Learn why collecting, clarifying, and revoicing—often great teaching moves—do not always work.

# Browse

### Laura R. Van Zoest, Shari L. Stockero, Blake E. Peterson, and Keith R. Leatham

### Stacy K. Boote and Terrie M. Galanti

Elementary school students use physical manipulatives (e.g., pattern blocks) to make sense of the geometry and measurement ideas in a Code.org block-based programming lesson.

### Karen Zwanch and Bridget Broome

This game teaches algebraic generalizations through differentiated play in pairs, small groups, or as a whole class and uses manipulatives to bridge numerical and algebraic thinking.

### Katherine Ariemma Marin and Natasha E. Gerstenschlager

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

### Chris Harrow, Justin Gregory Johns, Ryne Cooper, and Vivekanand Mandel

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.

### Dana L. Grosser-Clarkson and Joanna S. Hung

This Perspectives on Practice manuscript focuses on an innovation associated with “Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task” from Volume 7, Issue 2 of *MTE*. The Flint Water Task has shown great promise in achieving the dual goals of exploring mathematical modeling while building awareness of social justice issues. This *Perspectives on Practice* article focuses on two adaptations of the task—gallery walks and What I Know, What I Wonder, What I Learned (KWL) charts—that we have found to enhance these learning opportunities. We found that the inclusion of a gallery walk supported our students in the development of their mathematical modeling skills by enhancing both the mathematical analyses of the models and the unpacking of assumptions. The KWL chart helps students document their increase in knowledge of the social justice issues surrounding the water crisis. Using the mathematical modeling cycle to explore social justice issues allows instructors to bring humanity into the mathematics classroom.

### Margaret Rathouz, Nesrin Cengiz-Phillips, and Angela S. Krebs

Issues of equity in mathematics classrooms existed prior to COVID-19. For many students, however, meaningful participation in mathematical discussions became nearly impossible in online settings during the pandemic. In this study, we note the diversity in and nature of participation in mathematical discourse in an online course for preservice teachers (PSTs). We investigate the influence of implementing two support strategies for discussion: (a) establishing a “rough-draft/revision” orientation to mathematical tasks; and (b) providing time and structure (tasks and prompts) in an online discussion board for PSTs to post their initial thoughts, react to peers’ solutions, and collectively revise their ideas. In this article, we highlight several benefits of these support strategies to equitable PST participation in a unit on number theory. For example, as compared with oral discussions where only a few PSTs offered their ideas, the written discussion format encouraged every PST to post their ideas. Using a rough-draft/revision stance in the prompts fostered sharing and revealed diverse mathematical approaches, perspectives, and ideas. We argue that giving students opportunities to interact with one another and the mathematics in a variety of ways promotes equitable participation.

### Blake E. Peterson, Douglas L. Corey, Benjamin M. Lewis, Jared Bukarau, and Introduction by: Wendy Cleaves

From the Archives highlights articles from NCTM’s legacy journals, previously discussed by the *MTLT* Journal Club.

### Daniel K. Siebert and Monica G. McCleod

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

### Charles F. Marion

The simplest of prekindergarten equations, 1 + 2 = 3, is the basis for an investigation involving much of high school mathematics, including triangular numbers, arithmetic sequences, and algebraic proofs.