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## Exploring Young Children’s Math Thinking in Sandcastle Building

Children explore concepts of capacity and height measurement through sand play in nursery class.

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## Construct It! Progressively Precise: Three Levels of Geometric Constructions

This article shares an activity scaffolding the construction of the circumcenter of a triangle, culminating with a Triangle-Ball Championship game.

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## Prove It! Graph Theory and Induction: The Next Big Thing

Eighth-grade students participated in a two-day lab exploring graph theory. In addition to learning about a completely new topic, they experienced a subtle introduction to proof by induction.

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Support students in conjecturing in ways that can promote their agency in the learning process.

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## GPS: Triangle Explorations and Constructions Using Robots

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.

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## Promoting Equitable PST Participation in Mathematical Discourse: Rough Drafts on an Asynchronous Discussion Board

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.

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## Linking Oral and Written Arguments

Teaching transparently about the process and goals can support students as they make and support mathematical claims.

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## Take a Seat at the Equation Café

Design projects to encourage your students’ self-efficacy and motivate mathematics learning by helping them apply their prior knowledge from real-world experiences.

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## Supporting Students in Critiquing Math Arguments

Using cases from early childhood, elementary, and secondary classrooms, we showcase the work that teachers do to support students in building a collective argument and critiquing an individual’s argument. We identify four areas of work central to teaching students to build and critique mathematical arguments.

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## Teaching Is a Journey: Partner Quizzes to Support Learning

This department provides a space for current and past PK–12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.