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2008 Conferences

American Educational Research Association (AERA)
March 24-28, 2008; New York, NY

CPTM-related activities and presentations: In case of mixed groups of presenters, the CPTM-associated presenter is highlighted.

The following presentation is part of the session SIG Research in Mathematics Education: SIG Poster Session.

Ginger Rhodes, Patricia S. Wilson, The University of Georgia
Preparing Mathematics Educators for Field-Based Education and Research
There is little known about the preparation and development of mathematics teacher educators. The study reported here investigated the learning experiences of doctoral students who were working with in-service and pre-service mathematics teachers during field experiences in secondary schools and simultaneously conducting research. We expanded a conceptual framework used to study the development of teachers to examine the complex relationships and multiple roles of doctoral students that accompanied working and learning in schools. Through this study, we gained an understanding of how the graduate students defined and conceived of professional development for secondary mathematics teachers, what they highlighted as beneficial or detrimental in working with secondary mathematics teachers in situations involving professional development, and how their professional identities evolved.

The following presentation is part of the session Assessing Teaching Practice.

Timothy A. Boerst, South Redford School District; Brent M. Duckor, Mark R. Wilson, University of California–Berkeley; Pamela A. Moss, Deborah Loewenberg Ball, University of Michigan; University of California-Berkeley
Developing an Integrated Assessment System (DIAS) in Elementary Mathematics Teacher Education: Constructing and Interpreting Records of Practice Session
This interactive symposium brings together scholars from four distinct, multi-disciplinary, programs of research in the development, implementation, and evaluation of assessments of teaching practice: two programs working inside teacher education and two working on assessment of practice at the in-service level.. Our goal is to illuminate challenges involved in assessing teaching practice and to share and critique approaches for addressing them. Each program incorporates assessment practices that are intended to support professional or organizational learning as well individual or program level evaluation/accountability. The interpretive foci vary from more general assessments of teaching practice to assessments focused in depth on particular instructional domains (e.g., leading a discussion) within subject area. Each draws on and integrates multiple kinds of data including various combinations of teacher and student artifacts, video- or audio-records, interviews with teachers and students, teachers' commentary and written reflections, surveys and questionnaires, assessments of students’ learning. Each considers the additional evidence, analyses, and social practices needed to address its purposes (including the validity with which those purposes are served).

The following presentation is part of the session Mathematics Teaching and Learning: Promising Practices, Promising Partnerships, Promising Results.

Jennifer M. Lewis, Mark Hoover Thames, Hyman Bass, Deborah Loewenberg Ball, University of Michigan
Identifying MKT: Mathematics Teaching and Learning to Teach Project
What teachers have to know and be able to do to carry out the work of teaching effectively is a significant question that could be investigated in a variety of ways. Our research group chose a to work “bottom up,” beginning with practice. This approach can be seen as a kind of “job analysis,” similar to analyses done of other mathematically intensive occupations, from nursing to engineering and physics (Hoyles, Noss, & Pozzi, 2001; Noss, Healy, & Hoyles, 1997), to carpentry and waiting tables. An eclectic group of researchers representing the fields of linguistics, mathematics, social psychology, philosophy, anthropology and others brought their disciplinary tools to study records of teaching practice. We focused on how teachers need to know that content as well as what else teachers need to know of and about mathematics and how and where might they might use such mathematical knowledge in contending with the regular day-to-day, moment-to-moment demands of teaching. These analyses helped to support the development of a practice-based theory of mathematical knowledge for teaching (Ball & Bass, 2003). The questions that guided our qualitative analyses research were: 1) What are the recurrent tasks and problems of teaching mathematics? What do teachers do as they teach mathematics? 2) What mathematical knowledge, skills, and sensibilities are required to manage these tasks? Central to the qualitative work has been a large longitudinal NSF-funded database, documenting an entire year of the mathematics teaching in a third grade public school classroom during 1989-90 . The records collected across that year include videotapes and audiotapes of the classroom lessons, transcripts, copies of students’ written class work, homework, and quizzes, as well as the teacher’s plans, notes, and reflections. In addition to this extensive set of records, we work also with other collections we have assembled over the last decade. These studies yielded important findings for teacher knowledge in the realms of teacher language, mathematical practices, and children’s participation structures that all contributed to children’s mathematical knowledge. This presentation will discuss what is meant by “practice-based research” and the development of a map of the tasks of teaching work, with particular attention to mathematics.

The following presentations are part of the session Mathematical Knowledge for Teaching: Explicating and Examining a Program of Research

Imani Masters Goffney, Deborah Loewenberg Ball, University of Michigan;
Attending to Mathematics and to Equity: Impact on Mathematical Knowledge for Teaching

Deborah Loewenberg Ball, University of Michigan; Heather C. Hill, Harvard University
Introductory Overview: Teachers’ Mathematical Knowledge and its Relationship to Practice

Jennifer M. Lewis, Geoffrey C. Phelps, Mark Hoover Thames, Hyman Bass, Deborah Loewenberg Ball, University of Michigan;
Identifying Mathematical Knowledge for Teaching: Mathematics Teaching and Learning to Teach Project.

Heather C. Hill, Harvard University; Mark Hoover, Laurie Sleep, Merrie L. Blunk, University of Michigan
Measuring MKT: Learning Mathematics for Teaching Project

Laurie Sleep, Kara Suzuka, Deborah Zopf, University of Michigan
Teaching and Learning Mathematical Knowledge for Teaching

Hyman Bass, University of Michigan
Mathematical Commentary: Method, Progress, and Pitfalls

Session Abstract:
Over the past decade, our research group has been studying classroom practice to identify the mathematical work of teaching and to analyze the mathematical demands of instruction. This research has led to the development of a practice-based theory of mathematical knowledge for teaching (MKT) — the mathematical knowledge, skill, and habits of mind that are entailed by the work of teaching. In this symposium, we examine retrospectively the research on MKT across a number of related research efforts, including the theoretical development of the construct itself, how it can be measured, its relationship to the mathematical quality of instruction, and its use in professional education.

The following presentation is part of the session Mathematics Instruction: Contexts for Teaching and Learning Mathematics.

Charalambos Y. Charalambous, University of Michigan
The Role of Mathematical Knowledge for Teaching in Creating High-Quality Learning Environments: An Exploratory Study
Converging evidence suggests that the selection of intellectually demanding mathematical tasks and their enactment in ways that maintain their cognitive challenge substantially impact student learning. This paper builds on two research areas and seeks to understand how teachers’ mathematical knowledge for teaching (MKT) contributes to creating such intellectually demanding environments. The analysis of videotaped lessons from a high- and a low-MKT teacher, coupled with a dissection of interview and curriculum documents, suggests plausible ways in which MKT informs teachers’ decisions and actions during selection, presentation, and enactment of cognitively demanding tasks. These findings imply that attempts to promote high-quality teaching of mathematics for all students should not be divorced from considerations of teachers’ MKT.

The following presentations are part of the session The Role of Rehearsal in Learning to Do Ambitious Practice.

Hala N. Ghousseini, University of Michigan;
Rehearsing Discourse Routines for Learning About and Leading Classroom Mathematics Discussions
In this paper, I examine the structure of deliberate rehearsal of practice in the context of a study that focused on preparing pre-service teachers to lead productive mathematics discussions, assuming that beginners need tools to reduce some uncertainties in practice. I describe an intervention that took place in the context of a mathematics methods course for secondary teachers that involved rehearsing discourse routines in order to lead productive classroom mathematics discussions.

Jennifer M. Lewis, University of Michigan;
Blurring Distinctions Between Rehearsal and Performance, Contingent and Non-Contingent: The Professional Development Model of Japanese Lesson Study
Lesson study is a Japanese form of professional development for teachers in which teachers work collaboratively to develop, teach, analyze, and reteach a single lesson. This model has promise, both because lesson study engages the content that teachers need in the context of the interactive work of teaching, and because its location in practice makes what is learned likely to be used in future practice . In this presentation, I consider the opportunities lesson study creates for teachers to rehearse teaching practice in the presence of critical observers.

Orrin T. Murray, University of Michigan;
Enabling the Use of Rehearsal in Teacher Education With Digital Tools
This paper is principally concerned with the technology structures that enable rehearsal, performance and feedback in a teacher education program focused on helping students learn in, from, and for practice. The basis for this analysis is a multi-year involvement with an effort aimed at reforming teacher education in a research university, and this paper draws primarily from the coursework of an elementary literacy methods course. The elementary literacy course provides a robust context for exploring how technology can both enable and constrain teacher education broadly, and rehearsals, specifically.

The following presentation is part of the session Preservice and Inservice Teacher Knowledge of Mathematics.

Gloriana Gonzalez, Patricio G. Herbst, University of Michigan;
How Teachers of Geometry Use Diagrams as Repository of the Collective Memory of a Class
This paper examines how geometry teachers utilize diagrams for shaping the collective memory of the class in two instructional situations, doing proofs and installing theorems. We analyze the proceeds of study group sessions with experienced geometry teachers who discussed animated stories about teaching geometry. Teachers' evaluative stances reveal that the two instructional situations involve different kinds of expectations about what students should remember. Tactical and strategic moves that concern diagrams are made and that impact public memory. The analysis shows that those things that a teacher expects students to remember become more or less valuable depending on the instructional situation which frames class work.

The following presentation is part of the session Interactions in Mathematics Classrooms.

Gloriana Gonzalez, Patricio G. Herbst, University of Michigan;
Students' Geometry Toolbox: How Do Teachers Manage Students' Prior Knowledge When Teaching With Problems?
In this paper we analyze proceeds of focus groups with geometry teachers where they watched and reacted to videos showcasing episodes of teaching with problems. The analysis reveals that in order to sustain the work of teaching with problems, teachers combine strategic and tactical moves to manage students' prior knowledge. We found that teachers play a major role in shaping what students should remember by organizing timely actions as students work on the problem. Also, teachers assess the products of students' work on a problem according to whatever students should remember later. Thus, the work of shaping the collective memory of the class could support how a teacher makes use of students' prior knowledge in teaching with problems.

The following presentation is part of the session Professional Development and Online Learning Environments

Lawrence M. Clark, University of Maryland-College Park; Orrin T. Murray, (University of Michigan;
Migrating Components of Face-to-Face PD Online: Results of the OPMD Project
With issues of education reform pressing educators to improve student achievement and the role seen for professional development, many organizations are rushing to build and offer online professional development. This rush to build online development opportunities is occurring in a broader professional development space where our understanding of how to implement successful face-to-face development opportunities is nascent. Moreover, few if any studies compare the differences between face-to-face and online learning in any instance. This study focuses on: Challenges and successes related to migrating components of a proven face-to-face professional development model to an online format Evidence of consistent mathematical content knowledge growth, and consistent adoption of standards-based mathematics instructional practices across both formats

Association of Mathematics Teacher Educators (AMTE)
Jan. 24-26, 2008; Tulsa, OK

CPTM-related activities and presentations: In case of mixed groups of presenters, the CPTM-associated presenter is highlighted.

Judith E. Jacobs Lecture

Edward A. Silver, University of Michigan
Mathematics Teacher Education in Dodge City: Desperately Seeking Wyatt Earp and Henri Poincaré
Teacher education has been called "the Dodge City of the education world... unruly and chaotic." In this talk, I will reprise some of the issues and concerns that give rise to this characterization, focusing on the ways in which these appear in mathematics teacher education. I will then sketch some ways that these criticisms might be addressed and the role that AMTE might play in this endeavor.

Session 11
Raven McCrory, Michigan State University; Beth Greene Costner, Winthrop University; LouAnn Lovin, James Madison University; Sybilla Beckmann, University of Georgia; Meg Moss, Pellissippi State Technical Community College
Mathematics Courses for Elementary Teachers: An Overview of Current Research Projects
What are we teaching in undergraduate mathematics courses for elementary and middle school teachers, and what are students learning? How do mathematics departments design and support these courses? Several research projects are investigating these questions at institutions across the country. We present results from projects looking at these questions from various perspectives.

Session 22
Charalambos Charalambous, Edward A. Silver, University of Michigan
Shifting from Proving to Improving: Using Assessment as an Integral Part of Instruction
The NCTM assessment principle recommends that assessment become an integral part of instruction rather than an interruption of it. In this presentation, we will share findings of our work with middle-school teachers that sought to help them reconsider their assessment practices.

Kara Suzuka, Deborah Ball, Laurie Sleep, Jennifer Lewis, Mark Thames, Hyman Bass, University of Michigan
Developing Mathematical Knowledge for Teaching: How Does an “MKT Problem” Compare with a Regular Mathematics Problem?
What kinds of tasks develop mathematical knowledge for teaching? How are these tasks different from “regular” mathematics activities? In this session, participants explore these questions through the analysis of materials that have been designed to develop MKT.

Session 37
Jennifer Lewis, University of Michigan; Tad Watanabe, Kennesaw State University; Kathy Morris, Sonoma State University
Lesson Study: Building Mathematics Knowledge Usable in Teaching
How do preservice teachers learn mathematics usable in instruction? In this interactive session, participants will consider the features of lesson study in a preservice math methods course that make it possible for preservice teachers to learn mathematics usable in instruction.

Session 38
Cynthia Schneider, University of Texas at Austin; W. Virginia Williams, National Council of Teachers of Mathematics; Kyle Schultz, University of Georgia; Winnie Peterson, Kutztown University; William Speer, UNLV Center for Mathematics and Science Education
Developing Future Leaders through NCTM Student Affiliates
The session will investigate the benefits gained by students, universities, and the professional community from the establishment of a Student Affiliate of NCTM. Presenters will share tips for forming a new Student Affiliate and discuss how Student Affiliates build future teacher leaders.

Session 41
Timothy Boerst, University of Michigan & South Redford School District; Laurie Sleep, Deborah Loewenberg Ball, Yaa Cole, University of Michigan
Practice as Evidence of Learning: Using Performance Assessments in a Methods Course
Focusing a methods course on practice creates unique challenges for assessing preservice teacher learning. In this session, participants explore video records and samples of preservice teachers’ practice to analyze performance assessments designed to capture and evaluate the work of teaching.

Session 44
Angel Abney, Georgia College and State University; Ginger Rhodes, Hyung Sook Lee, University of Georgia
Learning Students' Mathematics
Teachers’ understandings of their students’ mathematics influences their instructional practices. We will present three research studies that focus on ways that teachers make sense of students’ mathematics and how that understanding impacts their knowledge development and instructional decisions. Furthermore, we will share implications for theory and teacher education.

Session 129
Kathy Morris, Sonoma State University; Timothy Boerst, University of Michigan & South Redford School District
From Discourse Patterns to Practice: Scaffolding Preservice Teachers’ Learning
Our work investigates what MTEs can make available for preservice teachers’ learning from records of a routine instructional discourse practice. We will consider facets of the work of teaching through a sample classroom mathematics discussion led by an experienced practitioner.

Session 139
Kyle Schultz, University of Georgia; Thomas E. Ricks, Louisiana State University; Shelly M. Allen, Patricia S. Wilson, Jeremy Kilpatrick, University of Georgia
Teacher Developers’ Conceptions of Mathematical Knowledge for Teaching (MKT)
Using data from focus groups and from an online survey, we examine how teacher developers who had participated in an 8-day summer institute on MKT viewed that concept 2 years later and had used it in their practice.

2007 Conferences

American Educational Research Association (AERA)
April 9-13, 2007; Chicago, IL

The following two presentations are part of the session The Laboratory Class: A Multidisciplinary Approach to Studying the Teaching and Learning of Mathematics

Hyman Bass, Imani Masters Goffney, Sean F. Delaney, University of Michigan
Learning How to Know Mathematics: Reasoning and Proving in Fifth-Grade Mathematics
Proof is a fundamental concept of mathematics, and proving a fundamental practice. Mathematical reasoning (including proving) is no less than a basic skill. It is as fundamental to knowing and using mathematics as comprehension of text is to reading. Yet, for the most part, what we find in school materials, even in ambitious reform materials, is mostly what we call “reasoning of inquiry”, with very modest amounts of “reasoning of justification,” (where proving resides). But what could reasoning of justification look like at the elementary level? This paper traces students’ individual and collective work on a complex task of collective reasoning and proof that stretched over several days: Is it possible to arrange five sticks – one each of lengths 1, 2,3, 4, and 5 – end to end, such that every length from 1 to 15 can be made by removing adjacent sticks? This problem, in a combinatorial arithmetic, has no solution. At first the students worked relatively unsystematically on it, seeking a solution. As they progressed, they began to doubt their ability to produce a solution, but seemed to believe that a mathematician could do so. They also believed in the power of empirical force –– that is, that if they kept working, they would likely find a solution. With carefully designed instruction, developed jointly by the EML researchers, the class worked together to construct a non-existence proof. Our analysis of their struggle and eventual success with this problem contributes to elaborating and developing a framework for reasoning of justification in school that we introduced in our earlier work (see Ball and Bass, 2000, and Stylianides, 2005). The framework is intended to help understand, specify, and develop practices of proving in elementary mathematics instruction. It has four elements: (a) a base of common public knowledge; (b) norms for mathematical language, notation, and rules of inference; (c) norms of collective work; and (d) tasks and situations that create imperatives for proving. Each of these elements is analyzed, examining both individual students’ efforts and thinking as well as the group’s work as a collective. In addition, we analyze what the students say they know about the solution based on the collectively accomplished proof. We see that across several days, they gradually develop conviction in their mathematical conclusion, but we also see the fundamental leap that is required of them to understand what a proof proves.

Laurie Sleep, Deborah Loewenberg Ball, Kara Suzuka, University of Michigan
Teaching as Mathematical Work: A Practice-Based Job Analysis
Abstract: A premise of our work is that to understand the mathematical knowledge needed for teaching, one should study not just the curriculum and its relation to the discipline, but, at least as importantly, the actual practice of teaching itself. Hence, instead of investigating what teachers need to know by looking at what they need to teach, or by examining the curricula they use, we decided to focus on their work. What do teachers do, and how does what they do demand mathematical reasoning, insight, understanding, and skill? We seek to unearth the ways in which mathematics is entailed by its regular day-to-day, moment-to-moment demands. These analyses help to support the development of a practice-based theory of mathematical knowledge for teaching. We see this approach as a kind of “job analysis,” similar to analyses done of other mathematically intensive occupations, from nursing to engineering and physics (Hoyles, Noss, & Pozzi, 2001; Noss, Healy, & Hoyles, 1997), to carpentry and waiting tables. In this case, we ask: • What mathematical knowledge is entailed by the work of teaching mathematics? • Where and how is mathematical knowledge used in teaching mathematics? How is mathematical knowledge intertwined with other knowledge and sensibilities in the course of that work? We carry out this research through intensive observation and analysis of primary records (video and other artifacts) of practice. From this we derived theoretical portraits of the mathematical knowledge for teaching. Our work uses methods of mathematical and pedagogical analysis to focus on mathematics as it is used in the core task domains of teachers’ work. This paper, rooted in this theoretical perspective, analyzes four tasks of teaching that were significant in the Elementary Mathematics Laboratory: (1) selecting numerical and geometric cases or examples; (2) formulating problems and “hints”; (3) building definitions; (4) supporting mathematical explanations and proofs. Although each of these is something teachers do to teach, our analysis focuses on the mathematical reasoning entailed by each of these tasks. One finding of these analyses was the linguistic demands of the work, and the extent to which skills and sensibilities with mathematical language, were central. A second finding was to identify kinds of mathematical reasoning demanded in these tasks, including warrants for claiming that a particular “solution” (e.g., the choice of one numerical example over another) was valid.

The following presentation is part of the session Learning From Practice: Teacher Education for the 21st Century

Timothy A. Boerst, South Redford School District; Laurie Sleep, Deborah Loewenberg Ball, University of Michigan
Designing for and Capturing Preservice Teachers’ Enactment of High-Leverage Mathematics Teaching Practices
This paper presents our on-going efforts to design an elementary mathematics methods course that engages preservice teachers in the actual work of mathematics teaching, developing their skills at doing the work, not just analyzing it. This is a departure from typical teacher education courses that focus on developing preservice teachers' knowledge about teaching through analytic discourse, critical reading, and the construction of elaborate lesson plans. Although effective teaching clearly depends on knowledge, because teaching is a practice, we believe that preservice teachers will develop more robust and usable mathematical understandings and pedagogical skills through repeated and increasingly sophisticated engagement in actual practice. The paper focuses on three aspects of our work: 1. Identifying the work of mathematics teaching: What teaching practices should be the focus of a semester-long methods course? 2. Designing opportunities to practice: How can "practice" be used to engage preservice teachers in doing the work of mathematics teaching? 3. Assessing practice: What evidence is there of improved preservice teacher practice? Designing Opportunities to Practice Although recent literature shows that practice-based approaches are a productive way to learn about teaching, there is no consensus about what it means for a course to be grounded in practice. In this section, we describe the design of our course to illustrate our conceptualization of a practice-based approach. First, we use practice as a context for learning. Through the use of records of practice and placements in "real" classrooms, preservice teachers learn to do the work of teaching in virtual and actual settings. Second, we use practice as rehearsal, or multiple opportunities to engage in and receive feedback on practice. We draw on video data from class sessions and samples of preservice teacher work to illustrate our practice-based design approach. Assessing Practice Because practice is our goal for preservice teacher learning, course assessments must evaluate and provide feedback on the actual enactment of practice. This, however, is not easy to do: The ephemeral nature of practice makes it difficult to capture and assess. In this section, we report our efforts to capture and assess preservice teachers’ enactment of practice. In addition to providing evidence of preservice teacher learning, these course assessments serve as a lens for evaluating the content of the course and its design.

The following presentation is part of the session Video as a Research Tool for Studying Instructional Practice

Heather C. Hill (University of Michigan), Deborah Loewenberg Ball (University of Michigan)
Moving Video Research to Scale: Designing and Studying a Measure of Mathematical Knowledge for Teaching
Video, as a research tool, has been put to profitable use in creating detailed examinations of classroom practice and teacher change. Doing so has allowed both researchers and teachers to gain a depth of understanding of the often subtle classroom processes and changes that can contribute to student learning. But what is involved when a study needs consistent measures of classroom processes across many lessons, teachers, years, and even research projects? And, what is involved when the analyses require, for statistical modeling purposes, the quantification of aspects of the classroom processes seen on tape? These purposes raise the need for statistically reliable and generalizable instruments for coding videotape. This paper reports on one effort to design such an instrument, and considers some of the major issues involved in building a measure that can be used at moderate scale and in statistical models. The instrument grew from our project’s work investigating the mathematical knowledge used in teaching – a kind of specialized knowledge that teachers hold of mathematical explanations, representations, definitions, mathematical language, and other topics. We began in 2003 to design a set of video codes to quantify the quality of the mathematics in instruction, hoping to use this instrument as an indicator of 10 teachers’ mathematical knowledge for teaching. In 2006, we concluded development and coding with an instrument that boasted five sections and 48 substantive codes, and with roughly 90 hours of tape coded. In this paper, we report on three more technical problems that arose during the long process of developing our video codes. These issues are: achieving interrater reliability—e.g., achieving a standardized protocol and deciding where to set the “bar,” so to speak, in evaluating particular clips for the nature of knowledge use; conducting data reduction—deciding how best to combine the 48 codes to represent a teacher’s classroom practice in statistical analyses; and determining how many videotaped “observations” are necessary to achieve a reliable estimate of the mathematical quality of a teacher’s instruction (the answer: four or five, depending upon the construct being measured). Following presentation of these issues, we also briefly discuss additional topics, including the generalizability of our instrument to other research projects and the logistics concerning its use in research settings.

The following two presentations are part of the session Conceptualizing and Using Routines of Practice in Mathematics Teaching to Advance Professional Education

Timothy A. Boerst. South Redford School District; Laurie Sleep, University of Michigan
Investigating Uses and Meanings of Practice in Supporting the Development of Teaching Routines
In the first paper we investigate the notion of using "practice-based" activities and resources for teacher learning. This approach has garnered growing support (Ball & Cohen, 1999; Wilson & Berne, 1999; Darling-Hammond, 1998; Lampert & Ball, 1998), but there is no professional consensus about what it means for a methods course to be practice-based. In our presentation we will focus on "practice" in the design and enactment of a preservice elementary mathematics methods course. We illustrate how practice can be the content that preservice teachers learn – high leverage teaching practices that are central to mathematics instruction and high leverage mathematical practices that are central to teaching, as well as knowledge and principles that support professional engagement in those practices. We demonstrate how practice can be used in the design of preservice teacher learning opportunities in multiple ways: practice as a context for learning to engage in the work of teaching (which involves using records of practice, resources of practice and field-based experiences); and practice as rehearsal implying repeated opportunities to engage in and receive feedback on acts of teaching. These design uses of practice afford preservice teachers different vantage points on routines of mathematics teaching, as well as provide different degrees of engagement in particular routines. Finally, we will show how practice can be used as evidence of preservice teacher learning.

Hala N. Ghousseini, University of Michigan
Discourse Routines for Learning About and Leading Productive Discussions in the Secondary Mathematics Classroom
The emphasis on reasoning in mathematics education has placed mathematical discourse at its heart (NCTM, 1991). This makes it a necessity to prepare pre-service teachers for this aspect of ambitious mathematics teaching; no easy task given the complexity of this aspect of practice and the unfamiliarity of many prospective teachers with it. Prospective teachers need to be trained in doing this work because it is a skill that they do not have and that they are unlikely to develop simply from experience. Teacher educators have found that prospective teachers tend to struggle with this form of learning and teaching mathematics (Simon & Blume, 1996). In this presentation, I address the question of how we can prepare pre-service teachers to lead productive mathematics discussions, assuming that prospective teachers need tools to reduce some uncertainties in practice while learning to teach mathematics in intellectually responsible and responsive ways (Ball & Wilson, 1996). The use of such tools can harness some of the complexity in practice and enable prospective teachers to attend to core tasks of teaching. (Floden and Buchmann, 1993). If initial teacher preparation does not provide prospective teachers with such tools, novices will resort to whatever practices enable them to survive whether or not they represent reasonable practice in a given situation (Feiman-Nemser, 2001). I describe an intervention that took place in the context of a mathematics methods course for secondary teachers that involved using discourse routines in developing pre-service teachers' knowledge about leading productive mathematics discussions. I describe the nature of these routines and the way they were used to allow pre-service teachers to talk about important problems of practice involved in leading mathematics discussions.

The following presentation is art of the session The Nature and Role of Tasks That Foster Learning in Mathematics Teacher Education

Edward A. Silver, Lawrence M. Clark, Hala N. Ghousseini, Beatriz Strawhun, Charalambos Y. Charalambous, Jenny Sealy, University of Michigan
Show Me the Mathematics: Opportunities to Learn Mathematics in Practice-Based Professional Development
The paper reports on the mathematics that may be learned through practiced-based tasks. Central to this view is the role of professional learning tasks that are designed to make the work of teaching available for investigation and inquiry, thereby allowing teachers to treat particular aspects of teaching as problematic - as something to think about and improve through reflection on practice and consideration of alternatives. The presentation will examine how professional learning tasks can and do make available opportunities for teachers to work on and learn about mathematics. This is done by drawing on data collected from several sources (e.g., video transcripts, interviews, end of session reflections) in the BIFOCAL (Beyond Implementation: Focusing on Challenge And Learning) project. BIFOCAL is a multi-year, practice-based professional development project anchored by a careful consideration of cognitively demanding mathematical tasks and the ways in which teachers’ actions and interactions can facilitate (or inhibit) student learning from such tasks. The authors provide examples of how the professional development tasks/cases they used afforded their participants with three layers of opportunities to consider important mathematical ideas as well as how these ideas can be used in teaching. First, in each session, the participants were given an opening activity and asked to solve a rich mathematical problem and share and discuss their solutions with their colleagues; second, the participants read a case which portrays a teacher encountering several challenges when enacting the opening-activity problem or a similar one in her teaching. Finally, in discussing the case and reflecting on their own practice, the participants were offered an additional layer of opportunities to contemplate on these and other related mathematical ideas and their use in the context of teaching. Through this analysis, the authors identify and trace the ways in which the professional learning tasks used in the project provided teachers with opportunities to consider important mathematical ideas, first in a decontextualized mode, and then in the context of teaching. Finally, the presentation will conclude with a discussion of how the questions and the issues that the participants raised and their interaction with their colleagues and the facilitator created a community of collaborative practice akin to that advocated for learners in pre-college classrooms that supported teachers’ inquiry into the mathematics needed in their teaching.

The following presentations are part of the session A New Tool for Measuring Mathematical Knowledge in Teaching: The Quality of Mathematics in Instruction Instrument

Heather C. Hill, University of Michigan
What Role Does Mathematical Knowledge for Teaching Play in Instruction?
This paper uses results from both the video analyses and multiple choice assessments to ask how teachers’ mathematical knowledge influences the quality of instruction provided to students. Our data clearly show a strong relationship (r=.77) between both measures; further, project discussions and comparisons of participating teachers elucidated numerous ways in which having mathematical knowledge affects instruction. To illustrate, this paper structures two comparisons. The first is between two teachers intent on teaching conceptually-oriented mathematics, but who differ dramatically in their mathematical knowledge. The higher-knowledge teacher, as measured by her multiple choice score, has many features of high-quality mathematics instruction: few errors; an emphasis on mathematical explanation and meaning; strong linkages between representations; an ability to hear and respond to students’ mathematical ideas. The lower-knowledge teacher’s instruction features frequent errors; poor task design; and stretches of cutting, pasting, and coloring in which the mathematical “density” of instruction is low. The second comparison highlights two teachers who use more traditional methods to teach mathematics. The high-knowledge teacher uses Saxon mathematics; her knowledge of mathematical explanation and belief in multiple methods for solving problems, however, helps fill in where the curriculum does not venture. The low-knowledge teacher uses a conventional set of curriculum materials, and has in fact chosen to teach procedurally oriented mathematics as a compensation strategy for her lack of mathematical knowledge. Her instruction, while devoid of mathematical meaning, is largely procedurally accurate.

Laurie Sleep, University of Michigan
How Do Teachers Need to Be Able to Use Mathematical Language in Instruction?
Mathematical language plays an important role in instruction. To start, it is central to the discipline of mathematics: It is one of the foundations of mathematical reasoning, essential for constructing mathematical knowledge and providing resources for developing and justifying claims (Ball & Bass, 2003). Furthermore, mathematical language is not only something that students must learn to understand and use; it is also the primary medium of instruction. What is surprising, however, is that although it seems clear that mathematical language matters for mathematics teaching and learning, exactly what teachers need to know about mathematical language remains underexplored. That is, despite its crucial role in mathematics teaching and learning, an explicit discussion of how teachers must know and be able to use mathematical language has been largely missing from the literature on teachers’ subject matter knowledge. In this paper, we discuss our efforts to conceptualize how teachers must know and use mathematical language in instruction. Using a framework that has already proven useful for studying and categorizing the knowledge demands of practice, we begin to articulate the ways in which mathematical language is a central component of mathematical knowledge for teaching. The paper opens with a discussion of the framework for our practice-based theory of mathematical knowledge for teaching. To explore the central role of language in teaching, we then review other research on mathematical language in classrooms. We then propose ways in which mathematical language may be a central component of mathematical knowledge for teaching, using examples from our video data to illustrate our findings. These analyses show that teaching requires more than the teacher’s own proficient and careful use of mathematical language. Teachers must make decisions about how and when to introduce new mathematical terms, determine what definitions are most appropriate for their particular students, and assess how mathematical definitions of terms may be the same or different from the intuitive meanings students already have for these words. Teachers also need to recognize when language used by students is mathematically imprecise or ambiguous, and then make appropriate decisions about whether and how to correct or clarify the language. Teachers must have explicit knowledge of mathematical language, be able to make visible aspects of mathematical language that go unnoticed by those who are fluent, and manage sometimes competing considerations such as precision and accessibility. The paper concludes with an evaluation of our approach and the implications for teacher education and future research.

Imani Masters Goffney, University of Michigan
Using Mathematical Knowledge for Teaching: Implications for Issues of Equity
This paper illustrates elements of equitable mathematics instruction and then explores the resources, including mathematical knowledge for teaching, needed in order to teach equitably. This analysis focuses on three teachers from the project data set. These teachers had very diverse classrooms and very different teaching styles; together, their tapes revealed elements of equitable math instruction, including explicit talk about the meaning and use of mathematical language, soliciting and valuing broad participation in the mathematical work, and focusing instructional time on mathematics rather than simply gluing, cutting, and pasting. These in-depth case studies also allow an examination of the resources necessary for teaching mathematics equitably. Two teachers for this study have high levels of mathematical knowledge for teaching and many years of teaching experience but very different strategies for negotiating differences among students in their classes. Comparing lessons from these two teachers reveals that one teacher actively promotes equity through a repertoire of instructional practices that allow all her students broad access to the mathematical content of lessons, and by attending closely to the specific needs of struggling students. The other teacher uses her knowledge of mathematics to encourage only some students to engage in rigorous mathematics, while marginalizing other students and lowering task levels and expectations around their work. A third teacher has a clear commitment to helping her students achieve and demonstrates some ability to cross cultural and class barriers in relating to students; however, she has a low level of mathematical knowledge for teaching. While this teacher uses her positive relationship with students to maximize on-task instructional time and to encourage student effort, her weak mathematical knowledge for teaching erases any benefit these relational skills may have. Results from this paper can help to inform teacher preparation and professional development programs which seek to address academic achievement gaps by improving teachers’ capacities for providing equitable mathematics instruction.

Deborah Zopf, University of Michigan
Mathematics Content-Focused Professional Development: Its Influence on Teaching Quality
This paper searches for evidence of change in the mathematical quality of teachers’ practice as a result of their participation in content-focused, extended professional development. Previous research (Cohen & Hill, 2001; Garet, Porter, Desimone, Birman, & Suk Yoon, 2001; Richardson 200X) have established changes in teachers’ practice as a result of professional development experiences. However, research to date has not examined the effects of professional development on teachers’ use of mathematics in instruction. With the novel instrument we designed, and with other analyses of this unique dataset, we can begin to answer this question. Teachers participated in the Mathematics Professional Development Institutes (MPDIs), held in California in 2003, and which as a whole has been shown to improve teachers’ content knowledge (Hill & Ball, 2004). In the professional development, teachers worked on problem solving prompts adapted to various grade levels, multiple solution methods, representations, explanations, and pedagogy appropriate for meaning-oriented mathematics instruction. Our data show that teachers benefit differently from professional development, and these differences are linked to teachers’ personal goals for learning from professional development. In one case, a teacher wanted to learn mathematics; video data indicate improved mathematical quality and in particular, a heightened focus on honoring students’ varying solutions. Another teacher, however, saw the professional development as a means of getting activities to use with her students. While she does use the activities with her students, her lack of knowledge of the mathematics within the activities prevents the mathematics from becoming visible in the lesson.

The following presentation is part of the session: A Study of Undergraduate Mathematics Classes for Prospective Elementary Teachers: Methods and Results

Helen Siedel, University of Michigan
Analyzing Mathematics Textbooks: The Case of Multiplication of Integers
A study of the use of models for multiplication of integers in fourteen mathematics textbooks for prospective elementary teachers illustrates the challenges involved in analyzing the development of a mathematics topic within a single text and in comparing topic development across texts. This study introduces a method for using annotated analytic tables to investigate author approaches to mathematics, going beyond the presentation of procedural or conceptual content knowledge in order to explore what teachers might learn about mathematics. The tables show what teachers have an opportunity to learn about the models for multiplication of integers, and reveal what authors believe prospective teachers need to know about the way models represent the mathematics children need to learn. Issues for the design of textbook analyses are raised. The mathematics texts under discussion were written for students reviewing mathematics they saw as schoolchildren. Authors need to decide whether and how to blend a mature approach to mathematics, incorporating knowledge that is beyond the bounds of, but provides a foundation for K-12 mathematics, with mathematics as it is presented in the K-12 classrooms where these teachers will work. Given the different needs of children and teachers as learners of mathematics, one issue for textbook analysis is the extent to which texts for prospective teachers need to be reviewed differently than mathematics textbooks for children. A second issue is that the unusual character of prospective teachers as learners who are reviewing knowledge for which they now have a specialized need is not unique to mathematics. Would similar concerns about analyzing textbooks for prospective teachers exist for other disciplines? The models for multiplication of integers were selected for analysis because they are problematic. Real- world applications that coordinate with the mathematical ideas are too advanced for the pre-algebra position this topic usually takes in the elementary curriculum. Authors must decide which models to use with prospective teachers, and whether teachers should be equipped to evaluate the mathematical affordances and constraints of the models. Our investigation found that only one author provided any explicit evaluation of the models. This suggests that with regard to prospective teachers’ opportunity to learn mathematics, what is not in the texts may be as revealing as what is in the texts. This, too, seems a significant issue to consider in designing textbook analyses.

National Council of Teachers of Mathematics (NCTM)
March 21-24, 2007; Atlanta, GA
Research Presession: March 19-21, 2007

CPTM-related activities and presentations (In case of mixed groups of presenters the CPTM-associated presenter is highlighted):

Laurie Sleep, Deborah Loewenberg Ball, University of Michigan; Timothy Boerst, South Redford School District, Redford, Michigan
Learning to Do the Work of Teaching in a Practice-Based Methods Course
This session will report on the design and implementation of a methods course focused on helping pre-service teachers learn to enact “high leverage” practices. After presenting our criteria for high-leverage mathematics teaching practices, we will share data from the course to illustrate our varied use of “practice” in its design and implementation.

Patricia S. Wilson, University of Georgia
Structuring Field Experiences for Prospective Mathematics Teachers
Research-based ideas on how to structure field experiences for prospective secondary school mathematics teachers will be presented and discussed. Attention will be given to what has been learned about using field experiences that promote growth for student teachers, mentor teachers, and university teachers and that influence the practice of teaching mathematics.

Andreas J. Stylianides, University of California, Berkeley; Gabriel J. Stylianides, University of Pittsburgh
Mathematics for Teaching: A Form of Applied Mathematics
In this session, we propose a conceptualization of mathematics for teaching as a form of applied mathematics, and we will discuss ideas that this conceptualization implies for designing mathematics courses for preservice teachers. We will also describe a promising approach we followed in designing a course that is consistent with these ideas.

Kara Suzuka, Deborah Loewenberg Ball, Hyman Bass, Timothy Boerst, Laurie Sleep, Jennifer Lewis, Mark Thames, University of Michigan
Using Records of Practice as (Con)Texts for Learning Mathematical Knowledge
How can records of classroom practice (e.g., students’ work, tapes of lessons, teachers’ plans) be used to help teachers learn mathematical knowledge and skills needed for teaching? In this interactive session, participants will work with a package of records of classroom practice designed to foster the development of mathematical knowledge that teachers need in instruction.

Gwendolyn M. Lloyd, Virginia Polytechnic and State University; Edward A. Silver, Hala Ghousseini, Charalambos Charalambous, University of Michigan; Valerie Mills, Oakland School District, MI; George Philippou, University of Cyprus, Nicosia, Cyprus; Stephanie L. Behm, Virginia Polytechnic and State University; Thomas J. Cooney, University of Georgia
Mathematics Teachers’ Curriculum Use at Different Stages of Implementation
Research Symposium
This session includes three studies that consider issues in teachers’ curriculum use emerging at different stages of teachers’ careers. We consider teachers’ interactions with curriculum materials in teacher education, during initial implementation of new curricula, and at the point when teachers appear to have reached a curriculum implementation “plateau.”

National Symposium to Develop an Effective Model for the Professional Development of K-12 Engineering and Technology Education Teachers
February 12-14, 2007; Dallas, TX

Pat Wilson, Susan Mundry, David Burkhardt, and Michael Hacker
This session of the symposium will review research that defines effective professional development models in mathematics and science with the intent of identifying the critical elements of successful professional development models in mathematics and science. Discussion will focus on the extent to which these models appear to be applicable for engineering-oriented technology education.

Association of Mathematics Teacher Educators (AMTE)
January 25-27, 2007; Irvine, CA

CPTM-related activities and presentations: In case of mixed groups of presenters, the CPTM-associated presenter is highlighted.


Wednesday, Jan. 24, 2007- Thursday, Jan. 25, 2007
CPTM Summer 2004 Institute Follow-Up
CPTM faculty and graduate students from UMICH and UGA and participants of the Summer 2004 Institute worked on -- through a combination of activities and discussions -- two key problems:
1. What mathematical knowledge and practices play a central role in the everyday work of teaching?
2. What are promising approaches for helping teachers learn mathematics for teaching and learn to use it in their work?

The session overview and resources (slides, posters) for the Institute Follow-Up can be found at Resources.

Judith E. Jacobs Lecture

Deborah Loewenberg Ball, University of Michigan
The Core and Contemporary Challenges of Mathematics Teacher Education

This country has a large and pressing need for skillful teachers of mathematics. Addressing this need is a problem both of scale and detail, for learning to teach mathematics is not a natural extension of learning mathematics; it is in fact unnatural. What is involved in being able to teach mathematics and what does this imply for our work as teachers and teacher educators in the contemporary environment?

Other Sessions

Kara Suzuka, Deborah Loewenberg Ball, Hyman Bass, University of Michigan; Timothy Boerst, Southern Redford School District; Laurie Sleep, Jennifer Lewis, University of Michigan
Learning Mathematics in and for Practice: Using Records of Practice as (Con)texts for Learning Mathematical Knowledge for Teaching
How can records of classroom practice be used to help teachers learn mathematical knowledge and skills needed for teaching? This interactive session will engage participants in mathematical study designed to support the development of usable content knowledge. Aspects of the design will be examined, and affordances and possible pitfalls discussed.

Ginger Rhodes, University of Georgia
Preparing Teacher Educators: What are Meaningful Learning Experiences?
There is little known about how graduate students become professionals who orchestrate learning experiences for teachers (Crespo & Speer, 2004). Understanding more about graduate student experiences and learning will encourage the mathematics education community to examine current teacher education practices and ways to improve those practices. In my presentation I will explore one program that works to support graduate students in becoming teacher educators. I will share results from a research study in order to highlight experiences that graduate students identify as meaningful learning experiences while operating as professional developers.

Robert Floden, Raven McCrory, Michigan State University
Mathematical Knowledge for Teaching Algebra: Validating an Assessment of Teacher Knowledge
Report on progress in developing an assessment focused on teachers’ mathematical knowledge for teaching algebra. The session describes the assessment framework and the design and results of a validation study. Audience discussion will focus on how preservice preparation would affect scores on each of the dimensions of teacher knowledge measured.

Frank Lester, Indiana University: Sybilla Beckman, University of Georgia; Joanna Masingila, Syracuse University
What Mathematics MUST elementary Teachers Know?
This session is part of an effort to establish a Working Group on the Mathematics Education of Elementary Teachers. The focus of the discussion will be on the mathematics content knowledge necessary to be an effective mathematics teacher at the elementary level.

Melissa C. Gilbert, University of Michigan; W. Gary Martin, Auburn University; Stuart Karabenick, University of Michigan
Changing Mathematics Teachers’ Beliefs and Practices Through the Use of Student Data and Ongoing Professional Development
This session focuses on a series of workshops designed to change mathematics teachers’ beliefs (e.g., nature of mathematics, diverse students’ abilities to learn mathematics) and their practices (e.g., increasing students’ opportunities to learn and implementing standards-based instruction) through incorporating classroom data into ongoing site- and university-based professional development.

Francis (Skip) Fennell, President, NCTM; McDaniel College; Sybilla Beckman, University of Georgia; Rose Zbiek, Pennsylvania State University
The NCTM Curriculum Focal Points: A Quest for Coherence
A presentation of the NCTM Curriculum Focal Points for prekindergarten through Grade Eight. The presentation will present issues relative to the focal points, their development, and use. As with all AMTE sessions, time will be provided for questions and dialogue.

Signe Kastberg, Jacob Klerlein, Indiana University
Listening in and Learning about Children’s Mathematics
This working group is designed to explore the potential of a listening activity designed to support the development of future teachers’ listening skills and understandings of children’s mathematics. Participants will engage in a listening episode as experienced by students in the course and discuss cases of students’ work.

Kathy Morris, Sonoma State University; Megan Loef Franke, University of California-Los Angeles; Janine Remillard, University of Pennsylvania; Ricks Marks, Sonoma State University; Timothy Boerst, Southern Redford School District
Recording the Use of Records of Practice: Mathematics Teacher Educators Learning From Each Other
This interactive symposium focuses on two questions: How do we use multimedia records of teaching practice in our math methods course? How do [we] make our own teacher education practices public through the construction of multimedia records of MTE practice? We will provide multiple examples of both from our Carnegie QUEST projects.

M. Kathleen Heid, The Pennsylvania State University; Jeremy Kilpatrick, Patricia Wilson, University of Georgia; Rose Mary Zbiek, Glen Blume, The Pennsylvania State University; Ryan Fox, University of Georgia; Heather Godine, The Pennsylvania State University
Developing a Framework for Mathematical Knowledge for Teaching at the Secondary Level
In seeking to understand the construct of mathematical knowledge for teaching (MKT) as it might be applied to secondary school mathematics, we have developed a variety of sample situations and a framework. Participants in this work session will work with the situations and framework and discuss implications for teacher education.

Deborah Loewenberg Ball, Laurie Sleep, University of Michigan
Exploring the Use of Mathematical Language in Practice: What Do Teachers Need to Know?
This session investigates teachers’ use of mathematical language as one element of knowing mathematics for teaching. Using classroom video segments, we will first examine mathematical language issues that arise in teaching and consider the mathematical knowledge demands of using mathematical language in practice. We will then discuss tasks used in our content and methods courses to work on issues of mathematical language with prospective teachers.

Edward Silver, Hala Ghousseini, Charalambos Charalambous, Lawrence Clark, University of Michigan
How Can Practice-based Professional Development Help Teachers Learn Mathematics?
Practice-based professional development promotes teacher learning through engagement with authentic tasks of teaching. Nevertheless, it is not immediately obvious how teachers can learn mathematics in this way. In this presentation we illustrate several ways that practice-based, professional learning tasks can make available opportunities for teachers to enhance their mathematical knowledge.

Raven McCrory, Marisa Cannata, Michigan State University
The Mathematical Education of Elementary Teachers:The Content and Context of Undergraduate Mathematics Classes for Teachers
What mathematics classes are required for prospective elementary teachers? Who teaches them, what’s their content, where are they in students’ programs, what textbooks do they use, and how much variation is there across institutions? These and other questions will be discussed based on results from 75 institutions in three states.

2006 Conferences

North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA)
November 9 to 12, 2006
Mérida, Yucatán Universidad Pedagógica Nacional
Silvia Alatorre, Chair

Edward A. Silver, Charalambos Y. Charalambous, Beatriz T. Font Strawhun, Gabriel J. Stylianides, University of Michigan
Focusing on Teacher Learning: Revisiting the Issue of Having Students Consider Multiple Solutions for Mathematics Problems
Research report fom the BI:FOCAL project

Gabriel J. Stylianides, Andreas J. Stylianides (UM graduates)
Promoting Teacher Learning of Mathematics: The Use of "Teaching-Related Mathematics Tasks" in Teacher Education (research report)

Amy J. Hackenberg (UGA graduate), Portland State University
Sixth Graders' Construction of Quantitative Reasoning as a Foundation for Algebraic Reasoning (research report)

Alison May Castro (UM graduate)
Learning How to Use Mathematics Curriculum Materials in Content and Methods Course (short oral)

Alison May Castro (UM graduate)
Understanding Teachers' Use of the Teacher Guide as a Resource for Mathematics Instruction (short oral)

Hyung Sook Lee, University or Georgia
The Impact of a Units-Coordinating Scheme on Conceptual Understanding of an Improper Fraction (short oral)

Denise Natasha Brewley-Corbin, University of Georgia
The Challenges of Infusing Equity Into a Mathematics Methods Course (poster)

Gloriana González, University of Michigan
Revealing Students' Conceptions of Congruency Through the Use of Dynamic Geometry (poster)

Daniel J. Brink, University of Georgia
Fraction Multiplication: Teacher and Student Understanding and Interpretation in a Reform-Based Classroom (poster)


Joint NSF-CLT Conference on Curriculum, Teaching & Mathematical Knowledge
University of Maryland, November 18, 2006

Glen Blume, Ryan Fox, Kathy Heid, Jeremy Kilpatrick, Evan McKlintock, Pat Wilson, Rose Zbiek
Identifying Mathematical Knowledge for Teaching at the Secondary Level (6-12) from the Perspective of Practice
Abstract: The reform curricula in mathematics have created goals and expectations that place new demands on both teachers and students. This session explored the mathematical knowledge needed by teachers to effectively teach reform curricula by presenting statements, questions, or events that (1) offered an opportunity to explore, discuss, or illustrate important mathematical ideas, and (2) occurred in 6-12 mathematics classrooms using reform curricula or in classes for preservice or inservice teachers preparing to use reform curricula in grades 6-12.

TEAM-Math Conference
Tuskegee University, August 26, 2006

Keynote Address

Patricia S. Wilson, University of Georgia
Developing a Deep Understanding of Mathematics
The first recommendation of the Mathematics Education of Teachers report states, “Prospective teachers need mathematics courses that develop a deep understanding of the mathematics they will teach.” Although those who teach mathematics to teachers usually have a deep understanding of mathematics, they may not have been prepared to help others develop that deep understanding of mathematics. This session will identify the diverse group of people who teach mathematics to teachers, propose characteristics of a deep understanding of mathematics for teaching, and offer examples of initiatives that prepare and support those who teach mathematics for teachers.

International Group for the Psychology of Mathematics Education (PME)
July 16-21, 2006; Prague, Czech Republic

CPTM work session:
Teresa McMahon, Paola Sztajn, Hala Ghousseini, Deborah Loewenberg Ball
Purposeful Design for Mathematics Teacher Educator Professional Development

Mathematical Sciences Research Institute (MSRI)
Raising the floor: Progress and Setbacks in the Struggle for Quality Mathematics Education for All
May 07-10, 2006

The conference was held in the new Simon's Auditorium in Berkely, CA, and was organized by Deborah Ball, Herb Clemens, Carlos Cabana, Ruth Cossey, Bob Megginson, Bob Moses

Knowledge of mathematics in the technology and information age has been likened to reading literacy in the industrial age. In each case knowledge is the enabler, the ticket to full participation in society and to some measure of economic well-being. This conference will explore the historical and current challenges to quality and equity in the teaching and learning of mathematics, both in the U.S. and internationally. The exploration will feature case studies of successful and not-so-successful efforts, with the goal of learning together how to improve and refine that which works and correct that which doesn't. The intended audience is broadly inclusive: policy-makers, mathematics educators, mathematicians and teachers. There is no registration fee for this workshop. The only costs to attend are the lodging and travel expenses. Please note, this workshop requires each participant to apply to participate, as space is limited. All applications will be reviewed, and invitations will be sent as space allows.

National Council of Teachers of Mathematics (NCTM)
April 26-29, 2006; St. Louis, Missouri
Research Presession: April 24-26, 2006

Edward Silver, University of Michigan
Joining Research & Practice: Asking Hard Questions, Questioning Easy Answers

Ginger Rhodes, Thomas Ricks, Dennis Hembree, Erik Tillema, University of Georgia
Examining Mentor Teachers' Deprivatization in School Communities (Work Session)
Session Summary:
Current calls for reform in professional development necessitate a better understanding of community development. We will present our research project that investigates the deprivatization of mentor teachers’ practice within school communities. In particular, we invite participants to examine artifacts and current findings from our project for analysis and discussion.

Kathleen Heid, Susan Peters, Patrick Sullivan, Pennsylvania State University; Patricia Wilson, University of Georgia; Ismail Ozgur Zembat, Hacettepe University; Neil Portnoy, Stony Brook University
Prospective Secondary Mathematics Teachers’ Ways of Mathematical Thinking (Research Symposium)
Session Summary:
Research teams associated with the Mid-Atlantic Center for Mathematics Teaching and Learning have been investigating the mathematical (and statistical) understandings of prospective secondary school mathematics teachers (PSMTs). We have observed the ways that PSMTs understand mathematics. We will generate some hypotheses about characteristics of the mathematical thinking of PSMTs.

Patricia S. Wilson, Ginger Rhodes, Kanita Kimmons DuCloux, University of Georgia; Janet Tomlinson, North Oconee High School, Bogart, Georgia; Frances Curcio, Alice Artzt, Queens College/City University of New York
Practice into Research (Thematic Presentation)
Session Summary:
Situating research within the context of schools and the work of practicing teachers provides a rich environment for studying the learning and teaching of mathematics. A panel will stimulate group discussion by sharing research investigating the learning of mathematics as an intentional component of field experiences in high schools.

Symposium sponsored by the Center for Proficiency in Teaching Mathematics (CPTM)
A Case of Practice-Based Professional Development for Teacher Educators
Examining a professional development experience for mathematics teacher educators that used a laboratory class of prospective elementary teachers, we discuss theories of design, identify five features used to enhance participants’ ability to study teaching, and explore participants’ interactions with learning opportunities. We will study video of practice during this session.

Summary of Presentations:

  • Teresa McMahon, Deborah Ball, University of Michigan; Paola Sztajn, University of Georgia
    Introduction and Mathematical Knowledge for Teaching
    We present the general theories and design of the institute. We will discuss one of the main goals of the institute, which was to enhance participants’ understandings of Mathematical Knowledge for Teaching (MKT) by having them consider how elementary teachers need to know and use mathematics in their teaching.

  • Hala Ghousseini, Laurie Sleep, University of Michigan
    Making Practice “Studyable”
    We report the findings from a case study analyzing the implicit design of this professional development experience. This study identifies five support features that were used to mediate and enhance the participants’ ability to observe and discuss teaching, as well as to analyze and use records of practice.
    Participant Activity – Practicing Observing Practice
    Participants will have the opportunity to use the support features identified in the second presentation to “study” videotape of the lab class.

  • Doug Corey, University of Michigan; Dennis Hembree, Andrew Tyminski, Sarah Ledford, University of Georgia
    “What was really accomplished here today?”
    Understanding Participants’ Interactions with the Curriculum

    The third presentation uses analysis of field notes, video of participant interactions and participant journals to explore the ways in which participants with differing characteristics interacted with the curriculum.

National Council of Supervisors of Mathematics (NCSM)
April 24 - 26, 2006; St. Louis, MO

Ed Silver, Valerie Mills, Lawrence Clark, Hala Ghousseini, Alison Castro, Dana Gosen, Gerri Devine, University of Michigan
Moving Beyond Implementation: Teachers Working Collaboratively to Refine Their Practice
This session includes lessons learned with and from teachers about issues that lurk at the root of the implementation plateau. These pertain to aspects of teaching that are crucial to effective use of standards-based curricula and illuminate persistent dilemmas of good mathematics teaching that are not "solved" by introducing new curriculum materials.

American Educational Research Association (AERA)
April 7-11; San Francisco, CA

Integrating Case Analysis and Lesson Study in Mathematics Teacher Professional Development: A Conceptual and Empirical Analysis of Design and Efficacy

  • Ed Silver, Valerie Mills, Alison Castro, Hala Ghousseini, University of Michigan
    Conceptualizing the Integration of Two Practice-based Approaches to Teacher Professional Development
  • Ed Silver, Valerie Mills, Dana Gosen, Beatriz Strawhun, University of Michigan
  • Integrating Case Analysis and Lesson Study in Mathematics Teacher Professional Development: Design Principles and Implementation Features
  • Ed Silver, Hala Ghousseini, Gabriel Stylianides, University of Michigan
    Examining the Efficacy of Using Case Analysis and Lesson Study in Synchrony

Summary pf presentations:
Contemporary discussions of teacher professional development often treat different approaches as if they were competing with each other, as professional developers seek the one approach that is optimal for all their needs. The participants in this symposium offer a contrasting view; namely, a conceptualization in which the strengths of one approach are seen as complementing the limitations of another. We examine the design and implementation of mathematics professional development project in which lesson study and case analysis are systematically integrated, drawing attention to the underlying design principles and reporting analyses of data that illuminate how the integration of approaches provides unusual opportunities for teachers to learn in ways that affect their thinking about preparing for and conducting mathematics lessons.
The first paper provides the theoretical underpinnings of the project and its integrated approach to professional development.
The second paper provides a detailed account of the mathematics professional development sessions in which lesson study and case analysis were systematically integrated, drawing attention to the underlying design principles.
The third paper offers an analysis of empirical evidence related to the impact on participants that can be traced to the synergistic integration of narrative cases and elements of lesson study.

Patricia S. Wilson, Kanita DuCloux, Stephen Bismarck, The University of Georgia
Relationships That Foster Learning Within a Student-Teaching Experience
Relationships that are built during student teaching are influential in the knowledge and the nature of the knowledge gained by both the mentor and the student teacher. Through a situative perspective, we have investigated the relationships built between mentors and students in secondary, mathematics classrooms by studying their interactions during a student teaching experience designed to foster community building. Thirty-nine mentors and thirty-two student teachers participated in the study located in ten schools with varying demographics. Interactions were analyzed and productive relationships are described. Although the student teaching experience was designed to foster collegiality, the traditional model of expert mentor and novice student teacher prevailed in most cases. Reasons and consequences are investigated.

Association of Mathematics Teacher Educators (AMTE)
January 26-28, 2006, Tampa, FL

Dennis Hembree, Ginger Rhodes, Margaret Sloan, Pat Wilson, University of Georgia
Hosting Student Teachers as a Site for Professional Development

Stephen Bismarck, Bob Allen, University of Georgia
Recognizing the Mathematical Knowledge for Teaching Geometry in a Professional Development Context
Using data from the 2003 Summer Institute sponsored by the Center for Proficiency in Teaching Mathematics, we will begin to describe the mathematical knowledge needed for engaging in-service geometry teachers in geometrical explorations. We invite audience members to critique and comment on our work.

Pat Wilson, University of Georgia; Kathleen Heid, Penn State University; Kanita Ducloux, Dennis Hembree, Bob Allen, University of Georgia; Jeanne Shimizu, Penn State University
Using Defining Moments in Mathematics Classrooms to Inform Teacher Education
Presenters will introduce a vignette that captures a defining moment from a high school mathematics lesson and a variety of pathways that extend the lesson. Participants will work on creating pathways for a set of defining moments and will explore uses of vignettes in courses and activities for mathematics teachers.

Ed Silver, Charalambos Charalambous, Alison Castro, University of Michigan
Cyclical Nature of BIFOCAL: An Iterative and Adaptive Approach to Professional Development
A basic premise of good professional development is that it should model and reflect the pedagogy of good instruction. In this session we will illustrate how an iterative, adaptive approach to professional development can enable one to achieve predetermined goals while also attending to emergent professional development needs of teachers.

Dorothy White, Judith Reed, University of Georgia
Preparing Future Mathematics Teacher Educators to Incorporate Issues of Equity and Diversity Into Their Methods Courses

Laurie Sleep, Tim Boerst, University of Michigan
A Different Slice of Practice: Helping Preservice Teachers Navigate the Complexities of Teaching Mathematics Through Routine Engagement in High Leverage Tasks of Teaching

Alison Castro, University of Michigan
Preparing Elementary Preservice Teachers to Use Mathematics Curriculum Materials

Tim Boerst, University of Michigan; Paola Sztajn, University of Georgia; Laurie Sleep, University of Michigan; Judy Flowers, UM at Dearborn
Supporting Teacher Educator Practice and Learning Through Cross-Institutional Course Implementation

AMTE Preconference Workshop

Using Mathematical Knowledge for Teaching as a Learning Opportunity for Teacher Developers
Sponsored by The Center for Proficiency in Teaching Mathematics (CPTM)
Organizer: Teresa McMahon (
Mathematical Knowledge for Teaching is one of the main arenas for the work of both mathematicians and mathematics educators and as such can, we believe, provide a productive focus for our own professional development as teacher educators. In this presession, we'll begin by defining what we mean by Mathematical Knowledge for Teaching. We'll then examine artifacts - such as video clips and student work - from a preservice content class for elementary teachers of mathematics. Across all our activities, our intention will be to make practice more visible in order to provide opportunities to consider what mathematical knowledge and practices play a central role in the everyday work of teaching as well as what approaches help teachers learn mathematics for teaching and learn to use it in their work.

American Mathematical Society
AMS-MAA Joint Mathematics Meetings
January 12-15, 2006; San Antonio, TX

Jeremy Kilpatrick, University of Georgia
Math War Veteran Tells All
The so-called wars of the new math era have been forgotten, dismissed as irrelevant, and badly misinterpreted. A veteran of the math wars then and now sees some persistent issues, as well as some persistent misunderstandings, as mathematicians and mathematics educators seek common ground.

2005 Conferences

North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA)
Frameworks that Support Research and Learning
Ocotober 20-23, 2005, Roanoke, VA
Virginia Polytechnic Institute and State University

Denise Mewborn, University of Georgia, Panelist
Framing Our Work
The theme of this conference, “Frameworks that Support Research and Learning,” invites us to take stock of where we are as a field with respect to frameworks, which are a critical element of scholarly inquiry. In an effort to take stock, I briefly review the purpose of frameworks, make the case for why we need more robust frameworks, and suggest approaches that might lead us to more robust frameworks.

Steven Williams, Brigham Young University, Discussant

Raven McCrory, Michigan State University
Undergraduate Mathematics Courses for Prospective Elementary Teachers: What's in the Books?
Are we teaching prospective elementary teachers the mathematics they need? That is the overarching question to which this research contributes. Specifically, the purpose of the research reported here is to explore what prospective elementary teachers have an opportunity to learn from textbooks written for undergraduate mathematics courses for preservice teachers, and to investigate how the content of these textbooks relates to current understandings of what teachers need to know. The research includes analyses of textbooks, interviews with authors of those textbooks, and comparisons with recent research on teacher knowledge.

Discussant: LouAnn Lovin, James Madison University

Amy Hackenberg, University of Georgia
Mathematical Caring Relations as a Framework for Supporting Research and Learning
Mathematical caring relations (MCRs), a framework for conceptualizing student-teacher interaction, was used in a year-long constructivist teaching experiment with 4 6th grade students. MCRs supported (1) the extension of previous research on how students construct improper fractions and (2) the learning of students and their teacher (the researcher). Establishing a MCR entails aiming for mathematical learning while attending to affective responses of both student and teacher. Although all students entered the experiment with the splitting operation deemed necessary for constructing improper fractions (Steffe, 2002), during the experiment 2 students did not construct improper fractions. One of these students is the focus of this paper. The current hypothesis is that splitting does not automatically engender the coordination of 3 levels of units that seems necessary to construct improper fractions. Analyzing MCRs in research is seen to facilitate interactions that can lead to learning and to validate the experiential difficulties of learning.

Mathematical Sciences Research Institute (MSRI)
The Mathematical Knowledge for Teaching (K-8): Why, What, and How?
May 25-28, 2005, Asilomar Conference Center, Pacific Grove, CA

Workshop organizers: Deborah Ball, University of Michigan; Herb Clemens, Ohio State University; David Eisenbud, MSRI; Jim Lewis, University of Nebraska;
CPTM workshop contributors: Deborah Ball, Hyman Bass, Raven McCrory, Mark Thames, University of Michigan; Sybilla Beckmann, Jeremy Kilpatrick, University of Georgia.

International Commission of Mathematical Instruction Study Conference
The Professional Education and Development of Teachers of Mathematics
May 15-21, 2005, Águas de Lindóia, Brazil

Paola Sztajn, University of Georgia; Deborah L. Ball, Teresa McMahon, University of Michigan
And Who Teaches the Mathematics Teachers? Professional Development of Teacher Developers
How do we prepare people to work with teachers? What learning opportunities are needed and what should the curriculum of these opportunities be? This interactive symposium is designed to (a) frame the problem of the education of teacher developers; (b) offer participants experience with elements of one event designed to provide opportunities for teacher developers' learning; (c) examine evidence about the outcomes and challenges of the program; (d) discuss how elements of this program may be adapted to different contexts.

Edward Silver, Alison Castro, Hala Ghousseini, & Gabriel Stylianides, University of Michigan; Valerie Mills, Oakland County (MI) Schools
Complementary Approaches to Mathematics Teacher Professional Development: Integrating Case Analysis and Lesson Study in the BI:FOCAL Project
Discussions of teacher professional development often treat different approaches as if they were in competition to determine the best approach. Thus, video cases are viewed as competing with narrative cases, and case methods competing with lesson study or curriculum-based professional development. In this paper we offer a contrasting view; namely, that different professional development approaches each have strengths and limitations and that careful, intentional blending of approaches can allow the strengths of each approach to complement the limitations of the other. We apply this view to two distinct approaches that have generated considerable attention and interest in the mathematics teacher professional development community -- lesson study and case analysis and discussion. To illustrate key aspects of our conceptualization, we rely on analyses of data collected in BI:FOCAL (Beyond Implementation: Focusing On Challenge And Learning) -- a multi-year, mathematics teacher professional development project that systematically integrates these two approaches. We use data drawn from project work across one year to illuminate ways in which the synchrony of approaches creates powerful opportunities for teachers to examine the practice of mathematics teaching and to learn from this examination in ways that affect their own teaching practice.

Tim Boerst, University of Michigan; Wil Oonk, University of Utrecht, Freudenthal Institute
Reflection for Teaching: Nurturing and Noticing Reflection in Practice-based Professional Learning Experiences
The idea of reflection often lies at the heart of conceptions of learning in and from practice. The popularity of work on reflection has created an abundance of associated definitions, elements, and purposes in a number of fields including learning theory (Van Glasersfeld, 1984) and educational domains such as mathematics education (Cobb et al., 1997; Freudenthal, 1978) and teacher education (Zeichner, 1987). Because it has been connected with such different content and so many ways of thinking, the notion of reflection is in danger of becoming inundated. This situation impacts teacher educators’ abilities to encourage the development of reflection, as well as perceive its existence and development in preservice and inservice settings. In such a context, it is important to consider the ways in which more tightly defined notions of reflection could guide the planning, enactment, and assessment of practice-based professional education experiences for mathematics teachers. In this session the overarching question is: What are some ways in which reflective practice can be defined in professional preservice and inservice mathematics teacher education settings so that it can be nurtured, but also noticed and utilized to foster professional growth?

Ginger Rhodes, Dennis Hembree, University of Georgia
Professional Learning Communities: Hosting a Pre-Service Teacher for Professional Growth
To support on-going professional development, in-service teachers need opportunities to investigate their own teaching practices. At the University of Georgia, secondary in-service teachers at local schools participate in a multi-level professional development project in which hosting a preservice teacher provides a context for exploring teaching practices. In-service teachers have dual roles within the project; they investigate their own practice and act as professional developers of preservice teachers. A key component of the project is a focus on (school-based) professional learning communities. To encourage the development of professional learning communities, one university supervisor and a group of 3 to 5 preservice teachers are placed at each participating school. Members of each professional learning communities–in-service teachers, preservice teachers, and a university supervisor–meet weekly to explore aspects of students’ mathematical thinking through the use of artifacts from preservice teachers’ practice. The purpose of our paper is to describe this practice-based professional development project for in-service teachers.

Deborah Ball, Hyman Bass, Laurie Sleep, Mark Hoover Thames, University of Michigan
A Theory of Mathematical Knowledge for Teaching

Edward Silver, University of Michigan; Valerie Mills, Oakland Co. (MI) Schools; Alison Castro, Hala Ghousseini, Gabriel Stylianides, University of Michigan
Complementary Approaches to Mathematics Teacher Professional Development: Integrating Case analysis and Lesson Study in the BI:FOCAL Project

Paola Sztajn, University of Georgia
Documenting Learning Within School-Based Mathematics Education Communities of Teachers

Denise S. Mewborn, University of Georgia
Mathematics Teacher Education as Assisted Performance

2005 AERA Annual Meeting
American Educational Research Association
April 11-15, 2005, Montreal, Canada

Alison Castro, University of Michigan
Examining Mathematics Teachers' Use of the Teacher Guide during Planning
Given the potential importance of the Teacher Guide (TG) in shaping teachers’ planning decisions, this talk presents some preliminary findings about teachers’ use of the TG in their planning. Specifically, this paper explores how 12 middle school mathematics teachers use the TG from the Connected Mathematics Project (CMP) in their planning. The research questions guiding this study were: What constitutes use of the TG during planning? How do teachers use the TG in their daily planning? and What accounts for teachers particular use of the TG?

Paola Sztajn, Dorothy White, Martha Allexsaht-Snider, Amy Hackenberg, University of Georgia
Trust Among School-Based and University-Based Educators: Results From a Professional Development Project
This paper presents issues relating to trust in a school-based professional development project—Project SIPS (Support and Ideas for Planning and Sharing in Mathematics Education)—designed to help teachers improve the quality of their mathematics instruction by building a mathematics education community within their school. In the first year of SIPS, one of the main goals of the project was to begin building a mathematics education community at Adams Elementary School (pseudonym) and to develop trust among participants—in particular, trust among school-based and university-based educators. The paper discusses factors that helped the development of trust.

Deborah Ball, Geoffrey Phelps, Mark Hoover Thames, University of Michigan
Articulating Domains of Teacher Knowledge

Deborah Ball, Heather Hill, Hyman Bass, University of Michigan
Studying Mathematical Knowledge for Teaching

Hyman Bass, Jennifer Lewis, University of Michigan
Working Across Disciplines to Develop Measures of Teacher Learning

2005 NCTM Research Presession
National Council of Teachers of Mathematics
April 4-6, 2005, Anaheim, CA

Patricia Wilson, Dennis Hembree, University of Georgia; Tim Boerst, South Redford Elementary School/University of Michigan; Catherine Brown, Indiana University; Rheta Rubenstein, University of Michigan-Dearborn; Laurie Sleep, University of Michigan
Building Professional Communities of Mathematics Teacher Developers
The proposed thematic presentation will explore the notion of community building in relation to mathematics teacher developer learning. We propose to initiate a discussion on such communities by addressing: Who are mathematics teacher developers? What is the nature of professional development that could facilitate the learning and actions of teacher developers? How can we build professional communities to support the learning of mathematics teacher developers?

Deborah Ball, Laurie Sleep, Mark Thames, Teresa McMahon, University of Michigan; Paola Sztajn, Denise Mewborn, Andrew Tyminski, University of Georgia; Laura R. van Zoest, Diane Moore, Western Michigan University
Intentional Teacher Educator Preparation
Although there is a tendency to assume that successful classroom teachers or successful doctoral students will make successful teacher educators, the mathematics teacher education enterprise is sufficiently complex to warrant deliberate and specific attention during doctoral education. We consider approaches three different universities have taken to preparing Ph.D. students to be teacher educators and what we have learned about the development of teacher educators as a result. We will then engage in a discussion about the kinds of knowledge and experiences that will contribute to the development of effective teacher educators.

2005 NCSM Annual Conference
National Council of Supervisors of Mathematics
April 4-6, 2005, Anaheim, California

Invited Presentation: Deborah Loewenberg Ball
Learning the Mathematical Work of Teaching
Teaching mathematics involves substantial and often overlooked mathematical work. This session offers examples of that work, and explores practice-based ways to help teachers develop the necessary skill and fluency needed for these mathematical demands of teaching.

Valerie Mills, Oakland Schools, MI; Ed Silver, Dana Gosen, Gabriel Stylianides, Melissa Gilbert, University of Michigan; Geraldine Devine, Clarkston Community Schools, MI
Moving Beyond Implementation: Assisting Teachers to Use Standards-Based Mathematics Curriculum Materials to Promote Student Learning
Beyond Implementation: Focusing on Challenge and Learning (BI:FOCAL) is designed for experienced users of standards-based curriculum. Our professional development approach combines elements of lesson study with the analysis of narrative cases. We will illustrate this combined approachand describe some outcomes across two years of the project.

Annual Ethnography and Education Research Forum
February 25-26, 2005, Philadelphia, PA

Tim Boerst, University of Michigan and South Redfort School District (MI)
Using Public Knowledge of Mathematics Education: The Role of Localization in Supporting the Work of Practitioners and Professional Developers
There is increasing emphasis upon “results” and for educators to use “what works” to produce such results. Even if it were possible to agree upon what works, it is likely that such a body of knowledge would be expansive and require teachers to hold their knowledge in a far different way than in the past. Furthermore, chronic problems exist in disseminating and supporting teacher action based upon such information. This study contemplates the work of teachers in local professional development settings to collectively deliberate the meaning and utility of such information, but also what may need to be done to support teachers in their work to know, understand, and use publicly available information. Interactions of elementary teachers in professional development experiences and professional developers in the planning and reflecting upon those experiences are at the heart of this practitioner research. This session will provide rich descriptions and utilize discourse and frame analysis to unpack the ways in which professional developers and elementary teachers utilize and give meaning to public knowledge of mathematics education through a process of “localization” in their professional development work.

AMTE Ninth Annual Conference
Association of Mathematics Teacher Educators
January 28 – 29, 2005, Dallas, TX

AMTE Pre-Conference Work Session
Sponsored by The Center for Proficiency in Teaching Mathematics [CPTM]
The Professional Development of Professional Developers:
Continuing to Learn as Mathematics Teacher Educators

David Coffey, Grand Valley State University; Timothy Boerst, CPTM and South Redford School District; Laurie Sleep, University of Michigan.
Supporting Teacher Educator Learning: Four instances of teacher educator learning communities
Participants will examine several models currently employed by individuals associated with the Center for Proficiency in Teaching Mathematics that contribute to professional development of teacher educators — novice to expert. Participants will discuss important dimensions of professional development and ways to initiate novel forms of professional development at their own institutions.some of the mathematical games played with preservice teachers and will culminate with the analysis of their mathematical and pedagogical potential for teaching mathematics for elementary school preservice teachers.

Alison Castro, University of Michigan and Bob Allen, University of Georgia
A Novel Practice-Based Approach for the Professional Development of Teacher Developers.
In this session, we will describe the use of a laboratoryclass component in the design of professional development for teacher developers. Using video and textual artifacts from three different lab classes, we will engage participants in discussion around the affordances and limitations of laboratory classes as a tool for professional development.

Ed Silver, Alison Castro, and Hala Ghousseini, University of Michigan
Blending Elements of Lesson Study with Narrative Case Analysis and Discussion
In this session we consider how two popular approaches to mathematics teacher professional development can be blended. Using video and paper artifacts drawn from an ongoing project, we will describe and engage the attendees in discussion about the design and enactment of a synergistic approach that combines elements of lesson study with the analysis of narrative cases.

Ginger Rhodes, Judith Reed, and Dennis Hembree, University of Georgia
Expanding the Role of the Supervisor
In this session, we will report on a study investigating how university supervisors interpret their non-traditional roles as part of the PRIME project. This study informed our restructuring of university support to make the role more meaningful to both the supervisor and the participating mentor teachers.

MAA/AMS Joint 2005 Meeting
Mathematical Association of America and the American Mathematical Society
January 5-8, Atlanta, GA

Panel Discussion: Mathematicians as Educators
William McCallum, University of Arizona (moderator)

Kristin L. Umland, University of New Mexico
A Hybrid Model: The Role of Mathematician Educators in Mathematics Departments

Steven G. Krantz, Washington University in St. Louis
The Research Mathematician Looks at Classroom Teaching: a View from the Top

Raven McCrory, Michigan State University; Helen Siedel and Andreas Stylianides, Univ of Michigan
Undergraduate mathematics textbooks for prospective elementary teachers: Are books by mathematicians different?
We analyze four books written by mathematicians for undergraduate mathematics courses for elementary teachers (Beckmann, Darken, Jensen, and Parker/Baldridge). We contrast these texts with other books written for such courses, investigating whether they differ in systematic ways, and how they reflect different perspectives on mathematical knowledge. The paper includes a content analysis, which considers all the chapters and topics; and a topical analysis focused on multiplication, rational numbers, and reasoning and proof.
Results suggest that, although the content of the textbooks is similar, there are differences in the level of mathematical rigor; the extent to which the text uses pedagogical tools as mathematical objects; and the explicitness of attention to aspects of mathematical thinking such as the nature of definition, mathematical reasoning, or axiomatic system. The new books by mathematicians are less encyclopedic than the comparison books, and each has a perspective on mathematics that permeates both the rhetorical stance of the book and the actual presentation of the mathematics. While many of the texts give equal emphasis to all topics in the elementary curriculum, the mathematicians' books provide a more nuanced perspective on mathematics.

AMS-MAA-MER Special Session on Mathematics and Education Reform

Patricia S. Wilson and Jeremy Kilpatrick,University of Georgia
Faculty Resources for Improving the Mathematical Education of Teachers From the Center for Proficiency in Teaching Mathematics
The principal aim of the Center for Proficiency in Mathematics Teaching (CPTM) is to build the capacity of the system of professional education for pre-service and practicing teachers of mathematics. We focus on the improvement of teachers’ opportunities to learn mathematics for teaching and to learn to use mathematical knowledge effectively in practice. CPTM is a National Science Foundation (NSF)-funded Center for Learning and Teaching involving the University of Georgia and the University of Michigan. CPTM supports and investigates a variety of approaches for the education of professionals who prepare teachers of mathematics. This includes mathematicians, doctoral students in mathematics and mathematics education, post-doctoral fellows seeking to develop specialization in the mathematics education of teachers, mathematics educators, mathematics teacher leaders, local curriculum and professional education specialists. Our session will report and discuss its activities for those who teach mathematics for teachers at all grade levels. Our activities include doctoral programs, postdoctoral programs, certificate programs for doctoral students, summer institutes, study groups, research and materials preparation for professional development.

2004 Conferences

SSMA 2004 Conference
School Science and Mathematics Association
October21 - 23, 2004, Atlanta, GA

Bob Allen, Stephen Bismarck, and Tom Ricks, University of Georgia
Discussant: Mark Hoover Thames, University of Michigan
Tensions within Professional Development Experiences
Any educator who has participated in professional development activities will attest to the difficulty of being simultaneously both a learner and someone who is trying to reflect on that learning with an eye toward incorporating it into teaching practice. Through a presentation of examples from the NSF-funded Center for Proficiency in Teaching Mathematics, we will discuss structures and vocabulary for thinking about tensions within professional development. There will be a discussant and time for questions.

PME-NA 2004 Conference
North American Chapter of the International Group for the Psychology of Mathematics Education
October 21-24, 2004, Toronto, Ontario, Canand

Melissa Gilbert, Alison Castro, Dana Gosen, and Edward Silver
Beyond Implementation: Improving Teachers' Use of an Innovative Middle School Mathematics Curriculum
This presentation traces changes in teachers' thinking about lesson planning during the first year of a multi-year professional development project that addresses the needs of middle school mathematics teachers who are experienced users of one innovative mathematics curriculum for the middle grades, Connected Mathematics. We analyze the components of lessons that draw their attention in planning, the resources on which they draw when planning, the nature of their engagement with resources for planning, and their self-assessment of the impact of planning on their students' opportunities to learn.