Developing Mathematical Ideas courses are a set of coordinated professional development experiences for teachers, teacher-leaders, math specialists, math coaches, building principals, central office staff, and/or professional development providers.

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 video 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.

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

We offer weeklong Developing Mathematical Ideas courses each summer. Please refer to our schedule to see when they are offered. Below is a description of each institute.

Building a System of Tens: Calculating with Whole Numbers and Decimals

Participants explore the base-ten structure of the number system, consider how that structure is exploited in multi-digit computational procedures, and examine how basic concepts of whole numbers reappear when working with decimals. (New 2016 edition)

Making Meaning for Operations in the Domains 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 2016 edition)

Reasoning Algebraically about Operations in the Domains of Whole Numbers and Integers

In a culture of communal inquiry, 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. (New 2018 edition)

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.

Other DMI Modules

There are four other DMI modules in the the series. Email grad-math-education-programs-g@mtholyoke.edu to learn more about these options.

Examining Features of Shape (EFS)
Participants examine aspects of 2D and 3D shapes, develop geometric vocabulary, and explore both definitions and properties of geometric objects. The course 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 (MS123)
Participants examine different aspects 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.

Statistics: Modeling with Data (SMWD)
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.

Patterns, Functions, and Change (PFC)
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.