# What We Offer

MATM consists of 18 credits in mathematics content and 14 credits of educational leadership courses. The core curriculum of the math courses is based on the Developing Mathematical Ideas (DMI) and Connecting Arithmetic to Algebra (CAA) professional development materials.

Developing Mathematical Ideas (DMI) is a professional development curriculum designed to help teachers think through the major ideas of K-8 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 video clips of mathematics classrooms, to examine the Common Core Standards for Mathematical Practice, to analyze lessons taken from innovative elementary mathematics curricula, and to read overviews of related research.

Courses 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 how core mathematical ideas develop across the grades.
• Learn how to continue learning about children and mathematics.

### X.MATH 462: Fostering Algebraic Reasoning 

Description: 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. In addition, they investigate the thinking of their own students working on similar ideas by recording and analyzing their own lessons and interviews with their students. Examination of the links between Common Core Math Practice Standards is also included.

Credits: 3

### X.MATH-400 | Developing Mathematical Ideas: Building a System of Tens 

Description: Participants will 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. They will study the various ways children naturally tend to think about separating and combining numbers and what children must understand in order to work with numbers in these ways.

Credits: 2

Offered: Summer

Format: Live classes on campus or online via Zoom

### X.MATH-401 | Developing Mathematical Ideas: Making Meaning for Operations 

Description: This course provides opportunities for participants to examine the actions and situations modeled by the four basic operations. The course will begin 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.

Credits: 2

Offered: Summer

Format: on-campus

### X.MATH-402 | Developing Mathematical Ideas: Examining Features of Shape 

Description: Participants examine aspects of two-dimensional and three-dimensional 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 three-dimensional objects and their two-dimensional representations. Participants examine how students develop these concepts through analyzing print and video cases as well as reading and discussing research articles.

Offered: Summer

Credits: 2

Format: Live classes on campus or online via Zoom

### X.MATH-405 | Developing Mathematical Ideas: Measuring Space in One, Two and Three Dimensions 

Description: Participants will 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 will also explore conceptual issues of length, area, and volume, as well as their complex interrelationships.

Offered: Summer

Credits: 2

Format: Live classes on campus or online via Zoom

### X.MATH-406 | Developing Mathematical Ideas: Patterns, Functions and Change 

Description: 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. Participants examine how students develop these concepts through analyzing print and video cases as well as reading and discussing research articles.

Offered: Summer

Credits: 2

Format: Live classes on campus or online via Zoom

### X.MATH-407 | Reasoning Algebraically About Operations 

Description: 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.

Offered:  Summer

Credits: 2

Format: Live classes or online via Zoom

### X.MATH-424 | Developing Mathematical Reasoning 

Description: Developing Mathematical Reasoning builds on and extends the work of X.MATH-460 | Connecting Arithmetic to Algebra. Students will work with a five-phase model for instruction in mathematical argument: Noticing, Articulating, Representing Specific Instances,Creating Mathematical Argument, and Comparing and Contrasting Operations. They will examine and implement a set of lessons designed to engage their own students with generalizations about the operations using these phases of instruction. Developing Mathematical Reasoning investigates how this approach to mathematics thinking supports a range of mathematics learners including those who have difficulty with grade-level mathematics and those who need additional challenge. A major focus of the course are student thinking assignments in which participants describe the thinking of their own students and the teacher moves they utilize to support them.

Credits:  4

Offered:  Spring

Format:  Online, mostly asynchronous with four live sessions

### X.MATH-460 | Connecting Arithmetic to Algebra 

Description: Connecting Arithmetic to Algebra (CAA) is a year-long professional development experience in which teachers consider generalizations that arise from the study of number and operations in grades 1 through 7. They examine cases of students who are engaged in the process of articulating general claims, working to understand those claims, and learning how to prove them. The course also focuses on how this approach to mathematical thinking supports a range of mathematics learners, including those who have difficulty with grade- level mathematics and those who need additional challenge.

Offered: Fall

Credits: 4

Format: Online, mostly asynchronous with four live sessions

### X.MTHED 462: Fostering Algebraic Reasoning 

Description: 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. In addition, they investigate the thinking of their own students working on similar ideas by recording and analyzing their own lessons and interviews with their students. Examination of the links between Common Core Math Practice Standards is also included.

Credits: 1

### X.MTHED-409 | Educational Leadership I: Exploring the Rules of Math Teacher Leadership 

Description: This course will explore the roles of teacher leadership in math education at the local, state, and national level. Topics will include coaching, mentoring, writing (blogs, journals, op-eds, articles), professional learning communities (virtual and face-to-face), and advocacy. Participants will consider current issues and challenges facing students and teachers with regard to math education and will work to develop action plans to address these issues in the coming school year.

Offered: Summer

Credits: 2

Format: Live classes on campus or online via Zoom

### X.MTHED-410 | Developing Mathematical Ideas: Facilitator Training 

Description: This course focuses on understanding the process of facilitating Developing Mathematical Ideas seminars. Students will analyze key mathematical and pedagogical ideas, examine the affordances of various instructional formats, learn how to respond in writing to the ideas of their seminar students, discuss issues of engaging adult learners, become familiar with the links between Developing Mathematical ideas and the Common Core content and practice standards as well as the NCTM teaching practices, and explore how to situate Developing Mathematical Ideas seminars in their own systems. Students will be actively engaged in every session, working in small group and whole group formats.

Credits: 2

Offered: Summer

Format: Live classes on campus or online via Zoom

### X.MTHED-411 | Educational Leadership II: Facilitating Adult Learning 

Description: This course will support students in developing skills and knowledge to enable them to design and implement professional learning opportunities in mathematics for adults. Activities focus on four aspects: the importance of identifying key ideas and goals for professional learning, strategically using both small and whole group formats, an analysis of the range of professional learning experiences for teachers, and opportunities to practice facilitating professional learning with an audience of teachers.

Offered: Summer

Credits: 2

Format: Live classes on campus or online via Zoom

### X.MTHED-465 | Action Research on Learning and Teaching 

Description: This course will include action research on the mathematics learning of students and pedagogical moves of teachers. Participants will produce written cases of practice based on audio or videotaped classroom discussions and interviews with their own students.  Participants will analyze their own cases and those of their colleagues to examine the learning of students and the impact of teacher moves. Course instructors will also provide individual feedback based on the classroom cases.

Offered: Academic Year

Credits: 4

Format: Online, mostly asynchronous with four live sessions

### X.MTHED-466 | Advocacy through Math Teacher Leadership 

Description: The course involves exploring teacher leadership roles in mathematics education and how to advocate for change in the field. Students will create an action plan related to a change initiative in math education, develop a capstone project, and share findings and reflections so the group can provide critical feedback and support. The scalable nature of this work allows each student to define a leadership role and project to fit their interests and professional goals.

Credits: 2