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Constructing & Critiquing Mathematical Arguments

Course Description: 

Constructing viable arguments and critiquing the reasoning of others (CCSS.MP3) is a vital standard of mathematical practice in the Common Core; it is also a call to action to expand our definition of proof from a process generally limited to Geometry classes to the broader, more social mathematical habit of mind of "convincing your skeptical peers," a habit that can be practiced in every math classroom each and every day. In this course, we will share, reflect upon, and develop classroom structures, tasks, teacher moves, and assessments to help make this value visible and effective in helping student sensemaking. We will explore how to help students construct informal mathematical arguments and explanations, along with how and when to make these arguments more rigorous. We will also look at a crucial complement to constructing arguments: building a classroom culture of skeptical peers who critically examine, respond to, and build on the reasoning and arguments of others. 

Course participants will actively engage in doing, making sense of, and reflecting upon mathematics and teaching. Our goal is for this course to be challenging (in a good way) both mathematically and pedagogically.

Keywords: mathematical practices, common core, mathematical arguments, proof, CCSS.MP3, mathematics, Common Core, sensemaking

Audience: Middle and high school math teachers

Dates & Times: Jul 31 - Aug 4, 2017

  • Mon | 10:00a - 4:00p
  • Tue - Thu | 9:00a - 4:00p
  • Fri | 9:00a - 1:30p
Format of Course: In-person at Stanford University, with follow-up virtual learning communities throughout the school year


  • $750 (Individual)
  • $700 (Group - 3 or more teachers from the same school or district)
Units: 2 Status: Registration opens Tuesday, Jan 17, 4:00p PT

*Please note: The cost for this course includes morning coffee/tea service, lunch, and a reception. This cost does not include lodging or transportation. Please see the Festival Location, Lodging, & Transportation page.  

Connecting teachers from around the globe to share and grow in teaching excellence. This course is part of the Stanford Teaching Festival (STF). The STF aims to bring together teachers from varied classrooms and contexts worldwide. Teachers participate in a common, in-person, high-quality professional learning experience over the summer, and are provided with the resources, tools, and support to engage and grow with one another in meaningful learning communities throughout the school year. 

Course Facilitators: 

Anna Blinstein is passionate about mathematics education. She has a B.A. in Mathematics and Molecular Biology and is a graduate of the Stanford Teacher Education Program, where she became interested in how students construct mathematical understanding. Anna has been teaching math to middle and high-school aged students for 13 years and is a founding teacher of the Nueva Upper School, where she works on developing curriculum and teaching methodology based on rich tasks, projects, and modeling activities.

Avery Pickford is currently a fifth- and sixth-grade math teacher at the Nueva School in Hillsborough, CA. He has taught math and science for eighteen years to students ranging from third grade to graduate school. He enjoys leading and participating in hands-on professional development and is always eager to discuss mathematics as a verb.