DMI is a project within the Center for the Development of Teaching, Education Development Center, Inc.

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Developing Mathematical Ideas*

Developing Mathematical Ideas (DMI) is a professional development curriculum designed to help teachers think through the major ideas of K-7 mathematics and examine how children develop those ideas. At the heart of the materials are sets of classroom episodes (cases) illustrating student thinking as described by their teachers. In addition to case discussions, the curriculum offers teachers opportunities: to explore mathematics in lessons led by facilitators; to share and discuss the work of their own students; to view and discuss videotapes of mathematics classrooms; to write their own classroom cases; to analyze lessons taken from innovative elementary mathematics curricula; and to read overviews of related research.

DMI seminars are designed to bring together teachers from kindergarten through middle grades to:

  • learn mathematics content
  • learn to recognize key mathematical ideas with which their students are grappling
  • learn to support the power and complexity of student thinking
  • learn to appreciate the power and complexity of student thinking
  • learn how core mathematical ideas develop across the grades
  • learn how to continue learning about children and mathematics

School systems that have adopted innovative mathematics curricula have found DMI to be an important support. The materials have been used with practicing teachers in both summer institutes and school-year settings. In addition, DMI has served as core curriculum for programs designed for teacher-leaders, administrators, parents, and for pre-service teachers.

DMI Seminar Descriptions
DMI is comprised of seven seminars:

  • Number and Operations, Part 1: Building a System of Tens • Number and Operations, Part 1: Building a System of Tens Participants explore the base-ten structure of the number system, consider how that structure is exploited in multidigit computational procedures, and examine how basic concepts of whole numbers reappear when working with decimals.

  • Number and Operations, Part 2: Making Meaning for Operations • Participants examine the actions and situations modeled by the four basic operations. The seminar begins with a view of young children's counting strategies as they encounter word problems, moves to an examination of the four basic operations on whole numbers, and revisits the operations in the context of rational numbers.

  • Geometry: Examining Features of Shape • Participants examine aspects of 2D and 3D shapes, develop geometric vocabulary, and explore both definitions and properties of geometric objects. The seminar includes a study of angle, similarity, congruence, and the relationships between 3D objects and their 2D representations.

  • Geometry: Measuring Space in One, Two and Three Dimensions • Participants examine different attributes of size, develop facility in composing and decomposing shapes, and apply these skills to make sense of formulas for area and volume. They also explore conceptual issues of length, area, and volume, as well as their complex inter-relationships.

  • Working with Data • Participants work with the collection, representation, description, and interpretation of data. They learn what various graphs and statistical measures show about features of the data, study how to summarize data when comparing groups, and consider whether the data provide insight into the questions that led to data collection.

  • Number and Operations, Part 3: Reasoning Algebraically about Operations • Participants examine generalizations at the heart of the study of operations in the elementary grades. They express these generalizations in common language and in algebraic notation, develop arguments based on representations of the operations, study what it means to prove a generalization, and extend their generalizations and arguments when the domain under consideration expands from whole numbers to integers.

  • Patterns, Functions, and Change • Patterns, Functions, and Change Participants discover how the study of repeating patterns and number sequences can lead to ideas of functions, learn how to read tables and graphs to interpret phenomena of change, and use algebraic notation to write function rules. With a particular emphasis on linear functions, participants also explore quadratic and exponential functions and examine how various features of a function are seen in graphs, tables, or rules.

Materials for Participants: The Casebooks

Each seminar is built around a casebook containing 25 to 30 cases, grouped into seven chapters, which track a particular mathematical theme from kindergarten through grade six. Casebooks begin with an overview of the seminar, and each chapter contains an introduction intended to orient the reader to the major theme of the cases in that chapter. They conclude with an essay summarizing the ideas explored in the seminar through the lens of educational research or from the perspective of a mathematician.

Materials for Facilitators

The DMI Facilitator’s Guides include detailed agendas for each session. Other components are intended to help facilitators: identify particular strategies useful in leading case discussions and mathematics activities; plan seminar sessions; understand the major ideas to be explored in each session; and think through issues of teacher change.

The DMI Video Cases show students in a wide variety of classroom settings with children and teachers of different races and ethnic groups. While written cases allow users to examine student thinking at their own pace, returning, if necessary, to ponder and analyze particular passages, video offers users the opportunity to listen to real student voices in real time and provides rich images of classrooms organized around student thinking.

DMI Institutes

The Developing Mathematical Ideas Institute is designed to provide classroom teachers, teacher-leaders, mathematics specialists, coaches, and administrators an opportunity to experience one of the DMI modules in a supportive learning community. At the one-week seminar, participants experience all eight sessions of the DMI module of their choice as a learner in sessions conducted by staff. The 2008 DMI Institute will be held at Mount Holyoke College in MA July 12-18. The fee for the program is $2000. Click here for more information.

The DMI Facilitation (DMIF) Institute is designed for teams of staff developers, teacher-educators, teacher-leaders and others who support teachers' professional development in mathematics K-8. Institute participants work in a community of peers to inquire into the goals of professional development for elementary and middle school mathematics, reflect on the kinds of structures and activities that can support those goals, and become familiar with DMI as a tool to forward the mathematics education agenda at their sites. The 2008 DMI Facilitation Institute will be held at Mount Holyoke College in MA July 12-18. The fee for the program is $2000. Participants may also create a two-week program by linking the DMI Institute with the DMIF program for a fee of $2600. Click here for more information.

For More Information

To order materials from Pearson Learning, call (800) 321-3106 or click here to visit the Pearson website. For more information about the DMI Institutes, visit the Mathematics Leadership Program website.

Since the DMI materials became available for field testing in 1996, facilitators have come forward with advice to other users. Some of these suggestions are captured in the pages access through the link Advice from DMI Users.

Associated with DMI are a variety of research and direct service projects. The linked page, Research into the Use and Impact of DMI, lists the questions that are currently being investigated and identifies the researchers. The following linked pages describe the different projects.

Teaching to the Big Ideas 2 (1998-2003) funded by the National Science Foundation , Deborah Schifter, Virginia Bastable, and Susan Jo Russell, coPIs.

Teaching to the Big Ideas, (1993-99) funded by the National Science Foundation, Deborah Schifter, Virginia Bastable, and Susan Jo Russell, co-PIs

Network for Inquiry into Mathematics Education, (1995-99) funded by the National Science Foundation, Linda Davenport and Deborah Schifter, co-PIs

The DMI Network, (1997-2000) funded by the DeWitt Wallace-Readers Digest Fund, Linda Davenport, director

Cultivating Inquiry into the Teaching of Mathematics: A Seminar for Undergraduates, (1997-99) funded by the Exxon Educational Foundation, Jill Lester, director

When the learners' thinking takes center stage: A study of teacher and classroom change, (1997-99) funded by the Spencer Foundation, Sophia Cohen, director

Middle Grades Geometry Project: Examining Features of Shape (2000-2001), funded by the SummerMath for Teachers Program at Mount Holyoke College, Virginia Bastable

Developing Mathematical Ideas, Pre-service Working Group (1999-present),
funded by the ExxonMobil Foundation, Jill Bodner Lester

For more information about these projects and about sites at which DMI has been used, please contact:

Deborah Schifter
Center for the Development of Teaching
Education Development Center, Inc.
55 Chapel Street
Newton, MA 02158
617-969-7100x2564
Dschifter@edc.org

* The DMI curriculum is the result of a collaboration among the Educational Development Center, Inc., TERC, and Mount Holyoke College with funding provided by the National Science Foundation and the ExxonMobil Foundation. Project directors are Deborah Schifter, Susan Jo Russell, and Virginia Bastable

 

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