
20062007 CPTM
Colloquium Series – UM
Details (including audio and video feeds) on 20062007 colloquia at UMICH can be found at http://cptm.soe.umich.edu/umcolloquia.html
March 2007
Mary Kay Stein, University of Pittsburgh
February 2007
Carol Malloy, University of North Carolina
January 2007
Miriam Sherin, Northwestern University
December 2006
Michael Weiss, University of Michigan
Mathematical Knowledge for Teaching Geometry: The Case of
Math 431
Abstract:
I will report some preliminary findings from a study
of Math 431 ("Topics in Geometry for Teachers"), a math department
course required for all preservice secondary mathematics teachers
at UM. In particular, I will discuss the role that specialized
mathematical knowledge and experiences can play in the teaching
of high school geometry, and the role that a course like Math 431
could play in helping to prepare preservice teachers for the challenges
they will face in their future practice.
Mary Kennedy, Michigan State University
Where is the Role for Knowledge in Teaching?
November 2006
Michael Battista, Michigan State University
Cognition Based Assessment in Elementary Mathematics: Student
and Teacher Learning
Heather Hill, University of Michigan
The Mathematical Knowledge of Middle School Teachers: Implications
for the No Child Left Behind Policy Initiative
September 2006
James W. Stigler, UCLA and LessonLab Research Institute
UCLA and LessonLab Research Institute Improving Mathematics
Teaching: A Journey Beyond TIMSS Video
Patricio Herbst, University of Michigan
Representations of Teaching and Their Use in Studying the
Rationality of Practice
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20042005 CPTM
Colloquium Series – UM
April 2005
Daniel Bernard Martin,University of Illinois at Chicago
Mathematics Learning and Participation as Racialized Forms
of Experience:
African Americans Frame Mathematics, Teachers, and Mathematics Teaching
Abstract: This presentation draws on findings from three interrelated studies of the mathematical experiences and identities of African American adults and adolescents. I draw from earlier findings suggesting that as participants situate mathematics learning and literacy within larger social, cultural, political, and economic contexts, they render mathematics learning and participation as racialized forms of experience. I wish to extend these findings, arguing that mathematics education reform efforts which frame equity as a residual effect or natural outcome of 'good teaching' and the implementation of 'good curriculum materials' are shortsighted, not only in their conceptualizations of teaching and curricula, but of equity as well. Missing from this frame, I argue, is a fuller consideration that regards equity as being inextricably part and parcel of teaching and curricula. In my research with African Americans adults and adolescents, good teaching and good curricula are viewed as necessary but not sufficient considerations in highly racialized contexts surrounding mathematics learning and participation.
About the presenter:
Danny Martin is an associate professor in mathematics
education at the University of Illinois at Chicago. He holds a Ph.D.
in mathematics education and a M.A. in mathematics, both from the
University of CaliforniaBerkeley, a B.S. degree in mathematics and
physics from Carroll College, Wisconsin. His research and writings
focus on mathematics success and failures among African American youth
and issues of Identity and Agency among African American Adults and
Adolescents.
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December 2004
Hyman Bass, University of Michigan
Mathematics, Mathematicians, and Mathematics Education
Abstract: The talk probes two related
questions: What is special about what research mathematicians can
bring to solving problems of mathematics education? What does it
take to foster productive involvement of mathematicians in mathematics
education?
Mathematics is, quintessentially, a discipline not only of discovery
and creation, but also of learning and teaching. As new ideas develop,
the professional community absorbs, critiques, transforms and transmits
its collective knowledge. However, the learning of mathematics
outside the profession has often been a site of difficulty as children
and their teachers struggled to reach and use the tools and ideas
of the discipline, which are subtle, powerful, and elegant even
at the most elementary levels. Some mathematicians have therefore,
across time, concerned themselves with the learning of young people
for whom the knowledge and skills of mathematics compose both an
essential literacy and a rich cultural heritage.
Involvement in the challenges of mathematically educating diverse populations of children is a form of professional work in which there is now a growing interest among mathematicians. This involvement can be usefully understood as a form of "applied mathematics," in that the work entails application of mathematical knowledge and skills, but combined with sensitive understanding of extramathematical aspects of the contexts in which the mathematical problems are situated. Still, what mathematicians can contribute, and in what ways, is far from obvious. After all, they typically know little about how young learners encounter and develop mathematical ideas. The forms in which mathematicians hold their knowledge are highly compressed and efficient. Yet teaching, especially at the elementary levels, requires an "unpacking" of this knowledge that is neither natural nor easy for professional mathematicians. And much universitylevel instruction is remote from practice in schools.
This talk examines three cases of mathematicians' work on educational problems. I analyze the focus and nature of their educational work, and consider some of the contributions yielded in each case, and how those contributions drew on their mathematical training, habits, knowledge, and dispositions. In each case, specific examples will be illustrated, and an inside view of the nature of the mathematical work analyzed. I have chosen two prominent examples  Felix Klein and Hans Freudenthal  to illustrate the sorts of work that leading mathematicians have done in education. I chose them because their stories provide edifying examples of what mathematicians are able to contribute professionally, and because their contributions can inspire others. In the third case, which focuses on my own work with Deborah Ball on the nature of the mathematical knowledge needed for teaching, I consider also what I have been learning about what supports effective engagement of mathematicians in educational problems.
About the presenter:
Hyman Bass is the Roger Lyndon Collegiate Professor of Mathematics and Professor of Mathematics Education at the University of Michigan. Prior to 1999 he was Adrain Professor of Mathematics at Columbia University. His mathematical research publications cover broad areas of algebra with connections to geometry, topology, and number theory. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences. Bass is president of the American Mathematical Society. He recently chaired the Mathematical Sciences Education Board at the National Research Council, and the Committee on Education of the American Mathematical Society; he is currently President of the International Commission on Mathematics Instruction.
During the past five years he has been collaborating with Deborah Ball and her research group at the University of Michigan on the mathematical knowledge and resources entailed in the teaching of mathematics at the elementary level. He has helped to build bridges between diverse professional communities, especially between mathematicians and other stakeholders involved in mathematics education.
October 2004
Anna Sfard, Michigan State University & University of Haifa in Israel
Mathematics as a Form of Communication:
What it means and how it adds to our understanding of teaching and
learning
Abstract:
In the domain of mathematics education, the term discourse seems
to be these days on everybody's lips. Although traditionally regarded
as only auxiliary to thinking, mathematical communication is believed
to enhance mathematical learning. In my research, I am going farther
than that: I conceptualize mathematics as a special form of communication.
By doing this, I promote mathematical discourse from the role of
a mere instructional means to that of the object of learning. During
the meeting, we shall explore the implications of the communicational
perspective for our vision of mechanisms of learning and teaching.
To help with the task, I will present in parallel two classroom
studies, one devoted to the learning of signed numbers and the other
dealing with young children first introduced to school geometry.
The analysis of the empirical data will be guided by three queries:
(1) The question about mathematics: What is it that is supposed
to change in children's discourse in the course of learning? (2)
The question about teaching: What is supposed to induce the change?
(3) The question about learning: What are the short and longterm
effects of the discoursemolding attempts orchestrated by the teacher?
The results of these analyses will compel us to take a critical
look on a number of popular pedagogical beliefs.
About the presenter:
With a formal background in mathematics and physics, and with a lifelong interest in history, philosophy and language, Anna Sfard specializes today in mathematics education, focusing her research on the intricacies of human learning and creative thinking. The overarching theme of her work is the constitutive role of language. More specifically, she investigates the implications of the assumption that human thinking as a particular case of communicative activity. In her research she tries to map the development of mathematical discourse, with the word development referring both to learning and to the historical evolution of this discourse. In this endeavor, a special place is devoted to the issue of objectification, that is, to the origins of mathematical objects and, in particular, to the question of the transition from operational to structural thinking (reification). In a series of studies she has been conducting in Israel, Canada, and US, most of them together with her PhD students, she has been investigating such topics as the development of algebraic discourse, the discourse on negative numbers, early numerical discourse, the mathematical discourse of students diagnosed with learning disabilities and of those who count as highachievers, and the professional discourse of highschool mathematics teachers. The results of this research have been published in numerous articles and book chapters and are being summarized in the book in writing. In addition to her research work, she has been participating for many years in developing new mathematics curricula for Israeli senior secondary schools and serving as the editor of the Israeli Journal for Mathematics Teachers.
September 2004
Deborah Ball, Hyman Bass, Ed Silver, The University of Michigan
Teaching the Teachers of Teachers:
Supporting People Who Teach and Work With Teachers of Mathematics
Abstract:
The primary focus of the Center for Proficiency in Teaching Mathematics is on the development of leaders among those who provide education and professional development for teachers of mathematics. At the basic level, CPTM's research and development efforts address what constitutes highquality professional education for teachers. We design and study approaches to teachers' learning, with particular emphasis on the development of teachers' mathematical knowledge for teaching and situating teachers' professional learning in practice.
In this third year of its five year grant period, the Center focuses on the following questions: What do the "teachers of teachers" have to know and be able to do to help teachers learn from their own practice and from that of others? How do those professionals have to know mathematics? What are effective approaches to the design and delivery of professional development of teachers of mathematics?
In this talk, we will discuss the design of alternative approaches to supporting the learning of those who work with teachers, from study groups to intensive national workshops and community building, and we will discuss how our ongoing research examines the demands and effects of these different approaches. Our research questions are closely tied to our work on developing teachers' mathematical knowledge, to connecting teachers' learning opportunities to practice, and to both facilitating and examining carefully the professional learning of those who teach and work with teachers of mathematics.
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Mathematics Education Leadership Conference
MathematicalKnowledgeforTeaching (MKT)
Cosponsored by UM School of Education and CPTM
May 21, 2004 – 8:30 a.m. – 4:15 p.m.
University of Michigan School of Education
 What is the mathematical knowledge needed for teaching?
 How can we design opportunities for teachers to gain that knowledge?
Featured Keynote Speaker:
Judith Ramaley heads the Education and Human Resources Directorate of the National Science Foundation.
Invited presenters included:
Deborah Loewenberg Ball (UM), Hyman Bass (UM), Timothy Boerst (South Redford School District), Judith Flowers (UMDearborn), Patricio Herbst (UM), Heather Hill (UM), Mark Hoover (UM), Magdalene Lampert (UM), Valerie Mills (Oakland Intermediate School District), Raven Wallace (MSU)
Topics included:
Exploring the connections between mathematics content learning and mathematics methods in both elementary and secondary levels
Measuring mathematical knowledge for teaching
Using Case Studies as a resource in developing mathematical knowledge for teaching through professional development
Assessing and developing resources for mathematics teacher education
The Center for Proficiency in Teaching Mathematics is funded
by the National Science Foundation (NSF.gov) from the Centers for
Learning and Teaching Program.
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20032004 CPTM Colloquium Series – UM
Abstracts follow in reverse chronological order.
April 2004
Guershon Harel – University of California, San Diego
On the Learning and Teaching of Proof
Abstract:
The presentation will address
the following questions: what are students’ understandings of proof?
Are students’ difficulties with proofs avoidable? What can we learn
from history about the difficulties students encounter with the
concept of proof? What sorts of experiences seem effective in shaping
students’ understandings of proof? Are there promising frameworks
for teaching the concept of proof so that students appreciate the
value of justifying, the role of proof as a convincing argument,
the need for rigor, and the possible insights gained from proof?
February 2004
Valerie Mills – Oakland County Schools
Edward Silver – University of Michigan
Refocusing Attention to Build Proficiency: Helping Teachers Support Student Thinking and Learning in the Mathematics Classroom
Abstract:
In this presentation we will discuss our work in the
BI:FOCAL project with middle school mathematics teachers in the Oakland
Intermediate School District. We will explain how the project addresses
fundamental issues in mathematics teacher professional development
and illustrate how we do so using a blend of three practicebased
approaches: curriculumbased professional development, case analysis
and discussion, and lesson study. We will also discuss BIFOCAL as
an instantiation of several core, defining themes of the Center for
Proficiency in Teaching Mathematics (CPTM).
January 2004
A Showcase of Professional Development Opportunities
Deborah Ball, Hyman Bass, Teresa McMahon, and Edward Silver
will present an overview of the Center for Proficiency in Teaching
Mathematics (CPTM) professional development activities taking place
in Ann Arbor this spring. Each event provides a number of opportunities
for interested students to gain experience in planning, implementation,
and/or research. Events include:
Mathematics Education Leadership Conference: Friday, May 21, 2004
CPTM Summer Institute for Educators of Mathematics Teachers: June
512, 2004
CPTM Summer Institute Doctoral Seminar: Held in conjunction with
Summer Institute and taught by Edward Silver (University of Michigan)
and Jeremy Kilpatrick (University of Georgia)
Margaret Schwan Smith – University of Pittsburgh
Tracing the Development of Teachers’ Understanding of Proportionality in a PracticeBased Course
About the presenter:
Dr. Smith currently
works with preservice elementary, middle, and high school mathematics
teachers at the University of Pittsburgh, with doctoral students in
mathematics education who are interested in becoming teacher educators,
and with practicing middle and high school mathematics teachers and
coaches in the L.A. Unified School District. Her primary interest
is in the professional education of teachers of mathematics. Dr. Smith
is also the coauthor of Implementing StandardsBased Mathematics
Instruction: A casebook for professional development, that grew out
of the work of the QUASAR project. In addition, she has authored a
book entitled, Practicebased Professional Development for Teachers
of Mathematics. She is currently the director of the NSFfunded ASTEROID
project, which is studying what teachers learn from COMET cases and
other practicebased professional development experiences, and of
the ESP project that is focusing on enhancing the preparation of preservice
secondary mathematics teachers.
November 2003
Patricio Herbst
Asking Epistemological Questions About Educational Practice: The place of proof in geometry instruction
Abstract:
Mathematical activity inside schools is different
than in mathematical research or in streetselling – how so and why?
What is it about doing mathematics in classrooms that shapes the subject
in ways that are surprising to outsiders? These broad questions point
to a way of inquiring into mathematicseducational practices that
seeks to describe epistemological phenomena and explain them in terms
of the institutional and interactive conditions that make room for
and shape those practices. This talk will delve into that way of inquiry
in general, and will illustrate how such inquiry proceeds in the particular
case of examining the place of proof in high school geometry instruction
in the U.S.
October 2003
Orrin Murray
Taking Records of Practice to the Next Level: Using personal digital technologies to develop records of practice in support of continuous improvement of practice
Abstract:
In 1989, Magdalene Lampert and Deborah Ball took
records of teaching practice into the world of multimedia. The Mathematics
and Teaching Through Hypermedia (MATH) project demonstrated the
power of record making, supported by technology, for both the inclass
educator and the education researcher interested in teacher education.
This talk will consider how personal digital technologies, such
as digital cameras and laptop computers, can be used by any teacher
to create and make use of records of their own teaching practice.
Will Oonk
Freudenthal Institute, Netherlands
Going the Extra MILE: Practicebased professionalization in mathematics teacher education
Abstract:
This talk will describe six years of development of
a multimedial learning environment (MILE) for elementary mathematics
education students in the Netherlands and associated research on the
project. Research on student teachers’ use of theoretical knowledge
as they reflect on practice will be presented, with a focus on how
the level of structuring and scaffolding by the multimedia environment
and the teacher educator affects students’ use of video cases.
September 2003
Magdalene Lampert
Teaching Materials, School Organization, and Teacher Learning
Abstract:
This talk will report on part of a three year research study of
teaching and teacher learning. Using data collected in a school
for the teaching of Italian in Rome, it will describe the construction,
maintenance, and function of an archive of tasks for teaching and
learning used by all teachers in the school. It will investigate
how the nature of tasks provide opportunities for teachers to learn
about students and subject matter. It will examine the relationship
between the archive as a resource for teachers' ongoing professional
development and the organization of a school with a focus on how
the structure of the school supports resource use. Implications
for developing proficiency in teaching mathematics will be discussed.
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20022003 CPTM Colloquium Series – UM
Abstracts follow in chronological order
November 2002
Ruth Heaton and James Lewis  University of Nebraska, Lincoln
Abstract:
The mathematics education of teachers should be viewed as a partnership
between mathematics and mathematics education faculty. We recommend
that there needs to be collaboration between mathematics faculty
and school math teachers. We will review a partnership at the University
of NebraskaLincoln that involves faculty in mathematics, mathematics
education, and Lincoln Public School teachers. The Math Matters
project is designed to strengthen the preparation of future mathematics
teachers, the centerpiece of which is a block of courses that integrates
math instruction with pedagogical instruction and field experiences.
We will discuss our experiences in building a partnership between
education and mathematics faculty, and mathematics teachers as well
as our efforts to deepen students’ mathematical understanding while
connecting the mathematics to their work as a teacher.
February 2003
Anna Sfard – University of Haifa, Israel
Mathematical Identities for Better or Worse, or the Collective
Making of Mathematical Success and Failure
Abstract:
Why do some students succeed in mathematics, while others do not?
This talk explores the possibility that mathematical successes and
failures are not the simply result of the abilities and disabilities
of individual learners, but instead are produced collectively by
all those involved in the process of learning, teaching and assessing.
Two examples will be used to show that how successful a student
is in becoming mathematically competent depends on her/his "designated
identity", that is, on how she/he is perceived as a mathematics
learner by teachers, fellow students, institutions, parents, etc.
The two studies show that collectively constructed designated identities
of the students are a doubleedged sword, and while they always
seem to have a decisive impact on students’ learning, this impact
is sometimes for better, and sometimes for worse.
Panel Discussion
Mathematicians and the Mathematical Education of Teachers
Panelists:
Dick Askey – University of Wisconsin
Roger Howe – Yale University
Jim Lewis – University of Nebraska
Bill McCallum – University of Arizona
Dick Stanley – University of California, Berkeley
H. H. Wu – University of California, Berkeley
Abstract:
The panel of research mathematicians will address
the following questions:
Why should mathematicians take an interest in the math education
of preservice teachers?
What do you see as the biggest problems that need attention in how
preservice teachers at all level learn math for teaching?
What do mathematicians have to learn to engage productively in teaching
such courses?
Besides teaching, what are other ways that mathematicians can contribute
helpfully to the math education of teachers?
How can mathematics departments support teacher education?
Anna Sfard – University of Haifa, Israel
Mathematical Identities for Better or Worse, or the Collective Making of Mathematical Success and Failure
Abstract:
Why do some students succeed in mathematics, while others do not?
This talk explores the possibility that mathematical successes and
failures are not the simply result of the abilities and disabilities
of individual learners, but instead are produced collectively by
all those involved in the process of learning, teaching and assessing.
Two examples will be used to show that how successful a student
is in becoming mathematically competent depends on her/his “designated
identity”, that is, on how she/he is perceived as a mathematics
learner by teachers, fellow students, institutions, parents, etc.
The two studies show that collectively constructed designated identities
of the students are a doubleedged sword, and while they always
seem to have a decisive impact on students’ learning, this impact
is sometimes for better, and sometimes for worse.
Richard Colvin – Deputy Director of the Hechinger Institute on Education and the Media at Teachers College, and an awardwinning education writer for
the L.A. Times
Misguided Metaphors: Miscommunication, Misunderstanding and Missed Opportunities
Abstract:
Educators rely heavily on metaphors for communicating their methods
and philosophies to one another as well as to the public, but many
of these metaphors are overused and serve to obscure rather illuminate.
The popular press has picked up on those metaphors as a shorthand,
pitting “reform” math teaching against “traditional” math teaching
and “whole language” against phonics. At a time when practitioners
and researchers are increasingly finding common ground, they need
to also work on developing new language to talk about their agreements,
even as they continue to explore areas of disagreement as to which
camp they need to pledge allegiance. Journalists also need to find
new ways to illuminate these debates more clearly and resist the impulse
to foment conflict.
March 2003
Suzanne M.Wilson – Michigan State University
Based on her new book, California Dreaming: Reforming Mathematics Education
Abstract:
This is the complex story of a serious multidisciplinary effort to
change and improve mathematics instruction in California, designed
with attention to the multiple layers of reform. In part, this discussion
is also about much more than the struggles of educational policy and
practice in California. The issues in this presentation and book are
of interest to more than the mathematics educators, policy researchers,
and the players whose stories populate the book.
May 2003
James Hiebert – University of Delaware
TIMSS 1999 Video Study of Mathematics Teaching: Are the findings relevant for the U.S. debate?
Abstract:
The recent TIMSS video study shows that highachieving countries teach
mathematics in different ways – different from each other and different
from the U.S. While some features of teaching on which these countries
differ are often contested in the U.S, a few of these features seem
to be shared among highachieving countries. Both cases will be examined
for their relevance to current discussions about mathematics teaching
in the U.S.
June 2003
Sarah Theule Lubienski – Iowa State University
Race and SESRelated Trends in NAEP Data
Abstract:
Drawing from her analyses of 1990, 1996 and 2000 data from the National
Assessment of Educational Progress (NAEP), Dr. Lubienski will discuss
race and SESrelated trends in student mathematics achievement,
beliefs, classroom experiences, course taking patterns, and teachers’
educational backgrounds. Although overall mathematics achievement
increased from 1990 to 2000, racerelated achievement gaps did not
improve. This study reveals similarities and differences in students’
classroom experiences and attitudes, thereby shedding light on factors
that could shape achievement differences.
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