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Supporting Reasoning and Explanations - Facilitator Edition is a Course

Supporting Reasoning and Explanations - Facilitator Edition

Started Jul 1, 2019


Full course description

Note: Module content is available to professional development facilitators, without fees, for use with professional learning communities in accordance with the use agreement.

This course, featuring Deborah Lowenberg Ball, is designed for facilitators to engage teachers in professional learning about the mathematical practices of reasoning and explanation. It includes opportunities to learn more about making, justifying and evaluating mathematical conjectures; unpacking students’ ways of reasoning and explaining; exploring teaching practices for uncovering and enhancing students’ reasoning; and developing ways to learn from video recordings of their own teaching.

Processes and practices are foundational to doing mathematics: They are crucial in how mathematical knowledge is leveraged to address problems and provide mechanisms for developing new mathematical knowledge. Mathematical practices are consistently included in standards for student learning (CCSS, NCTM, etc.). There is great potential for integrating such practices across the teaching of various strands of mathematics content and teachers are asked to find ways of meaningfully and consistently doing so. This module focuses on developing the knowledge and skills teachers need to understand and engage their students in using the mathematical practice of reasoning and explanation.

Although there is considerable demand for skilled professional development facilitation—few opportunities exist for facilitators to develop the knowledge and skills needed for this work. Developing Teaching Expertise (DTE) modules aim to address this need by creating professional development materials that increase access to expert teacher educators, while also increasing the capacity of individual facilitators.

Featured Mathematics Teacher Educator

Deborah Loewenberg Ball is the William H. Payne Collegiate Professor of Education at the University of Michigan, an Arthur F. Thurnau Professor, and the founding director of TeachingWorks.


This module packages content, materials, and tools to support the work and learning of a professional development facilitator who is (or will be) supporting the learning of a group of practicing elementary classroom teachers.

Learning Objectives

Professional development facilitators will develop knowledge and skills needed for facilitation while supporting practicing teachers in developing expertise with respect to four core elements of teaching reasoning and explanations- mathematics content, student thinking, teaching practices, and ways of learning from engagement in teaching:

  • Mathematics: using mathematical reasoning, explanations, and language

  • Student Thinking: supporting mathematical practices in the classroom

  • Teaching Practices: examining ways students make sense of and explain mathematics

  • Learning from Practice: studying the teaching and learning of mathematical practices through video workshops

Work on these elements is integrated across the ten sessions. Simultaneously working on the four core elements is important because the work of elementary mathematics teaching requires integrated attention to these elements in practice. When used with classroom teachers, the sessions can be used as 90-minute sessions that provide participants with opportunities to practice, build on, and extend ideas over time.

Certificate of Completion

A certificate of completion for this module is available through Canvas Catalog from the Developing Teaching Expertise (DTE) @ Mathematics project at the University of Michigan School of Education.

Developers of the materials

Developing Teaching Expertise (DTE) @ Mathematics is a materials development project based at the University of Michigan School of Education. The multidisciplinary, cross-institution team builds practice-focused professional development modules for elementary mathematics teachers. The multimedia materials create opportunities for PD groups and professional learning communities to learn from leading mathematics teacher educators about key topics in elementary mathematics education.


This material is based upon work supported by the National Science Foundation under Grant No. 1118745. Any opinions, findings, conclusions, and/or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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