Center for Mathematics Education
An EDC project in the
Center for Mathematics Education Projects
Think Math! is a comprehensive K-5 mathematics curriculum funded by the National Science Foundation. The series, developed under the working title Math Workshop, is published by School Specialty. Think Math! does not pit skill against problem solving. Rather, it builds computational fluency through plentiful practice in basic skills as students investigate new ideas and solve meaningful problems. Lessons provide glimpses of ideas to come, letting students build familiarity and develop conceptual understanding as they apply, sharpen, and maintain skills they already have. Think Math! was also designed with teachers in mind, honoring their need, as adults, to have something that attracts and holds their interest, and acknowledging their need, as learners with little available time, to have a learning-by-doing opportunity for professional growth.
Developed by EDC's Center for Mathematics Education, CME Project is a coherent, four-year, NSF-funded high school program published by Pearson. The series is designed around how knowledge is organized and generated within mathematics: the themes of algebra, geometry, analysis, probability, and statistics. Many standard curricula look at each of these areas as sets of results and techniques. Many integrated programs look at them as threads that run through varying contexts. CME Project sees these branches of mathematics not only as compartments for certain kinds of results, but also as descriptors for methods and approaches - the habits of mind that determine how knowledge is organized and generated within mathematics itself. As such, they deserve to be centerpieces of a curriculum, not its byproducts.
This project provides two years of professional development and lesson study support to teams of middle and high school teachers in the Greater Boston area, as well as building a community of teachers around lesson study in mathematics. Our goals are to enhance knowledge of mathematics and pedagogy, introduce teachers to lesson study, build a community of teachers interested in lesson study, and learn how the Japanese lesson study model can be adapted to become a successful professional development model for U.S. secondary school mathematics teachers. Teacher teams attend workshops at EDC and complete four or more full cycles of lesson study with the support of a team coach/advisor.
Boston University's Program in Mathematics for Young Scientists (PROMYS) has offered high school students challenging experiences of mathematical exploration since 1989. PROMYS and CME are now collaborating on a project that will extend the PROMYS experience by engaging local high school teachers in the program's summer activities and by hosting professional development seminars during the academic year. During the summer component, teachers and students work together to develop independent mathematical projects under the supervision of research mathematicians. These projects are refined for use in the high schools as enrichment projects to complement the new and emerging curricula. The participants' work in the summers is supported by daily discussions and problem sets designed to develop the habits of thought necessary for creative mathematical research. Projects are transported back to the high schools where they are presented and further developed in collaboration with other students. During the academic follow-up years, seminars for teachers are offered jointly by CME and the Boston University Mathematics Department. These seminars are devoted to exploring particular research ideas and how they can be used to enrich the curricula being used in the schools.
Some of our completed projects
The K-12 Mathematics Curriculum Center, a collaboration with other EDC staff, supports school districts as they consider and implement new mathematics curricula that align to the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards for School Mathematics. The Center offers a variety of products and services to assist district leadership with curriculum selection and implementation. Print resources include Curriculum Summaries; Choosing a Standards-based Mathematics Curriculum, a guide that suggests a process for considering new instructional materials; and a collection of Curriculum Perspectives from teachers, administrators, and developers who use these new programs. In addition, the Center offers a series of seminars focused on considering new standards-based curricula, professional development for successful implementation, and leadership for curricular change.
The Number Crew is a multimedia K–1 mathematics curriculum originally developed for use in the United Kingdom. Public Media Education, Inc. has provided funding for adapting the materials (video, print, and CD-ROM) for use in the U.S.
Seeing the Connections was a collaboration of the University of New Hampshire, Stony Brook University, and Education Development Center. The Seeing the Connections staff is producing, piloting, and disseminating curriculum modules for use in mathematics courses that help preservice teachers develop a knowledge of mathematics for teaching. Building on successful NSF-funded proof-of-concept projects, the Seeing the Connections curriculum helps secondary teachers develop important mathematical knowledge and skills required in their future careers—designing effective lessons, emphasizing certain ideas over others, connecting ideas across the grades, understanding germs of insight in students' questions, and placing topics in the precollege curriculum in the broader mathematical landscape.
In collaboration with the Math Forum (and initially funded but NSF), this project provides teachers, students, and parents with a searchable Web resource of problems complementing the NSF mathematics curricula grades 6–12. We have designed orchestrated problem sets to help students develop both deep conceptual understanding and technical skills, and to practice, assess, and integrate these concepts and skills. This database classifies problems by topic, difficulty level, and use of computational technology.
Connected Geometry is a geometry curriculum, funded by the National Science Foundation, designed to help teachers and students engage in meaningful mathematical activity by offering students a chance to understand and appreciate the connections and unifying themes within mathematics, and to build on the connections between students' backgrounds and mathematics. The Connected Geometry text has been revised, and is now CME Project — Geometry.
This project, in collaboration with other EDC staff, develops curriculum materials for use in professional development programs for practicing grade 7-12 mathematics teachers. The curriculum modules are designed to connect advanced mathematical ideas with problems and contexts that occur in secondary school curricula. The materials created by the CwM team were published by Corwin Press as Ways to Think About Mathematics: Activities and Investigations for Grade 6-12 Teachers.
A mathematics research experience for secondary students seems like a good but infeasible idea: How can they contribute to a field that builds on itself the way mathematics does? We have developed a collection of research projects that allow typical high school students to engage in a mathematical research experience, involving problems appropriate to their mathematical backgrounds. While these projects may not contain new results, they embody a true research experience in that students can begin with a problem, build a model, conduct experiments, make conjectures, and work towards a deductive proof as a final goal.
The M2HS curriculum takes seriously the methods by which mathematics is created and applied. Field-tested with typical high school students, these materials promote useful mathematical habits of mind, teach techniques that are rarely taught in school but that technical professionals use all the time, provide opportunities to think mathematically about hard problems, and let students and teachers in on the process of creating, inventing, conjecturing, experimenting, revising, and proving. The program takes up many traditional topics in high school mathematics, but its focus is on the mathematical thinking that underlies the topics. In addition, it treats some areas that are new to the high school curriculum, including the mathematics behind the codes that make electronic communications secure, methods for fitting mathematical functions to a wide variety of situations, and a historical introduction to the ideas behind calculus. The Mathematical Methods materials have now been incorporated into the CME Project.
Mathematical Methods in High School: A Mathematical Companion
This project is developing a resource book for teachers centered around the topics in our Mathematical Methods in High School curriculum. Topics include mathematical induction, difference calculus, number theory and cryptography, polynomials, complex numbers, trigonometry, and ideas from calculus. The materials are specifically designed for teachers, making connections to secondary classrooms, developing the history of ideas that led to the major advances, and helping teachers develop or refresh their understanding of topics that are somewhat new to the secondary curriculum.
This project was a collaboration among Education Development Center, the University of Massachusetts at Lowell, and the Eastern Massachusetts Association of Mathematics Department Heads. We designed and implemented a professional development program for mathematics department heads and lead teachers at the 7–12 level. This project's content has four strands: (1) engaging in new mathematics; (2) developing leadership skills; (3) planning for and providing professional development opportunities for teachers in participants' schools or districts; and (4) understanding new mathematics curricula and the issues involved in implementing them. At the conclusion of this program we hosted a national conference to help other leaders throughout the country design and implement similar programs for building regional capacity.