**Introduction to Critical Issues in Mathematics Education 2011: Mathematical Education of Teachers**Sybilla Beckmann

This is the introduction given by Sybilla Beckmann before the lectures for the Critical Issues in Mathematics Education 2011: Mathematical Education of Teachers at MSRI.

**Why Content Knowledge Matters in Teaching and the Implications for Teacher Education**Denise Spangler

This is a talk given by Denise Spangler regarding "mathematical knowledge for teaching." The lecture looks at some examples of student work to see why teachers' mathematical knowledge matters and to think about how using student work in teacher education can help develop mathematical knowledge for teaching.

**The Mathematical Education of Inservice Teachers: Lessons Learned, Opportunities, and Challenges**Diane Briars, President of the National Council of Supervisors of Mathematics (NCSM)

**Learning to Teach Something in Particular: How the Common Core Can Leverage Radical Improvement in Teacher Training**Deborah Ball (University of Michigan)

David Cohen recently published an article in the *American Educator* entitled, "Learning to Teach Nothing in Particular,” in which he argued that the lack of a common K-12 curriculum in this country has been a major impediment in teachers' training. In this talk, we show how we could use the CCSS together with a common core for teaching practice to build a reliable system for preparing teachers for responsible practice.

### How Can the Community of All Mathematics Teachers Work Together and Learn From Each Other to Improve Mathematics Teaching?

**Could the mathematics teaching community become as successful as the mathematics research community?Sybilla Beckmann**

Conditions leading to the success of the mathematics research community are contrasted with the case of mathematics teaching at all levels. Lesson Study: A Promising Means to Support the Learning of Students, Teachers, and Mathematicians? Presentation 2: Catherine Lewis This session will take up Sybilla Beckmann’s call to create a community of all mathematics teachers, and will examine lesson study as one possible means to accomplish this. The session will present recent research on the impact of lesson study on both teachers’ and students’ mathematical knowledge, drawing on data from a recent randomized controlled trial. The session will explore the role of high-quality mathematical materials in lesson study, and will illuminate models of university-school collaborative lesson study from Japan as well as the United States. It will focus on the progress that has occurred in the US, and the challenges that remain, to create a community of all mathematics teachers.

### Panel on Curriculum and Teacher Education in Light of the Common Core

Zalman Usiskin, University of Chicago

Paul Goldenberg, EDC

Andy Isaacs, University of Chicago

Early Algebra and the Common Core: What Do Teachers Need to Know?
Susan Jo Russell, TERC and Deborah Schifter, EDC
The phrase “properties of the operations” recurs throughout the elementary grades in the Common Core State Standards. How might elementary teachers introduce these properties to their students in ways that support students’ work in computation and provide a link between arithmetic and algebra? What do teachers need to know in order to enact the standards in these ways? In this talk, we will consider a constellation of Common Core content and practice standards that relate to early algebra, offer classroom examples that illustrate how elementary students can engage with these standards, and engage with participants to consider what teachers need to know to enact such lessons.

### Research Findings About Teacher Education (2 presentations)

**Achievement in Mathematics Classes for Future Elementary Teachers: What Matters?
Raven McCrory **

In this talk, two aspects of undergraduate mathematics courses for future elementary teachers will be addressed. 1. What do these courses look like? That is, who teaches them, what is the content, how are courses organized, how do they differ across institutions, etc. 2. What systematic factors explain differences in learning across these courses, with different instructors and at different institutions? Data come from a study of over 2000 undergraduate students at certifying institutions in four states, and include pre- and post-tests of students taking a mathematics course required for elementary certification; surveys of instructors of these courses; and interviews with mathematics department chairs.

Results suggest that, controlling for students’ prior knowledge, two factors that matter are use of a textbook specifically written for a mathematics course for teachers; and teaching in a way that engages students with doing mathematics. These two factors have differential impact on students depending on students’ prior knowledge. Models will be explained and implications of results for the design and implementation of mathematics classes for teachers will be discussed.

**Mathematics Teacher Preparation: An International Perspective
Maria Teresa Tatto **

The Teacher Education and Development Study in Mathematics collected data from approximately 24,000 future primary and secondary mathematics teachers in 17 countries. We will present findings and discuss implications for mathematics teacher preparation in the U.S.

### Panel on Curricula and Teacher Learning (3 presentations)

**Common Core Implementation and the Mathematical Education of Teachers: Policy Perspectives and Support **

**Joan Ferrini-Mundy**

The policy formulations that resulted in the establishment of the Common Core State Standards (CCSS) initiative by the National Governors Association and the Council of Chief State School Officers were rooted in the need to provide clear and consistent frameworks to prepare our children for college studies and, ultimately, successful working lives in science, technology, engineering, and mathematics (STEM) careers. Forty-one States, the District of Columbia and the U.S. Virgin Islands have formally adopted the common core standards in mathematics. We are poised at the doorstep to implementation activities, state-by-state, as well as important policy research to brace the efforts.

The new standards in mathematics elicit a well-known problem: If we expect children to demonstrate deeper mathematical understanding and be able to articulate their own reasoning, then we must strengthen programs for the education of both existing and future teachers of mathematics and align that preparation with what is expected by the common core in mathematics. Scholarly organizations across the country are already at work (the Conference Board of the Mathematical Sciences has issued recommendations on January 1, 2011) and this workshop is part of that national effort.

In this talk, I will offer a NSF perspective about the challenges and opportunities in reaching tens of thousands of current mathematics teachers (as well as the undergraduate and graduate students in mathematics education programs that will soon join the workforce). What is NSF planning in terms of support for building the knowledge base to fortify these efforts? What are other federal and non-federal funders planning in terms of providing the resources for both professional development and teacher preparation?

**Navigating Standards: Teacher and Student Learning through Different Instructional Paths**

**Aki Murata**

Standards and curricula present varied images of mathematics instruction that may at times seem conflicting and confusing to teachers. By contrasting how mathematics content is treated across grade levels in standards (e.g., Common Core Standards, California Content Standards) and curricula (e.g., Everyday Mathematics, Japanese mathematics textbooks), we will discuss how they can frame students’ learning and experiences in different ways, and how these paths may also guide teachers’ understanding of student learning of mathematics.

**Textbooks: Math as Arbitrary Rules**

**W. Stephen Wilson**

Some logic gaps in the development of mathematics in standard texts will be discussed. Examples will be given.

### Lesson Study Models: What Models of Mathematics Lesson Study Have Emerged in the U.S. and What Can They Each Contribute?

Catherine Lewis, Ruth Cossey, Elizabeth Baker, Aki Murata, Bindu E. Pothen, Jackie Hurd, Ben Ford, Stan Pesick, Marlene Wilson, David Foster, and Tracy Sola

In this session, we will hear from experienced organizers and participants of four different lesson study models: preservice, schoolwide, district‐based, and regional. Each model will be briefly described, with a focus on its particular niche within the improvement of mathematics instruction. Half the session will be devoted to Q & A with the audience, and suggestions will be provided for session participants who want to learn more about this model. Several different lesson study models have emerged in the U.S. and have now been sustained, in some cases, for 5‐10 years. Panelists will very briefly introduce examples of these different models of lesson study from the greater San Francisco Bay Area, focusing on the role each can play in building and spreading mathematical knowledge for teaching. Half of the session will be devoted to Q & A with session participants. Each presentation will (1) briefly describe the lesson study model; (2) illustrate what this model can accomplish (why it is important); and (3) provide references for session participants who want to learn more about this model.

### Lesson Study: Advice From K-12 and University based Lesson Study Practitioners

Catherine Lewis, Elizabeth Baker, Ruth Cossey, Brigitte Lahme, David Foster, Jackie Hurd, Stan Pesick, Marlene Wilson, Tracy Sola, Jane Decker, and Erik Moll

Experienced lesson study participants from departments of mathematics and mathematics education, and from elementary and secondary schools, will share thoughts about what is needed to build toward Sybilla Beckmann’s vision of one community of mathematics teachers, and how lesson study can contribute. During the first half of the session, panelists will discuss the following questions:

- How is lesson study similar to and different from other forms of professional learning you have experienced?
- What have you learned about mathematics and its teaching/learning through lesson study?
- How did your learning of mathematics occur–what were the supports and catalysts for it?
- What advice do you have for mathematicians and mathematics educators who may be interested in initiating or participating in lesson study work?
- What tools and resources are useful for mathematics lesson study–both generic tools for lesson study and specific types of mathematical resources?
- What kinds of mathematical resources tend not to be useful?
- How should teachers’ mistakes be handled?

The second half of the session will be devoted to Q & A with the audience.

### Developing preservice elementary mathematics teachers’ knowledge bases through Standards-based curriculum materials

Andrew Tyminski

Our research with pre‐service elementary mathematics teachers (PSTs) focuses on what they learn as a result of interactions with Standards‐based elementary mathematics curriculum materials. We examine PSTs’ learning in the domains of curricular knowledge (Shulman, 1986) and mathematical knowledge for teaching (Ball, Thames, & Phelps, 2008). Example activities and results will be shared. The session will conclude with a discussion regarding the kinds of knowledge PSTs will need to be prepared to teach using the Common Core Standards.

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### Follow-Up Efforts to the Common Core State Standards (2 presentations)

The Mathematical Education of Teachers II

Jim Lewis

Projects to support success of the Common Core State Standards for Mathematics

William McCallum