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.
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Stacy Musgrave, Cameron Byerley, Neil Hatfield, Surani Joshua, and Hyunkyoung Yoon
Gülseren Karagöz Akar, Merve Saraç, and Mervenur Belin
In this study, we investigated prospective secondary mathematics teachers’ development of a meaning for the Cartesian form of complex numbers by examining the roots of quadratic equations through quantitative reasoning. Data included transcripts of the two sessions of classroom teaching experiments prospective teachers participated in, written artifacts from these teaching sessions, and their answers to pre-and-post written assessment questions. Results point toward prospective teachers’ improved meanings regarding the definition of complex numbers and the algebraic and geometrical meanings of the Cartesian form of complex numbers. Implications for mathematics teacher education include providing specific tasks and strategies for strengthening the knowledge of prospective and in-service teachers.
Chris Harrow and Justin Gregory Johns
Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to mtlt@nctm.org. If published, the authors of problems will be acknowledged.
Casey Hawthorne and John Gruver
This instructional sequence develops your students’ meaningful understanding of algebraic expressions.
Kristin Doherty
Support students in conjecturing in ways that can promote their agency in the learning process.
Alison Williams and Lisa Lamb
Easy to implement, this strategy has a powerful positive impact in mathematics classrooms.
Isabel White, Michael Foster, and Joanne Lobato
Explore three challenges that students faced and how they made progress.
Sharon B. Hoffert and Introduction by: Candies Cook
From the Archives highlights articles from NCTM’s legacy journals, previously discussed by the MTLT Journal Club.
Laura Bofferding and Yi Zhu
Different types of tangram puzzles can encourage students to make sense of problems and engage in the computational thinking practice of debugging.
George J. Roy, Matthew Cunningham, and Kenneth Rafanan
Teachers have the opportunity to make mathematics relevant. We leveraged the popularity of Star Wars to engage students in exploring and connecting two dimensions and three dimensions to careers in toy design.
