
2008
2007
2006
2005
2004
2003
2008 Conferences
American Educational Research Association
(AERA)
http://www.aera.net/meeting/
March 2428, 2008; New York, NY
CPTMrelated activities and presentations: In
case of mixed groups of presenters, the CPTMassociated 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 FieldBased Education and Research
Abstract:
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
inservice and preservice 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 CaliforniaBerkeley
Developing an Integrated Assessment System (DIAS) in Elementary
Mathematics Teacher Education: Constructing and Interpreting Records
of Practice Session
Abstract:
This interactive symposium
brings together scholars from four distinct, multidisciplinary,
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
inservice 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 audiorecords, 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
Abstract:
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
daytoday, momenttomoment demands of teaching. These analyses
helped to support the development of a practicebased 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 NSFfunded
database, documenting an entire year of the mathematics teaching
in a third grade public school classroom during 198990 . 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 “practicebased
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 practicebased 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 HighQuality Learning Environments: An Exploratory Study
Abstract:
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 lowMKT 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 highquality 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
Abstract:
In this paper, I examine the structure of deliberate rehearsal of practice in the context of a study that focused on preparing preservice 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 NonContingent: The Professional Development Model of Japanese Lesson Study
Abstract:
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
Abstract:
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 multiyear 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
Abstract:
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?
Abstract:
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 MarylandCollege Park; Orrin T. Murray, (University
of Michigan;
Migrating Components of FacetoFace PD Online: Results of the OPMD Project
Abstract:
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 facetoface development opportunities is nascent. Moreover, few if any studies compare the differences between facetoface and online learning in any instance. This study focuses on: Challenges and successes related to migrating components of a proven facetoface professional development model to an online format Evidence of consistent mathematical content knowledge growth, and consistent adoption of standardsbased mathematics instructional practices across both formats
Association of Mathematics Teacher Educators
(AMTE)
http://www.amte.net/conf_index_2008.shtml
Jan. 2426, 2008; Tulsa, OK
CPTMrelated activities and presentations: In
case of mixed groups of presenters, the CPTMassociated 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
Abstract:
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
Abstract:
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
Abstract:
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 middleschool
teachers that sought to help them reconsider their assessment practices.
Session34
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?
Abract:
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
Abstract:
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
Abstract:
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
Abstract:
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
Abstract:
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
Abstract:
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)
Abstract:
Using data from focus groups and from an online survey, we examine
how teacher developers who had participated in an 8day summer institute
on MKT viewed that concept 2 years later and had used it in their
practice.
2007
Conferences
American Educational Research Association
(AERA)
http://www.aera.net/meeting/
April 913, 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 FifthGrade Mathematics Abstract:
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 nonexistence 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 PracticeBased 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 daytoday, momenttomoment demands. These analyses
help to support the development of a practicebased 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 HighLeverage Mathematics Teaching Practices
Abstract:
This paper presents our ongoing 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 semesterlong 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 practicebased 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 practicebased 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 practicebased
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
Abstract:
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
Abstract:
In the first paper we investigate the notion of using "practicebased"
activities and resources for teacher learning. This approach has
garnered growing support (Ball & Cohen, 1999; Wilson & Berne, 1999;
DarlingHammond, 1998; Lampert & Ball, 1998), but there is no professional
consensus about what it means for a methods course to be practicebased.
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 fieldbased 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
Abstract:
The emphasis on reasoning in mathematics education has placed mathematical
discourse at its heart (NCTM, 1991). This makes it a necessity to
prepare preservice 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 preservice 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 (FeimanNemser,
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 preservice teachers' knowledge
about leading productive mathematics discussions. I describe the
nature of these routines and the way they were used to allow preservice
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 PracticeBased Professional Development
Abstract:
The paper reports on the mathematics that may be learned through
practicedbased 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 multiyear,
practicebased 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 openingactivity 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 precollege 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?
Abstract:
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 conceptuallyoriented
mathematics, but who differ dramatically in their mathematical knowledge.
The higherknowledge teacher, as measured by her multiple choice
score, has many features of highquality 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 lowerknowledge 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 highknowledge
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 lowknowledge
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?
Abstract:
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 practicebased
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
Abstract:
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 indepth 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 ontask
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 ContentFocused Professional Development: Its
Influence on Teaching Quality
Abstract:
This paper searches for evidence of change in the mathematical quality
of teachers’ practice as a result of their participation in contentfocused,
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 meaningoriented 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
Abstract:
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 K12 mathematics, with mathematics
as it is presented in the K12 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 prealgebra
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)
http://www.nctm.org/
March 2124, 2007; Atlanta, GA
Research Presession: March 1921, 2007
CPTMrelated activities and presentations (In
case of mixed groups of presenters the CPTMassociated 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 PracticeBased
Methods Course
Abstract:
This session will report on the design and implementation of a methods
course focused on helping preservice teachers learn to enact “high
leverage” practices. After presenting our criteria for highleverage
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
Abstract:
Researchbased 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
Abstract:
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
Abstract:
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 K12 Engineering and Technology
Education Teachers
February 1214, 2007; Dallas, TX
Pat Wilson, Susan Mundry, David Burkhardt, and Michael Hacker
Abstract:
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 engineeringoriented technology education.
Association of Mathematics
Teacher Educators (AMTE)
http://www.amte.net/
January 2527, 2007; Irvine, CA
CPTMrelated activities and presentations: In
case of mixed groups of presenters, the CPTMassociated presenter
is highlighted.
PreSession
Wednesday, Jan. 24, 2007 Thursday, Jan. 25, 2007
CPTM Summer 2004 Institute FollowUp
Abstract:
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
FollowUp can be found at Resources.
Judith E. Jacobs Lecture
Deborah Loewenberg Ball, University of Michigan
The Core and Contemporary Challenges of Mathematics Teacher Education
Abstract:
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
Abstract:
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?
Abstract:
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
Abstract:
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?
Abstract:
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
Abstract:
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 standardsbased
instruction) through incorporating classroom data into ongoing site
and universitybased 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
Abstract:
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
Abstract:
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 CaliforniaLos 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
Abstract:
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
Abstract:
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?
Abstract:
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 Practicebased Professional Development Help Teachers
Learn Mathematics?
Abstract:
Practicebased 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
practicebased, 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
Abstract:
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 (PMENA)
PMENA
November 9 to 12, 2006
Mérida, Yucatán Universidad Pedagógica Nacional
Silvia Alatorre, Chair
http://www.pmena.org/2006/
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 "TeachingRelated 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 UnitsCoordinating Scheme on Conceptual
Understanding of an Improper Fraction (short oral)
Denise Natasha BrewleyCorbin, 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 ReformBased Classroom (poster)
Joint NSFCLT 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 (612) 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 612 mathematics classrooms using reform curricula
or in classes for preservice or inservice teachers preparing to
use reform curricula in grades 612.
TEAMMath Conference
Tuskegee University, August 26, 2006
Keynote Address
Patricia S. Wilson, University of Georgia
Developing a Deep Understanding of Mathematics
Abstract:
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)
http://igpme.org/
July 1621, 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 0710, 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 wellbeing. 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 notsosuccessful 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:
policymakers, 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)
http://www.nctm.org/
April 2629, 2006; St. Louis, Missouri
Research Presession: April 2426, 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 MidAtlantic 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 PracticeBased Professional Development for Teacher
Educators
Description:
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)
http://ncsmonline.org/
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 standardsbased curricula and illuminate persistent
dilemmas of good mathematics teaching that are not "solved" by introducing
new curriculum materials.
American Educational Research Association
(AERA)
http://www.aera.net/meeting/
April 711; 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 Practicebased
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 StudentTeaching
Experience
Abstract:
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. Thirtynine mentors and thirtytwo 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)
http://www.amte.net/
January 2628, 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 inservice
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
CrossInstitutional 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 (teresam@umich.edu)
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
AMSMAA Joint
Mathematics Meetings
January 1215, 2006; San Antonio, TX
Jeremy Kilpatrick, University of Georgia
Math War Veteran Tells All
The socalled 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 (PMENA)
Frameworks
that Support Research and Learning
Ocotober 2023, 2005, Roanoke, VA
Virginia Polytechnic Institute and State University
Denise Mewborn, University of Georgia, Panelist
Framing Our Work
Abstract:
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?
Abstract:
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
Abstract:
Mathematical caring relations (MCRs), a framework for conceptualizing
studentteacher interaction, was used in a yearlong 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 (K8): Why, What, and How?
May 2528, 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 1521, 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
Abstract:
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
Abstract:
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 curriculumbased
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 multiyear, 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 Practicebased Professional Learning Experiences
Abstract:
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 practicebased
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 PreService
Teacher for Professional Growth
Abstract:
To support ongoing professional development, inservice teachers
need opportunities to investigate their own teaching practices.
At the University of Georgia, secondary inservice teachers at local
schools participate in a multilevel professional development project
in which hosting a preservice teacher provides a context for exploring
teaching practices. Inservice 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 (schoolbased) 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–inservice 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
practicebased professional development project for inservice 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 SchoolBased 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 1115, 2005, Montreal, Canada
Alison Castro, University of Michigan
Examining Mathematics Teachers' Use of the Teacher Guide
during Planning
Abstract:
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 AllexsahtSnider, Amy Hackenberg,
University of Georgia
Trust Among SchoolBased and UniversityBased Educators:
Results From a Professional Development Project
Abstract:
This paper presents issues relating to trust in a schoolbased 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 schoolbased and universitybased 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 46, 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 MichiganDearborn;
Laurie Sleep, University of Michigan
Building Professional Communities of Mathematics Teacher
Developers
Abstract:
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
Abstract:
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 46, 2005, Anaheim, California
Invited Presentation: Deborah Loewenberg Ball Learning
the Mathematical Work of Teaching Abstract:
Teaching mathematics involves substantial and often overlooked mathematical
work. This session offers examples of that work, and explores practicebased
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
StandardsBased Mathematics Curriculum Materials to Promote Student
Learning
Abstract:
Beyond Implementation: Focusing on Challenge and Learning (BI:FOCAL)
is designed for experienced users of standardsbased 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 2526, 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
Abstract:
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
PreConference 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
Abstract:
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 PracticeBased Approach for the Professional Development
of Teacher Developers.
Abstract:
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
Abstract:
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
Abstract:
In this session, we will report on a study investigating how university
supervisors interpret their nontraditional 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 58, 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?
Abstract:
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.
AMSMAAMER 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
Abstract:
The principal aim of the Center for Proficiency in Mathematics Teaching
(CPTM) is to build the capacity of the system of professional education
for preservice 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, postdoctoral
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
Abstract:
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 NSFfunded 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.
PMENA
2004 Conference
North American Chapter of the International Group for the Psychology
of Mathematics Education
October 2124, 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
Abstract:
This presentation traces changes in teachers' thinking about lesson
planning during the first year of a multiyear 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 selfassessment of the impact
of planning on their students' opportunities to learn.
