Past Presentations

2008

"The CME Project— Promoting Mathematical Habits of Mind in High School"

Al Cuoco, Wayne Harvey, Sarah Sword, Kevin Waterman, Education Development Center

The Future of High School Mathematics Conference, Washington, DC, September 25–27, 2008.

Abstract: The Center for Mathematics Education at the University of Maryland, along with "Math Is More" and a group of progressive curriculum development projects, hosted a conference of leaders in high school and collegiate mathematics education. This presentation, describing CME Project, was given as part of the Showcase of Promising Programs, which featured presentations and in-depth discussion of the ways that innovative curriculum, instruction, and assessment principles are embodied in materials produced by active curriculum development projects and the evidence about effects of those programs in school trials.

“Algebra in the Age of CAS—Examples from The CME Project (and Beyond)”
Al Cuoco, Education Development Center
USACAS Conference, Northfield, Illinois, June 28–29, 2008.

Abstract: The human mind can establish facts about mathematical objects even when the objects are difficult (or impossible) to write down explicitly. In this talk, we will look at some examples of how we use CAS environments as a platform for experimenting, to reduce computational overhead, and to build computational models of algebraic objects.

“Algebra for Teaching—Some Recommendations for Teacher Preparation”
Al Cuoco, Education Development Center
Critical Issues in Education Workshop: Teaching and Learning Algebra,
MSRI Workshop, Berkeley, California, May 14–16, 2008.

Abstract: The development of the CME Project began in 1992 with a grant from NSF to develop a geometry course, but the basic principles upon which the program rests evolved over nearly four decades. The basic position of the development team is that the real utility of mathematics—both for students who specialize in mathematically related fields and for those who take other directions—lies in a style of work, a collection of mathematical habits of mind, that mathematicians use to make sense of the world, such as visualization, performing thought experiments, reasoning by continuity or linearity, and mixing deduction with experiment. The basic results and methods of high school mathematics—the Pythagorean theorem, the techniques for solving equations or graphing lines or analyzing data—are the products of mathematics. The actual mathematics lies in the thinking that is used to create and develop these results. It is essential to develop both the results and the thinking. The entire program, from the uses of technology to the design of the problem sets in each lesson, is devoted to helping students become mathematical thinkers as they develop the content knowledge to apply that mathematical thinking competently.

This presentation gives examples of how this philosophy plays out in the context of the program’s development of algebra in high school. There are several mathematical habits that are dominant in algebra: reasoning about and picturing calculations and operations, seeking regularity in repeated calculations, purposeful transformation and interpretation of algebraic expressions, “chunking” (changing variables in order to hide complexity), and seeking and modeling structural similarities in algebraic systems that include the number systems of arithmetic but also include other algebraic systems. The presentation shows how these habits are introduced and strengthened across algebra strand of the program, providing students with general-purpose tools that allow them to solve problems, make and use abstractions, and develop mathematical theories.

“Some Organizing Principles for High School Algebra”
Al Cuoco, Education Development Center
Critical Issues in Education Workshop: Teaching and Learning Algebra,
MSRI Workshop, Berkeley, California, May 14–16, 2008.

Abstract: An examination of the day-to-day work of high school teachers shows that fundamental ideas and results from abstract algebra, linear algebra, and number theory are useful tools for teaching high school algebra and, more generally, for bringing coherence and texture to much of the high school curriculum. Furthermore, these ideas and results are useful in lesson planning, task design, and in other “out of classroom” activities essential to the profession. The talk concludes with some suggestions for how undergraduate mathematics courses can make explicit connections to these aspects of mathematics teaching.

“Algebra in the Age of CAS: Implications for the High School Curriculum”
Al Cuoco, Education Development Center
Center for the Study of Mathematics Curriculum (CSMC)
Second International Curriculum Conference: Future Curricular Trends in School Algebra and Geometry,
Chicago, Illinois, May 2–4, 2008.

“General-Purpose Tools in Mathematics”
Al Cuoco and Bowen Kerins, Education Development Center
NCTM Annual Meeting, Salt Lake City, Utah, April 9–12, 2008.

Abstract: For many students, the utility of mathematics lies in a style of work—the habits of mind that allow one to look at the world through a mathematical lens. This presentation shows activities from a new NSF curriculum, the CME Project, that promote these habits.

“Developing Proof throughout High School Mathematics”
Kevin P. Waterman, Anna Baccaglini-Frank, and Doreen Kilday, Education Development Center
NCTM Annual Meeting, Salt Lake City, Utah, April 9–12, 2008.

Abstract: Using strategies from a new, NSF-funded curriculum, the CME Project, this presentation shows techniques to help students develop and write formal proofs in algebra and geometry, with special attention on constructing a complete logical chain of reasoning.

“Using Computer Algebra Systems (CAS) to Promote Mathematical Habits in High School”
Bowen Kerins and Doreen Kilday, Education Development Center
NCTM Annual Meeting, Salt Lake City, Utah, April 9–12, 2008.

Abstract: CAS can be used to build computational models of mathematical objects. This presentation uses examples from a new NSF curriculum, the CME Project, to illustrate applications of this model building, including monthly payments on a loan.

“Curriculum and Technology: Evolving Together”
Kevin Waterman, Education Development Center
T3 International Conference, Dallas, Texas, March 1, 2008.

Abstract: As the CME Project (published by Pearson Education) was developed, the development team found many cases where technology, especially a Computer Algebra System (CAS), enhanced the desire to develop mathematical “habits of mind.” This session looks at how the development of TI-Nspire™ technology influenced and was influenced by CME’s high school curriculum goals. This session also looks at field-tested approaches to using CAS in order to solve algebraic equations, factor and expand polynomials, look for patterns, understand functional language and make sense of iterative definitions of functions.

 

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2007

A Day of Mathematics, a symposium sponsored by EDC's Center for Mathematics Education and the Massachusetts Department of Elementary & Secondary Education, November 15, 2007 in Tyngsboro, Massachusetts.

The symposium provided teachers of Algebra 2 and other grade 11–12 high school courses with a chance to

In addition to panel discussions and a keynote address by Bill McCallum, the symposium involved two breakout sessions in which teachers had a choice of one of four concurrent workshops, each demonstrating a different use of function modeling language (FML) in the high school mathematics curriculum:

“Computer algebra systems and high school mathematics,” Ryota Matsuura and Sarah Sword.

“How does the bank figure the monthly payment on a loan?” Jean Benson and Doreen Kilday.

“The mathematics behind game shows,” Bowen Kerins.

“Mathematical induction and other stuff,” Al Cuoco.

“A Brief Introduction to CME Project — Geometry”
Paul Goldenberg, Education Development Center
Pearson Prentice Hall, New York, New York, 2007.

“The CME Project”
Anna Baccaglini-Frank, Education Development Center & University of New Hampshire
Ninth International Conference "Mathematics Education in a Global Community" September 7–12, 2007.

Abstract: This talk describes the CME Project, an NSF-funded four-year comprehensive high school mathematics curriculum being developed by Education Development Center, Inc. and being published by Pearson Prentice Hall. In addition to describing the philosophy of the curriculum, the presentation shares a number of examples that illustrate the approach.

“Curriculum and Technology: Evolving Together”
Kevin Waterman, Education Development Center, and Gosia Brothers, Texas Instruments
4th Annual USACAS Conference, Northfield, Illinois, June 16–17, 2007.

Abstract: EDC and Texas Instruments have enjoyed a close working relationship for nearly 20 years. Both TI's new line of handhelds, the TI-Nspire, and EDC's forthcoming curriculum, the CME Project, have evolved from this relationship.

This presentation looks at how curriculum and classroom needs drove the new interface, and how the new interface influenced the timing and development of certain key topics. Among other things, the talk looks at field–tested approaches to using CAS to:

“U.S. CAS–Active Curriculum Panel”
Kevin Waterman, Education Development Center, James Fey, University of Maryland, M. Kathleen Heid, The Pennsylvania State University, Zalman Usiskin, University of Chicago, Natalie Jakucyn (Moderator), Glenbrook South High School, Glenview, IL
4th Annual USACAS Conference, Northfield, Illinois, June 17, 2007.

Abstract: The panelists, all of whom are U.S. CAS–active curriculum developers, each provided brief summaries of such issues as a brief history of their curriculum project, how CAS is used, some sample CAS lessons and problems, the challenges of writing and developing a CAS–active curriculum, and some lessons learned from their efforts.

“Computer Algebra Systems: Tools for Developing Algebraic Habits of Mind”
Al Cuoco, Bowen Kerins, Sarah Sword, and Kevin Waterman, Education Development Center
NCTM Annual Meeting, Atlanta, Georgia, March 21–24, 2007.

“CME Project: Promoting Mathematical Habits of Mind in High School”
Al Cuoco, Bowen Kerins, Sarah Sword, and Kevin Waterman, Education Development Center
NCSM Annual Meeting, Atlanta, Georgia, March 19–22, 2007.

 

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2006

“Some Tested Approaches to Topics in High School Mathematics”
Al Cuoco & CME Project Staff, Education Development Center
NCTM Annual Meeting, St. Louis, Missouri, Friday, April 28, 2006.

Abstract: This presentation looks at effective approaches to topics across the high school curriculum, including algebra word problems, geometric proofs, mathematical induction, and optimization. These approaches, many of which use technology, are being implemented in the CME Project.

“Using Computer Algebra Systems to Develop Algebraic Habits of Mind”
Al Cuoco, Education Development Center
NCTM Regional Meeting, Chicago, Illinois, September 20–22, 2006.

Abstract: Algebra is more than just a high school course sequence. Certain habits of mind lead to algebraic proficiency across the grades, and Computer Algebra Systems can help develop these habits. Among other things, this presentation looks at field-tested approaches to using Computer Algebra Systems to:

These approaches are being implemented in the CME Project.