more Filling the knowledge gap in the limited research on professional development leaders is an urgent issue if teacher learning is to be improved. This research and development project is studying how leaders learn to cultivate mathematically rich professional development environments. The authors adapted two frameworks from classroom-based research—sociomathematical norms and practices for orchestrating productive discussion—to support leaders’ understanding of facilitation of mathematics professional development. In this article, the authors describe the use of these frameworks in their work and argue for a third framework—the mathematical knowledge for teaching. Based on the analysis of their work, they believe that mathematics professional development leaders need to cultivate particular sociomathematical norms for teacher explanation and employ practices for orchestrating discussions to achieve the purposeful development of teachers’ specialized knowledge of mathematics for teaching.
Currently, the field of teacher education is undergoing a major shift—a turn away from a predomin... more Currently, the field of teacher education is undergoing a major shift—a turn away from a predominant focus on specifying the necessary knowledge for teaching toward specifying teaching practices that entail knowledge and doing. In this article, the authors suggest that current work on K-12 core teaching practices has the potential to shift teacher education toward the practice of teaching. However, the authors argue that to realize this vision we must reimagine not only the curriculum for learning to teach but also the pedagogy of teacher education. We present one example of what we mean by reimagined teacher education pedagogy by offering a framework through which to conceptualize the preparation of teachers organized around core practices. From our perspectives, this framework could be the backbone of a larger research and development agenda aimed at engaging teachers and teacher educators in systematic knowledge generation regarding ambitious teaching and teacher education pedago...
We analyze a particular pedagogy for learning to interact productively with students and subject ... more We analyze a particular pedagogy for learning to interact productively with students and subject matter, which we call “rehearsal.” Our goal is to specify a way in which teacher educators (TEs) and novice teachers (NTs) can interact around teaching that is both embedded in practice and amenable to analysis. We address two main research questions: (a) What do TEs and NTs do together during the kind of rehearsals we have developed to prepare novices for the complex, interactive work of teaching? and (b) Where, in what they do, are there opportunities for NTs to learn to enact the principles, practices, and knowledge entailed in ambitious teaching? We detail what happens in rehearsals using quantitative and qualitative methods. We begin with the results of our quantitative analyses to characterize how typical rehearsals were structured and what was worked on. We then show how NTs and TEs worked together to enable novices to study principled practice through qualitative analyses of a pa...
The study describes teachers' collective work in which they developed deeper understanding of the... more The study describes teachers' collective work in which they developed deeper understanding of their own students' mathematical thinking. Teachers at one school met in monthly workgroups throughout the year. Prior to each workgroup, they posed a similar mathematical problem to their students. The workgroup discussions centered on the student work those problems generated. This study draws on a transformation of participation perspective to address the questions: What do teachers learn through collective examination of student work? How is teacher learning evident in shifts in participation in discussions centered on student work? The analyses account for the learning of the group by documenting key shifts in teachers' participation across the year. The first shift in participation occurred when teachers as a group learned to attend to the details of children's thinking. A second shift in participation occurred as teachers began to develop possible instructional trajectories in mathematics. We focus our discussion on the significance of the use of student work and a transformation of participation view in analyzing the learning trajectory of teachers as a group.
ABSTRACT We share insights from our work in a project investigating what leaders learn about cult... more ABSTRACT We share insights from our work in a project investigating what leaders learn about cultivating mathematically rich professional development environments for teachers. We discuss what leaders need to do when facilitating mathematical tasks with teachers if the goal is to develop teachers' specialized content knowledge (SCK) for teaching (Ball, Thames, & Phelps, 2008). SCK is the mathematical understandings and reasoning unique to teaching. With such a goal in mind, we argue for the importance of articulating the differences between doing mathematics in professional development and in the K-12 classroom. Developing teachers' SCK for teaching requires that leaders design and use tasks in ways that orient teachers to SCK, foster particular sociomathematical norms for explanation and representational use, and orchestrate discussions to make specialized knowledge explicit.
In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual ... more In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia (Vol. 1). Palmerston North, NZ: MERGA. ... Developing Pedagogies in Teacher Education to Support Novice
It is commonly argued that teachers need ongoing engagement with ideas about using student reason... more It is commonly argued that teachers need ongoing engagement with ideas about using student reasoning, pedagogy, and subject matter if they are to make sense of the complex demands of current reforms in mathematics education. Drawing on similar arguments about the potential benefits of using student work to organize professional development, this study charts the development of one teacher workgroup over a year. The analysis addresses two questions: (1) How did teachers' talk about student work develop? and (2) What kinds of mathematical and pedagogical issues were raised as a result of their ongoing and changing talk? The study locates teacher learning in their interactions with one another in the workgroup. In monthly cross-grade meetings, teachers brought and discussed student work that was generated by a similar mathematical problem posed to students in each of their classrooms. The paper documents the teachers' efforts to detail their students' reasoning and discuss how their engagement with mathematical and pedagogical concerns created opportunities for teacher learning.
This paper presents case studies of four students' experiences with writing in a fourth/fift... more This paper presents case studies of four students' experiences with writing in a fourth/fifth grade classroom. The paper focuses on the following questions: What is the relationship between children's social and intellectual identities and their successes or struggles in writing? How do ...
This paper presents a critical discourse analysis of a classroom event in which fourth and fifth ... more This paper presents a critical discourse analysis of a classroom event in which fourth and fifth grade students in a highly diverse urban school interpreted, discussed and responded to a district survey intended to illuminate the social climate of the city's schools, with a particular focus ...
The children in Ruth's fourth/fifth-grade classroom had been engaged for weeks in a literacy... more The children in Ruth's fourth/fifth-grade classroom had been engaged for weeks in a literacy project in which they researched and shared an aspect of their cultural background. The chil-dren interviewed their parents, ... The Aftermath of You're Only Half:
Instructional Explanations in the Disciplines, 2009
It has become commonplace among educational reformers to assert that all students should learn an... more It has become commonplace among educational reformers to assert that all students should learn and that learning should involve complex ideas and performances. In mathematics, the universal goal of education has been characterized as mathemat-ical proficiency in ...
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