The broader messages that we communicate through our choice of mathematical problems—how to do math, what math is for, and who it applies to—may privilege some students and exclude others. If “excellence in mathematics requires equity—high expectations and strong support for all students” (NCTM 2000, p. 12), one way to work toward equity within the classroom is to be careful about the messages we send to students through our problem choices.
News&Views: Is math politically neutral?
Mathew D. Felton
Common Core confusion about modeling
Mathew D. Felton-Koestler
Share news about happenings in the field of elementary school mathematics education, views on matters pertaining to teaching and learning mathematics in the early childhood or elementary school years, and reactions to previously published opinion pieces or articles. Find detailed department submission guidelines at http://www.nctm.org/WriteForTCM.
Book Review: Exploring Sfard's Commognitive Framework: A Review of Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing
Mathew D. Felton and Mitchell Nathan
Discourse as a medium of learning and instruction has gained tremendous ground among educational researchers and cognitive scientists. Yet earlier notions of cognition as computation have not been reconciled with views of knowing and learning as socially mediated processes. In Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing, Anna Sfard asks us to re-imagine thinking as communication, with the hopes that this will resolve many of the current dilemmas facing research on thinking in general, and in mathematics education in particular. In doing so, she argues that we should move beyond the metaphor of learning as acquiring knowledge—for example, treating knowledge of something like counting as an object that is “held” by the mind and applied when needed—to conceptualizing learning as participating in discourse—for instance, participating in a discourse that engages in counting when asked “which box has more?” Sfard begins with five quandaries facing paradigms that treat learning metaphorically as acquisition—such as, if a child “possesses” counting, then why would he or she not count when asked “which box has more?” Sfard then provides a thorough yet accessible review of previous learning paradigms, and lands finally on a redefinition of thinking as internalized communication. To break out of older modes of talking about thinking, she coins the term commognition as a mix of cognition and communication. By the end of the book, the new perspective of commognition is offered as a way to avoid the quandaries facing paradigms that treat learning as acquisition.
Preparing Teacher Leaders
Mathew D. Felton and Melissa Page
Findings from an extensive four-year program with a single cohort of elementary and early middle school mathematics instructors highlight several important themes that can inform other efforts in developing teacher leaders.
Commentary: Should Mathematics Teacher Education Be Politically Neutral?
Mathew D. Felton-Koestler and Courtney Koestler
Many current and prospective teachers, policy makers, and members of the public view mathematics as neutral and objective, and they expect mathematics teaching and teacher education to be neutral as well. But what would it mean to think of mathematics teacher education as politically neutral? Below we consider some questions that we see as highlighting why mathematics teacher education cannot be neutral. We are not the first to raise these issues, but we appreciate the opportunity to discuss and reflect on them among a community of mathematics teacher educators. Although these questions have always been relevant, we see their importance growing in the face of the increased mathematization of our world and a highly polarized political landscape with a seemingly increased public acceptance of oppressive discourse and actions (Potok, 2017).
Going with the Flow: Challenging Students to Make Assumptions
Mathew D. Felton, Cynthia O. Anhalt, and Ricardo Cortez
Future middle school teachers tested the waters of modeling in the classroom with a bath versus shower water conservation problem.
Construct It! What’s in a Name? Collecting, Organizing, and Representing Data
Eva Thanheiser, Courtney Koestler, Amanda T. Sugimoto, and Mathew D. Felton-Koestler
Build a classroom community by building representations and visualizations of data related to students’ names.
Mathematical Modeling in the High School Curriculum
Maria L. Hernández, Rachel Levy, Mathew D. Felton-Koestler, and Rose Mary Zbiek
Ideas from the GAIMME report illustrate how teachers can engage students in the modeling process.
“8 Teaching Moves Supporting Equitable Participation”
Marcy B. Wood, James Sheldon, Mathew D. Felton-Koestler, Joy Oslund, Amy Noelle Parks, Sandra Crespo, Helen Featherstone, and Introduction by: Sarah B. Bush
From the Archives highlights articles from NCTM’s legacy journals, as chosen by leaders in mathematics education.
8 Teaching Moves Supporting Equitable Participation
Marcy B. Wood, James Sheldon, Mathew D. Felton-Koestler, Joy Oslund, Amy Noelle Parks, Sandra Crespo, and Helen Featherstone
Try these suggestions to increase the mathematical participation of each student.