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Publication News!The Connecting with Mathematics materials are now available as Ways to Think About Mathematics: Activities and Investigations for Grade 6-12 Teachers, published by Corwin Press. Click here for ordering (and other) information. |
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Descriptions
of CwM components The Connecting with Mathematics (CwM) project was funded by National Science Foundation grant #ESI-9731244 |
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Empirical evidence consistently suggests that the single most important element in a child's success at learning is the quality of the teacher. Colleges and universities are called upon to strengthen their teacher preparation and teacher professional development programs. States and districts are also called upon to enhance their in-service opportunities. The materials of the Connecting with Mathematics (CwM) project are designed with the intention of filling these needs.The CwM materials help teachers learn new mathematical content directly relevant to the mathematics they are teaching, and also let them revisit familiar content approached in a new way. Teachers learn novel material through mathematical problem solving in an investigative style. Many curricula now give mathematical investigations a central role in their lessons. This adds an element of unpredictability to the directions that a lesson might take. Students discover something unexpected, or fail to understand something that is essential to the lesson. This places new demands on a teacher's flexibility and mathematical knowledge. Teachers need to know the possible directions students might pursue. They also need to know which directions are worth pursuing and will lead to development of mathematical concepts, and which directions are most likely dead ends. This knowledge helps them make critical pedagogical decisions as they facilitate or guide their students' work. The two main goals of the materials are:
- to engage participants in mathematical problem solving that supports their learning of college level mathematics, closely tied to the mathematics they teach to their students;
- to help participants to become comfortable with an exploratory style of learning and teaching mathematics.
The materials focus on:
- problem solving and reflecting on methods of solution;mathematical ways of thinking; analyzing problems;
- making connections among mathematical ideas, connections to current and emerging 6-12 curricula, connections to methods of effective teaching, and cross-grade connections.
The materials are intended to be used for:
- Professional development of 6-12 grades teachers of mathematics; Mathematics department in-house professional development or inservice summer workshops; Weekly or monthly PD courses for teachers taught at the universities; Courses in graduate programs for preservice or in-service mathematics teachers;
- Independent study or individual PD plans.
Several features distinguish our program from other preservice and professional development programs. First, during the course teachers work on rich exploratory mathematical problems from innovative curricula, then go beyond these problems to a deeper discussion of mathematical connections and more challenging problems, learning new content and approaches to problem solving along the way. Second, teachers learn how to conduct a mathematical investigation. After they solve a particular problem, they "tweak" the problem in a variety of ways, posing new problems that lead to investigations of more general or specific questions. Third, teachers learn how to use open-ended problems and investigations for the purpose of developing particular mathematical concepts. The CwM program emphasizes all components of mathematical investigation and problem solving: posing a problem; exploring the problem; making and modifying conjectures; testing conjectures; and proving conjectures. Fourth, teachers reflect on their explorations of rich mathematical problems in a group, an activity that they might promote with their students. They discuss the ways they can facilitate such investigations with their students and the goals they should pursue during such investigations.The materials were pilot tested during the fall and spring semesters of the 1999-2000 school year and during the Summers of 2000 and 2001 in four different settings:
- a district-wide professional development course for middle and high school teachers; a professional development course for middle and high school teachers from different districts; a graduate level methods course for preservice teachers;
- a summer institute for middle and high school mathematics teacher/leaders.
Connecting with Mathematics is one of the many projects in EDC's Center for Mathematics Education in the Division of Mathematics Learning and Teaching.
For further information, contact CwM at cwm@edc.org
©
Copyright 2004 Education Development Center, Inc.
(EDC)
