The Common Core State Standards for Mathematical Practice asks students to look for and make use of structure. Hence, mathematics teacher educators need to prepare teachers to support students’ structural reasoning. In this article, we present tasks and rubrics designed and validated to characterize teachers’ structural reasoning for the purposes of professional development. Initially, tasks were designed and improved using interviews and small pilot studies. Next, we gave written structure tasks to over 600 teachers in two countries and developed and validated rubrics to categorize responses. Our work contributes to the preparation and support of mathematics teachers as they develop their own structural reasoning and their ability to help students develop structural reasoning.
Characterizing Secondary Teachers’ Structural Reasoning
Stacy Musgrave, Cameron Byerley, Neil Hatfield, Surani Joshua, and Hyunkyoung Yoon
Experience First, Formalize Later
Sarah Stecher, Luke Wilcox, and Lindsey Gallas
The EFFL model empowers students to build strong conceptual understanding of mathematics through carefully designed, equity-minded activities that disrupt the traditional lecture-based classroom.
Using Series to Construct Pythagorean Triples
Darien DeWolf and Balakrishnan Viswanathan
This article provides a series-focused approach to computing Pythagorean triples.
From Notes to Strings
Rob Wieman, Lindsay Freedman, Paul Albright, Deb Nolen, and Jessica Onda
Four teachers and a teacher educator move from guided notes to strings in a series of problems that support students in increased engagement, reasoning, sense making, and problem solving.