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
Richard Kitchen, Libni B. Castellón, and Karla Matute
By examining some of Ms. Hill’s instructional moves, we demonstrate how a fifth-grade teacher simultaneously developed her multilingual learners’ mathematical reasoning and mathematics register.
Keith Dreiling
The Trammel of Archimedes traces an ellipse as the machine’s lever is rotated. Specific measurements of the machine are used to compare the machine’s actions on GeoGebra with the graph of the ellipse and an ellipse formed by the string method.
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.
Jana Dean
Two classic hands-on tasks address conceptual understanding of functions. The tasks center student discourse and rough draft mathematics as students grapple with the relationship between input and output.
Aubrey Neihaus, Crystal Kalinec-Craig, Priya V. Prasad, and Marcy B. Wood
A guide for revising tasks with harmful contexts
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.
Krystal Jones Carter
A well-crafted classroom engineering challenge can effectively answer compelling questions about social and global responsibility.
