National Summit on the Mathematical Education of Teachers:
Meeting the Demand for High Quality Mathematics Education in America

November 2 and 3, 2001, Tysons Corner Doubletree Hotel, Tysons Corner VA

Working Group Sessions - Presenters and Abstracts

The table below gives a brief overview of the small group working sessions, showing the level of teacher preparation (elementary, middle, or high school) and noting partnerships and other special features involved.  Abstracts of all the presentations follow the table. All participants will be asked their choices of sessions to attend and will be assigned working groups according to those choices and space available.  

#1. The Role of Understanding Children's Thinking in Convincing Teachers that They Must Develop a Profound Understanding of the Mathematics They Teach

Presenter: Judith Sowder, San Diego State University

A project that provides prospective teachers access to student thinking through interviews and videos will be described. The goal of the project is to convince future teachers, during their first mathematics content course, that they must understand elementary school mathematics at a level that will allow them to provide different approaches to teaching, and access to what children can do and understand. Mathematics and education faculty work together to provide these experiences to prospective teachers. Some video clips of children's mathematical reasoning will be shared and discussed.

#2. Developing Mathematical Ideas: A Resource for Teaching Mathematics

Presenter: Deborah Schifter, Center for Learning, Teaching, and Technology, Educational Development Center

Developing Mathematical Ideas (DMI) is a curriculum for teacher learning designed to help teachers think through the major ideas of K-7 mathematics and examine how children form these ideas. In this session, Deborah Schifter will provide an overview of the DMI materials and then take participants through the treatment of one idea in particular--that of the
area of the triangle--to illustrate some of the issues that many teachers (and many college students, too) must work on in order to learn this content.

#3. Strengthening the Mathematics Education of Elementary School Teachers: A Partnership between the Teachers College and the Department of Mathematics and Statistics at the University of Nebraska-Lincoln

Presenters: Ruth Heaton and James Lewis, University of Nebraska

The Mathematical Education of Teachers recommends that the mathematical education of teachers be viewed as a partnership between mathematics faculty and mathematics education faculty and further recommends that there needs to be more collaboration between mathematics faculty and school mathematics teachers. This session will review one such partnership at the University of Nebraska-Lincoln that brings together faculty in Teachers College, faculty in the mathematics department, and Lincoln Public School teachers.

UNL’s Math Matters is a NSF funded project designed to strengthen the preparation of future elementary school teachers. The centerpiece of the project is an 18-hour block of courses that integrates mathematics instruction with pedagogical instruction and field experiences. Math Matters students take integrated mathematics and methods courses two mornings each week and participate in a field experience two mornings each week under the supervision of master teachers at Roper Elementary School. The presenters will discuss their experiences in building a three-way partnership between education faculty, mathematics faculty and mathematics teachers as well as their efforts to deepen their students' understanding of mathematics by connecting the mathematics to the tasks faced by an elementary school teacher.

#4. Teaching, Learning, and Learning to Teach in Elementary Mathematics Methods

Presenters: Deborah Ball and Hyman Bass, University of Michigan

This working session will focus on the "math methods" course. Drawing from records of teaching and learning to teach elementary mathematics methods, we will discuss how we have collaborated on this course, each teaching our own section, and drawing on and extending our research on knowing mathematics for teaching. In addition, we have been working with five advanced doctoral students in mathematics and teacher education, three of whom are also teaching their own sections of the course. In this way, the course offers a site for preparing beginning faculty. Artifacts from the course, including syllabi, assignments, student work, and videotaped segments of class, will be available for investigation and discussion. The session will take up some of the core challenges of this work and possible ways to contend with such challenges.

#5. Middle School Mathematics Teacher Development Program

Presenters: Ira Papick and John Beem, University of Missouri

The session will describe the University of Missouri middle school teacher preparation program developed and facilitated through a partnership of the College of Education and the Mathematics Department. The program includes a core set of mathematics courses consistent with mathematics preparation as outlined by The Mathematical Education of Teachers book. The courses utilize National Science Foundation (NSF) "standards based"  middle school mathematics curriculum materials to launch in-depth mathematical investigations. Course materials are being developed through a grant from the NSF. The courses will also be utilized in an accelerated post-baccalaureate teacher certification program currently under development. The session will include a description of the undergraduate middle school mathematics teacher certification program and will focus on the model of collaboration among mathematicians and mathematics educators in facilitating development of undergraduate and post-baccalaureate certification programs.

#6. Preparing Middle Level Mathematics Teachers - A Collaboration of Three Universities

Presenter: Marjorie Enneking, Portland State University, and Laurie Burton, Western Oregon University

Faculty and teachers-in-residence at Portland State University, Southern Oregon University, and Western Oregon University have been working together to develop or revamp distinct programs on each campus that are especially designed to prepare future middle school mathematics and that fit the particular institution's situation. Descriptions of the courses and programs, and practical considerations involved in developing and offering them, will be shared. Participants will receive handouts and sample materials such as course syllabi and sample activities that illustrate the nature of the courses. Issues such as recruitment of students, staffing of courses, and serving practicing but mathematically unprepared middle school middle school teachers will be discussed. Participants will have an opportunity to share information about their programs and to raise and discuss issues (and possible solutions) in developing on their own campus or in their area a program for preparing middle school mathematics teachers.

#7. Teachers' Mathematics: A Collection of Mathematics Deserving To Be a Field

Presenter: Zalman Usiskin, University of Chicago

Under a grant from the Stuart Foundation to the University of California at Berkeley, Dick Stanley of Berkeley, Elena Marchisotto of Cal State - Northridge, Tony Peressini of the University of Illinois and I have created materials for a sequence of two mathematics courses for high school mathematics teachers. These courses are meant to be taken by prospective teachers towards the end of their undergraduate experience (what some call capstone courses) or by experienced teachers in a graduate program. These materials are currently being tested at ten sites around the country.

We have been guided by the notion that there is some mathematics that is particularly appropriate for teachers that they do not normally encounter in their undergraduate experience. This teachers' mathematics includes ways of explaining ideas new to students, alternate definitions and their consequences, why concepts arose and how they have changed over time, the wide range of applications of the mathematical ideas being taught, alternate ways of approaching problems with or without technology, extensions and generalizations of problems and proofs, how ideas studied in school relate to ideas students may encounter in later mathematics study, responses to questions that learners have about what they are learning.

Teachers' mathematics is not merely a bunch of mathematical topics that might be of interest to teachers but a coherent field of study, distinguished by its own important ideas: the phenomenology of mathematical concepts; the extended analyses of related problems; and the connections and generalizations within and among the diverse branches of mathematics. We might view teachers' mathematics as a type of applied mathematics, applied because its subject matter emerges not from within mathematics but from the particular mathematics of the classroom, out of the teaching and learning of mathematics.

This session will begin with some examples of various aspects of teachers' mathematics, with the rest of the session being devoted to an open-ended discussion of the issues surrounding the mounting of mathematics courses for teachers.

#8. Raising Arizona: Improving Teacher Preparation through the "Four R's"--Recruitment of Students, Retention of Teachers, Reform of Curriculum, and Reward for Faculty

Presenters: Fred Stevenson and Marta Civil, University of Arizona

The University of Arizona has begun implementing initiatives and programs to address the critical state of mathematics education and teacher preparation in Arizona and in the country. We are focusing on the "Four R's:" Recruitment of students, Retention of teachers, Reform of curriculum, and Reward for faculty. We will discuss our new on-campus Center for Recruitment and Retention of Secondary School Mathematics Teachers. We will present the new University program for promotion and tenure of mathematics faculty whose contributions are in education, scholarship, and outreach. We will introduce the new curriculum we have written for secondary school mathematics teachers.

#9.  Teaching Statistics to Future K-8 Teachers 

Facilitator: Richard Scheaffer, President, American Statistical Association

Presenter: Larry Feldman, Mathematics Department, Indiana University of Pennsylvania

Statistics has been thought of as one of the most difficult topics to teach in elementary and middle schools. Pre-service teachers come to post-secondary institutions with much less preparation in Quantitative Literacy (QL) than in the algebra/geometry/trig/calculus sequence. Traditional university statistics courses have a reputation for being very formula-driven and hard to understand. The session will focus on successful approaches in teaching data analysis and probability to pre-service elementary teachers through the following programs: 

·        Mathematics content for pre-service elementary teachers -- a six-week unit focused almost entirely on teaching statistics through students carrying out their own statistical study

·        QL content appropriate for pre-service middle school teachers – a probability and statistics course for students concentrating in mathematics

·        SEQuaL (Statistics Education through Quantitative Literacy) -- workshops in K-12 QL, multidisciplinary QL, AP Statistics, and Data-Driven Mathematics (K-12). These workshops have been run at sites across Pennsylvania since 1992.

In addition, some of ASA’s statistics education materials will be shared such as specific examples of the Principles for Teaching Statistics, the Quantitative Literacy Series, and Data-Driven Mathematics. Time will be allotted for discussions of successful programs from participants and for discussion.

Presenter: Mick Norton, College of Charleston

The University of Charleston, SC, the graduate arm of the College of Charleston, has a multidisciplinary M. Ed. program in science and mathematics.  The program has been in existence for three years and attracts K-12 teachers who are required to take a mix of science, mathematics, and education courses.  The program reflects an unusual level of cooperation and collaboration between two departments in the School of Education and five departments in the School of Sciences and Mathematics.

Scientists and mathematicians who want to work with teachers teach the science/math content courses, and there is a defining philosophy that these courses share in terms of how science/math content necessary to understand grade level content is mixed with grade level classroom activities and teaching techniques.  The probability and statistics course for elementary and middle school teachers is a typical example.  The course content is shaped to be consistent with NCTM and state standards and with grade level curriculum.  One course component involves describing data and measuring variation in the context of industrial applications.  This provides teachers a beyond-the-classroom picture of using statistics to make decisions and the uncertainty involved in those decisions.  Another component involves teachers in hands-on simulation in a variety of games, where they learn to look for an underlying structure in how the game produces winners.  This allows them to advance their probability intuition and to better utilize Law of Large Numbers activities effectively in their classrooms.  Teachers also are exposed to a variety of classroom activities and get to design some of their own.

#10.  Teaching Statistics to Future High School Teachers

Facilitator: Ann Watkins, President, Mathematical Association of America

Presenter: Christine A. Franklin, Statistics Department, University of Georgia

Statistics is a rapidly growing area within the mathematics curriculum at the K-12 level. This is strongly supported with the Probability and Statistics strand in the NCTM Principles and Standards for School Mathematics.

With the rapid growth of AP Statistics, the need for secondary teacher training in Probability and Statistics has become essential. At the University of Georgia, a statistics course was developed by the Department of Statistics in conjunction with the College of Education to prepare both pre-service and in-service secondary teachers to teach statistics. The course is in its fourth year of offering and follows many of the recommendations stated in the MET document.

The course is entitled, "Probability and Statistics for Secondary Teachers". The course covers all the topics that an instructor would be expected to teach in an AP statistics course. It also covers sufficient mathematical reasoning necessary for development of these topics as well as advanced statistical topics. Emphasis is placed on the ideas behind statistics and how statistics is used in everyday situations. Data collection as well as data analysis is emphasized. The course integrates the use of technology by using statistical computing packages such as MINITAB and by the use of the TI-83 calculator. Activities that help to reinforce the concepts and topics covered in the course are utilized by individual and group projects. Potential resources, such as the DDM and QL materials written under joint projects between ASA and NCTM, that teachers  may be using when teaching at the secondary level are integrated into the course.

This course has been the beginnings of a productive working relationship between the Department of Statistics and the mathematics education department within the School of Education. We are presently working together to develop a new course in Probability and Statistics for K-8 teachers that will be taught for the first time in Spring 2002. Teacher preparation institutions must ensure statistics education of pre-service and in-service teachers. Ideally, statisticians, teacher educators, and mathematicians should be involved in this education. This type of interdisciplinary relationship benefits not only the teachers, but also the faculty and departments involved with the training.

Presenter: Robert Gould, Statistics Department, UCLA

Although the intersection between Statistics and Mathematics is quite broad, there is sufficient "extra-mathematical" content in Statistics to make it extremely challenging to develop a curriculum that will adequately prepare a teacher to teach both math and Statistics. In this presentation, I will present some examples of this "extra-mathematical" content and show how it is taught to current and future teachers at UCLA.

I will present some examples and lessons from a course offered by the UCLA Department of Statistics intended for advanced high school Statistics teachers.  This course typically attracts teachers  who are confident with the mathematical content of an AP Statistics level course but are uncomfortable and unfamiliar with applying the mathematical theory to real data. I will also report on the UCLA Mathematics Content Program's course to prepare future elementary, middle school, and high school teachers.  This program, which closely follows MET guidelines, is for teachers under-prepared to teach mathematics and offers a data analysis course -- their most popular course as it turns out -- intended as a "first course" for future Statistics teachers.

#11. Changing Pre-service Students' Beliefs about Mathematics and What it Means to Learn Mathematics: A Two-year College's Program to Improve the Mathematics Experiences of Future Teachers

Facilitator: Rikki Blair 1^st session; Susan Wood, President of AMATYC,  2^nd session

Presenter: Mercedes McGowen, William Rainey Harper College

As educators of pre-service elementary teachers, we face the challenge of developing a shared vision and clear expectations of what constitutes a "deep understanding of school mathematics" and how it is assessed. We also face the challenge of our students' limited understanding of what constitutes mathematics and what it means to learn mathematics.

Changing students' utilitarian view of mathematics and changing what they value in mathematics is more difficult than teaching them algorithms. Effecting lasting changes in those beliefs and values present significant practical and theoretical challenges for those of us who teach the content courses for prospective teachers. How do we change their severely procedural orientation to mathematics focused on 'correct answers' and peer validation?

A brief overview of the mathematics content courses at a two-year college which address these challenges will be presented. The remainder of the session will include open-ended discussion of issues of implementation and assessment of student understanding based on samples of student work.

#12. A Community College/University Partnership to Prepare Elementary Teachers Who Have Deep Content Knowledge in Mathematics

Facilitator: Susan Wood, President of AMATYC, 1st session; Rikki Blair 2nd session

Presenter: Jean Houck, Dean of the School of Education, California State University at Long Beach

Cerritos College and California State University, Long Beach have developed a standards-based, collaborative teacher preparation program that focuses on strong subject matter preparation. Students may complete the first two years of the teacher preparation program at the community college level, then transfer seamlessly to the university for the final two years.

Math, math education, and education faculty from K-12, the community college, and the university worked together to develop the curriculum, holding numerous meetings and workshops over a period of a year and a half. The first group of community college students entered the university in the fall of 2001. They moved seamlessly into the junior year of the four-year program preparing them for elementary classrooms.

The session presenter will distribute copies of the program curriculum, with information about the way the program has focused on strengthening subject matter, especially mathematics. There will be a discussion of the process and a description of the roles/activities of the higher education partners. Participants will have an opportunity to engage in discussion of issues encountered in developing such a collaborative program, as well as lessons learned in the process.

#13. Getting Connected with K-12 Teachers

Presenters: Margaret Owens and Bill Fisher, California State University at Chico

California State University, Chico has a long tradition of providing high quality teacher training programs dating back to its beginning as a normal school. The Mathematics Department values this tradition and is committed to its service to future teachers. With funding from the ExxonMobil Foundation we have been able to establish a Teacher-in-Residence program that provides an exciting link between the university and K-6 education. Building upon that model, we have extended our collaborations to secondary education. We will present an overview of some of our on-going work with K-12 teachers, including the ramifications for the mathematical preparation of future elementary and high school teachers, and for in-service teachers as well. Our focus will be on ways in which these connections with the K-12 mathematical community can be established and ways in which such connections can improve teacher education programs.

#14. The Texas Experience:  Collaborative Pathways to Reform

Presenters: Debbie Pace and Susan Hull, Dana Center, University of Texas

A higher education initiative in Texas has successfully encouraged and nourished a variety of partnerships across the state to improve the mathematical preparation of preservice teachers.  The Charles A. Dana Center at the University of Texas at Austin will summarize significant results of efforts to inform stakeholders, overcome obstacles, identify common goals, and mobilize leaders and resources around a shared vision.    Finally, we will lead discussion of specific ways participants could apply lessons learned in their own institutions.

#15. Building Effective Teachers of Mathematics Creates Success for Children

Presenter: Donna Little-Kuamo, Albuquerque NM School District

Nearly a decade ago, a group of thoughtful and committed teachers in Albuquerque NM began conversations about the kind of mathematics instruction they felt was needed, but lacking, in the district.  The initial focus was the mismatch these teachers perceived between what they knew from their college preparation and what they needed to know to become truly effective teachers of mathematics.  Thus began the Albuquerque project which, with support and encouragement from the ExxonMobil Foundation, has developed over the last decade into a journey of mathematical discovery for teachers in the district.  Careful study of mathematical content and the strategies needed to deliver that content to students have given insight into what needs to be modeled and taught to prepare strong teachers and to support their continued mathematical growth.  Results of evaluations over the last few years show that investment in strong preparation of teachers and continuing support for their mathematical growth does have a significant impact on the learning of their students. This session will discuss what we have learned about building successful elementary teachers and how it is affecting our current work and plans for the future.

#16. Courses that Develop Deep Understanding for Teaching Mathematics

Organizer and Facilitator: James Fey, University of Maryland, Director of the Mid-Atlantic Center for Mathematics Teaching and Learning

Presenters: M. Katherine Heid, Pennsylvania State University; William Moody, University of Delaware; Kenneth Berg, University of Maryland 

Mathematics and mathematics education faculty at university partners in the Mid-Atlantic Center for Mathematics Teaching and Learning (Delaware, Maryland, and Penn State) are working on three kinds of content courses designed to help teachers and teacher educators develop the kind of mathematical knowledge that is especially useful in teaching. 

•    At The Pennsylvania State University, mathematics and mathematics education faculty are engaged in work to identify foundational ideas for secondary mathematics and to develop plans and teaching materials for innovative collegiate mathematics courses that help future high school mathematics teachers develop deep understanding of those ideas.  These course plans and materials are being evaluated in a variety of settings to test the transportability and scalability of the reforms in teacher education that they encourage.

•     At the University of Delaware, mathematics and mathematics education faculty are developing a framework of goals and procedures for content and pedagogy preparation of teachers at elementary and middle school levels, specific curriculum materials supporting the recommended program of courses and field experiences, guidelines for school and university faculty involved in the process, and research studies of how the innovative ideas work in a variety of settings.  In particular, the Delaware group is applying the Japanese lesson study strategy to develop of the content courses for teachers.

•    Mathematics faculty from all three university partners are collaborating to develop Foundations of Mathematics courses for mathematics education graduate students that address the branches of mathematics most relevant to K-14 curricula—algebra, geometry, probability and statistics, analysis, and discrete mathematics—with a focus on underlying principles and ideas that connect the separate strands.  The purpose is to give specialists in mathematics education content knowledge and perspective for designing and teaching content courses for teachers, for developing school curricula and assessments that emphasize important concepts and methods of the subject, and for advising school systems on curricular issues.

#17. Studying Lessons Together: Practical Processes that Improve College and School Mathematics Teaching

Presenter: Daniel Goroff, Harvard University

#18. Preparing for the Teaching of Algebra in Secondary Schools: Challenges and Promising Directions

Presenter: Joan Ferrini-Mundy, Michigan State University

With standards-based curricula, a movement toward "algebra for all," and widely differing views about what school algebra should emphasize, it is difficult to know what the best preparation for secondary teachers of algebra should be. In this session we will discuss the MET recommendations and their implications in the context of a changing secondary school algebra landscape. Come prepared to share and consider new ideas, approaches, and programs for preparing secondary school mathematics teachers, especially to teach algebra.

#19. Some Lessons Learned in California

Presenters: Hung-Hsi Wu and Mary Burmester

For the past two years, Wu and Mary Burmester together with two other teachers have conducted professional development summer institutes for teachers of grades 4-6. They are part of the ongoing professional development effort in California. One institute is on numbers (whole numbers, fractions, decimals and rational numbers), and the other on geometry (solid and plane figures, Platonic solids and Euler's formula, basic theorems of triangles and circles, area and volume). The emphasis of the institutes is on mathematical content, especially the importance of precise definitions and mathematical reasoning. We will share our collective experience from these institutes by describing their basic structure and expectations, their detailed content, the reactions of the teachers, and teachers' frank evaluations of the effectiveness of this approach to professional development. We will also discuss the relationship between pre- and in-service professional development, as well as why our experience from these institutes is particularly relevant to pre-service professional development.