About Developing Mathematical Ideas (DMI)

Developing Mathematical Ideas (DMI) is a professional development curriculum designed to help teachers think through the major ideas of elementary and middle-school mathematics and examine how students 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 DVD clips 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.

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Revised DMI Materials DMI Casebook Cover CreateSpace

Thanks to the support of the Bill and Melinda Gates Foundation and the National Council of Teachers of Mathematics, two of the Developing Mathematical Ideas modules have been revised to highlight the connections to the Common Core content and practice standards. Revised modules (third edition) will be available through NCTM beginning December 2015. For facilitators who already have the second edition of the facilitator’s guides, supplements that contain the revisions to the guides can be found here.



DMI Seminars:

DMI seminars are designed to bring together teachers from Kindergarten through middle school 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 how core mathematical ideas develop across the grades
– Learn how to continue learning about children and mathematics


DMI Curriculum:

DMI consists of seven modules, each designed for eight 3-hour sessions of professional development.

Building a System of Tens: Calculation with Whole Numbers and Decimals
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. (New third edition.)

Making Meaning for Operations: In the Domain of Whole Numbers and Fractions
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. (New third edition.)

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.

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.

Reasoning Algebraically about Operations: In the Domain of Whole Numbers and Integers
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
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 into middle school. 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: understand the major ideas to be explored in each session; identify particular strategies useful in leading case discussions and mathematics activities; plan seminar sessions; and think through issues of teacher change.

The DMI DVD 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, the DVD clips offer users the opportunity to listen to real student voices in real time and provides rich images of classrooms organized around student thinking.

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