Current List of Abtracts:

· Joe Fiedler

(Thursday, June 30^th, 1:30 pm – 5:30 pm)

Traditionally Mathematics courses treat uses of mathematics as an afterthought relegated either to a section of "Applications" or worse, "Word Problems." Hand-held technologies that can collect, display, and analyze data offer both an excuse and a reason to rethink the interaction between School Mathematics and the World. In this hands-on workshop we will see how empirical observations of Galileo and Newton can be repeated and exploited to weave a dense skin of mathematical observations relevant to both pre-service college students and to their future high and middle school students. By approaching advanced mathematics from an elementary perspective we will attempt to build a new paradigm for the training of teachers.

· Jane Friedman

(Wednesday, June 29^th, 3:40 pm – 5:30 pm)

Title: Teaching Students Mathematical Reading

Session Description: Teaching students to read mathematics is an essential first step in teaching students to understand and write proofs.  Reading mathematics requires intense focus and attention to detail. Every word matters. In order to gain real understanding one should read mathematics with a pencil and paper and a questioning attitude. In this presentation we will discuss approaches to teaching students (especially future teachers) to read mathematics for understanding.

· Ted Gamelin and Heather Calahan

(Monday, June 27^th, 1:30 pm – 3:00 pm)

Title: The Role of the Mathematics Department in the Preparation of Future Teachers

Session Description: Our presentation will focus on the role that a research mathematics department can play in the undergraduate preparation of math teachers, and the shape that a mathematics subject matter preparation program might take within a research mathematics department. A critical ingredient of any such program is a capstone course. We will discuss our experiences implementing a capstone course, which is co-taught by mathematician and classroom teacher, and in particular our experiences with course textbook and materials. We will also discuss various changes that can be made in the syllabi for standard courses in order to make these courses more relevant for pre-service teachers. Finally, we discuss the sources of support (money) for our program, and our experiences dealing with state credentialing bodies concerning waiver approval for our program.

· Cathy Kessel

(Tuesday, June 21^st, 1:30 pm – 5:30 pm)

Title: Observing classes, interviewing students, discussing teaching and learning

Session Description: It is hard to discuss teaching and learning without reference to observations of classrooms and students. These can vary from a remark that a student made yesterday to the distilled experience from years of teaching. The way in which observations are made can help to make them more or less available for later discussion with others. This session will focus on discussion and practice of classroom observations and student interviews.

· Magnhild Lien

(Tuesday, June 21^st, 10:45 am – 11:45 am)

Title: MET Report, National and State Standards

Session Description: In this session we will go over the main parts of the Conference Board of the Mathematical Sciences’ report on the Mathematical Education of Teachers (MET) as it pertains to the preparation of secondary level teachers. In addition we will discuss how mathematics departments can use this report to enhance their programs to include an appropriate track for prospective mathematics teachers.

· Elena Anne Marchisotto

(Tuesday, June 28^th, 3:00 pm – 4:25 pm)

Title: Teaching Teachers How to Teach Proofs

Session Description: I hate proofs! How often do we hear our students say this? In this presentation I demonstrate strategies that I have found to produce a different response. I will focus on geometry. My approach helps students to understand the need for proof. It raises the question of what a geometry is, and fosters an appreciation of how proof reveals the heart of the subject. I will use collaborative learning exercises to illustrate ways to teach correct proving techniques and to use proof to give a deeper understanding of geometry. I will provide samples of discussion questions and problems and a list of resources for related study.

· Roxy Peck

Session 1 (Thursday, June 30^th, 8:30 am – 10:30 am)

Title: Statistics in the Mathematics Curriculum—To Integrate or Differentiate?

Session Description: This session will explore what distinguishes statistics from mathematics and will examine the role of statistics in the secondary mathematics curriculum. Relevant NCTM and California standards for data analysis and probability and the rapid growth of the AP Statistics course will be discussed, along with the implications for secondary mathematics teacher preparation.

Session 2 (Thursday, June 30^th, 10:45 am – 11:45 am)

Title: Some High Tech and Low Tech Demonstrations: Teaching Statistical Reasoning

Session Description: In this session, we will look at some hands-on activities that develop statistical reasoning. Demonstrations will include both “low tech” activities as well as those that incorporate technology (using Fathom). The Session will conclude with a discussion of available resources for teachers of statistics.

· Anthony L. Peressini

(Tuesday, June 28^th, 1:30 pm – 2:55 pm)

Title: Developing and delivering web based professional development short courses for high school mathematics teachers.

Session Description: Our Mathematics Department currently offers a series of professional development short courses through its Math Teacher Link (MTL) web site at: http://MTL.math.uiuc.edu/. The current offerings of short courses deal primarily with the integration of technology into the teaching of mathematics. I am currently developing some new MTL short courses that focus on useful mathematical content for teachers. My objective is to use dynamic and interactive web technology and web resources to explore and enhance the content presentation. This session will describe two of these new course modules in some detail. One of these short courses uses our book Mathematics for High School Teachers for a text. That presents a special challenge to me to develop the web portion of the course so that it complements and enhances rather than replaces the text presentation. I hope to engage the audience in a discussion the problems and opportunities associated with web-based professional development courses for mathematics teachers.

· Dick Stanley

Title: Delving Deeper

(Monday, June 27^th, 3:15 pm - 5:30 pm)

Session Description: This session illustrates an approach to the mathematical preparation of high school teachers that stays very close to high school level content, but that treats this content in a mathematically sophisticated way. The intent is to help teachers focus the kind of mathematical maturity that their undergraduate courses make possible on the actual content and problems of high school mathematics. Thus it treats high school mathematics from an "advanced standpoint". Still, it does not do this by appealing to higher levels of rigor or formality. Rather, it does so through developing the idea of sophisticated use of simple tools.

This approach takes advantage of the fact that, implicit in standard problems of the high school curriculum, there is an undercurrent of deeper mathematics that is seldom brought out for teachers. Seeing how to carry out deeper analyses of simple problems gives teachers a better appreciation of the mathematical substance of the high school curriculum, and at the same time helps them develop and use powerful mathematical ways of thinking.

· Mark Hoover Thames and Laurie Sleep

Together with workshop participants, we will explore the content of mathematics courses meant to prepare teachers. We will introduce the idea of an applied mathematics course for teaching and discuss ideas about what might be included in such a course. We will also consider ways of teaching mathematics so that prospective and practicing teachers find it relevant to their work and so that they are better able to use mathematics in their teaching.

Our sessions will mix presentations of research we have been doing in this arena with discussions about what workshop participants do in, and want to change about, the courses they currently teach. Together, we will design materials and approaches to teaching mathematical explanation and to using curriculum materials in an applied mathematics course for teaching.

Session 1 (Wednesday, June 22^nd, 1:30 pm – 5:30 pm)

Title: What Content Belongs in Mathematics Courses for Teachers?

Session Description: We will begin by considering why we should worry about teachers’ mathematical knowledge. What’s the evidence that it matters? And, what mathematics and in what ways do we think that mathematics matters? After some initial framing of these issues, we will hear from you about what you have tried and what you would like to work on further. We will also share with you distinctions among different types of mathematical knowledge needed for teaching and will introduce a body of specialized content knowledge that we think is particularly appropriate to include in mathematics courses for teachers. In closing, we will argue that mathematical practices, such as explaining or using representations, and mathematical tasks of teaching, such as analyzing errors or interpreting student thinking, are important aspects of the mathematical skill needed by teachers.

Session 2 (Wednesday, June 22^nd, 7:00 pm – 9:00 pm)

Title: Mathematical Practices Central to the Work of Teaching

Session Description: In this relaxed evening session, we will explore mathematical practices key to effective teaching, such as giving explanations, choosing appropriate definitions, and using mathematical representations. To focus our discussion, we will do some mathematics together and will watch some video of classroom teaching. In each case, we will ask what mathematical practices are and when and where they arise in the work teaching.

Session 3 (Thursday, June 23^rd, 1:30 pm – 3:30 pm)

Title: Mathematical Explanation: What There Is to Teach and Ways to Teach It

Session Description: Having explored a range of mathematical practices, we will now focus in on mathematical explanation. Using a videotaped interview of a calculus student and video of mathematical explanation being taught in a university mathematics course for teachers, we will refine our understanding of what mathematical explanation is, what there is to teach, and how we might go about teaching it.

Session 4 (Thursday, June 23^rd, 3:30 pm – 5:30 pm)

Title: Using School Curricula: Why and in What Ways

In this final session, we will explore ways of using school curriculum materials in university mathematics courses for teachers, and we will consider ways in which the mathematical work teachers do as they size up, select, modify, and use school curricular materials can be used to design mathematical activities for teachers. In conclusion, we will reflect on our work over the two past days and discuss additional ideas for what might be included in an applied mathematics course for teaching.