To learn mathematical practices, students need opportunities to engage in them. But simply providing such opportunities may not be sufficient to support all students. Simultaneously, explicitly teaching mathematical practices could be problematic if instruction becomes prescriptive. This study investigated how teachers might make mathematical practices explicit in classroom discourse. Analyses of 26 discussions from 3 mathematics classes revealed that teachers made mathematical practices explicit primarily after students had participated in them. I present a framework of 8 types of teacher moves that made mathematical practices explicit and argue that they did so without turning practices into prescriptions or reducing students' opportunities to engage in them. This suggests a need to expand conceptions of explicitness to promote access to mathematical practices.
Jacqueline Coomes and Hyung Sook Lee
A formative assessment framework is interpreted in light of the gaps between student work and proficient uses of the mathematical practices.
Kelley Buchheister, Christa Jackson, and Cynthia Taylor
Conversations from a second-grade class demonstrate how teachers can use mathematical games to emphasize key ideas from the Common Core's Standards for Mathematical Practice.
Esther M. H. Billings, David C. Coffey, John Golden, and Pamela J. Wells
A professional development workshop supports teachers' understanding of the Standards for Mathematical Practice and helps them transfer this knowledge to the middle school classroom.
Teachers can benefit from productive and manageable suggestions to align instruction to the intention of the Common Core's Standards for Mathematical Practice.
Nasir Na'ilah Suad and Maxine McKinney de Royston
This article explores how issues of power and identity play out in mathematical practices and offers a perspective on how we might better understand the sociopolitical nature of teaching and learning mathematics. We present data from studies of mathematics teaching and learning in out-of-school settings, offering a sociocultural, then a sociopolitical analysis (attending to race, identity, and power), noting the value of the latter. In doing so, we develop a set of theoretical tools that move us from the sociocultural to the sociopolitical in studies of mathematics teaching and learning.
Keith Weber, Juan Pablo Mejía-Ramos, and Tyler Volpe
goals that we have with proof should be epistemological in nature. For instance, mathematics educators want students to recognize that proof is crucial to mathematical practice and to appreciate the broad range of functions that proof can play in
Tonya Bartell, Anita Wager, Ann Edwards, Dan Battey, Mary Foote, and Joi Spencer
The Common Core State Standards for Mathematics (CCSSM) do not make any promises about the teaching practices that should be used to support students' enactment of the standards. Thus, equity gets framed as achievable through making the standards a goal for all students. We know from research on past reform efforts that standards without explicit (or companion) teaching practices, and teaching practices without explicit attention to equity, will inevitably result in the failure of the standards to achieve goals for students. This commentary provides a framework for future research that hypothesizes research-based equitable mathematics teaching practices in support of the CCSSM's Standards for Mathematical Practice, connecting research, policy, and practice in order to realize the equity potential of the CCSSM.
Stephen F. Bismarck, Jeremy Zelkowski, and Jim Gleason
“How much do you think gas will cost when I graduate from high school?” Like many commodities, the price of gasoline continues to rise, and these price changes are readily observed in gas stations' signage. Moreover, algebraic methods are well suited to model price change and answer the student's question. Over the course of one ninetyminute block or two forty-five-minute classes, students build functions and interpret them in context. This article presents the activity, describes its implementation, provides sample student work, and discusses its relationship to the Standards for Mathematical Practice from the Common Core State Standards. Data used in the activity are available at http://data.bls.gov/cgi-bin/surveymost?ap.
Melanie Wenrick, Jean L. Behrend, and Laura C. Mohs
See how the NCTM Process Standards in action integrate Common Core State Standards in a second-grade classroom.