X.MATH-400 Developing Mathematical Ideas: Building a System of Tens
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.
X.MATH-401 Developing Mathematical Ideas: Making Meaning for Operations
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.
X.MATH-402 Developing Mathematical Ideas: Examining Features of Shape
Participants examine aspects of two-dimensional and three-dimensional 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 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.
X.MATH-404 Developing Mathematical Ideas: Modeling With Data
Participants will work with the collection, representation, description, and interpretation of data. They will 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 provides insight into the questions that led to data collection.
X.MATH-405 Developing Mathematical Ideas: Measuring Space in One, Two, and Three Dimensions
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.
X.MATH-406 Developing Mathematical Ideas: 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. Participants examine how students develop these concepts through analyzing print and video cases as well as reading and discussing research articles.
X.MATH-407 Developing Mathematical Ideas: 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.
X.MATH-415 Early Numeracy Assessment and Instruction I
This course helps teachers identify and address challenges students are having with K-2 math skills. Interview assessments that help teachers develop strategies to monitor and support progress in number words and numerals, structuring numbers, and addition and subtraction are learned and put into practice. Through assessments, data and teaching tools, teachers will recognize their students' current levels of numeracy and make data-driven instructional decisions. This course supports Pk-2 educators with core instruction, and Pk-8 educators working with students who haven't yet learned the Pk-2 standards. This course provides a certificate of completion from the US Math Recovery Council.
X.MATH-424 Developing Mathematical Reasoning
Developing Mathematical Reasoning (DMR) builds on and extends the work of Connecting Arithmetic to Algebra. Participants 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. DMR 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.
X.MATH-460 Connecting Arithmetic to Algebra
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.
X.MATH-470 The Process of Teaching and Learning: Math Curriculum Development and Instruction
Students will learn about developmental math curriculum development and instruction in PreK-6 classrooms. They will construct more extensive understandings of math instruction by developing lessons that implement the Massachusetts Frameworks incorporating the Common Core State Standards for Mathematics. Emphasis will be on learning diverse management and instructional practices, such as the use of manipulatives, math talks, problem solving, cooperative learning, and project-based learning. Students will also become more adept at developing effective approaches to using assessment to guide instruction.
X.MTHED-408 Professional Development for Coaching Mathematics
This course is designed for elementary math specialists with responsibilities for supporting teachers in the development of strong mathematics education programs. Participants explore issues related to: learning mathematics while in the context of teaching; facilitating the professional development of colleagues; teachers' and students' ideas about mathematics and learning; and fostering a stance of collaborative investigation. By way of a central theme of mathematics learning, the institute will offer coaches opportunities to explore, through the coaching perspective, ideas of number and geometry in the elementary grades.
X.MTHED-409 Educational Leadership I: Exploring the Roles of Math Teacher Leadership
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.
X.MTHED-410 Developing Mathematical Ideas: Facilitator Training
This institute focuses on learning to teach one of the Developmental Mathematical Ideas (DMI) modules. Participants will choose a particular DMI module on which to concentrate their facilitation work. The institute will include examination of the central mathematical ideas of the module, identifying key goals for each session, discussion of the process of interacting with participants both in the institute sessions and through written responses, as well as opportunities for practice facilitation.
X.MTHED-411 Educational Leadership II: Facilitating Adult Learning
This course provides opportunities for participants to develop 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 opportunities for teachers, and opportunities to practice facilitating professional learning with an audience of teachers.
X.MTHED-465 From Theory to Practice: The Learning and Teaching of Mathematics
This course focuses on the teaching and learning of mathematics and considers how we move from theory to practice. The course focuses on the pedagogical moves of the teacher and the impact on students' mathematical experiences. Participants in the course will produce written cases of practice based on audio or videotaped classroom discussions and interviews with their own students. They 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 provide individual feedback based on the classroom cases.
X.MTHED-466 Advocacy Through Math Teacher Leadership
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.
