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Alyson E. Lischka and D. Christopher Stephens

The area model for multiplication can be used as a tool to help learners make connections between mathematical concepts that are included in mathematics curriculum across grade levels. We present ways the area model might be used in teaching about various concepts and explain how those ideas are connected.

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Asked & Answered March 2020

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Theresa J. Grant and Mariana Levin

One of the challenges of teaching content courses for prospective elementary teachers (PTs) is engaging PTs in deepening their conceptual understanding of mathematics they feel they already know (Thanheiser, Philipp, Fasteen, Strand, & Mills, 2013). We introduce the Diverge then Converge strategy for orchestrating mathematical discussions that we claim (1) engenders sustained engagement with a central conceptual issue and (2) supports a deeper understanding of the issue by engaging PTs in considering both correct and incorrect reasoning. We describe a recent implementation of the strategy and present an analysis of students’ written responses that are coordinated with the phases of the discussion. We close by considering conditions under which the strategy appears particularly relevant, factors that appear to influence its effectiveness, and questions for future research.

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Geraldo Tobon and Marie Tejero Hughes

We share our experiences and those of culturally diverse families who participated in math workshops. We tie our experiences with the importance of family engagement, in particular, viewing families as a resource to be tapped into. We do so, in hopes that other school personnel take on a similar venture.

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Hamilton L. Hardison and Hwa Young Lee

In this article, we discuss funky protractor tasks, which we designed to provide opportunities for students to reason about protractors and angle measure. We address how we have implemented these tasks, as well as how students have engaged with them.

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Matt Enlow and S. Asli Özgün-Koca

This month's Growing Problem Solvers focuses on Data Analysis across all grades beginning with visual representations of categorical data and moving to measures of central tendency using a “working backwards” approach.

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Richard Barwell

Research focused on learning mathematics in a 2nd language is generally located in individual 2nd-language contexts. In this ethnographic study, I investigated mathematics learning in 4 different second-language contexts: a mainstream classroom, a sheltered classroom for Indigenous students, a welcome class for new immigrants, and a French-immersion classroom. The study was framed by a view of learning as socialization and the Bakhtinian notion of centripetal and centrifugal language forces. I present 7 socialization events that were particularly salient in 1 or more of the classrooms. For each socialization event, I identify various socialization practices. Based on a comparison of socialization practices in the 4 classrooms, I propose a distinction between language positive and language neutral mathematics classrooms. In language positive mathematics classrooms, students’ socialization into mathematics and language includes explicit attention to different aspects of language use in mathematics. In language neutral mathematics classrooms, the role of language in mathematics tends to be implicit.

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George J. Roy, Jessica S. Allen and Kelly Thacker

In this paper we illustrate how a task has the potential to provide students rich explorations in algebraic reasoning by thoughtfully connecting number concepts to corresponding conceptual underpinnings.

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Tim Erickson

We modify a traditional bouncing ball activity for introducing exponential functions by modeling the time between bounces instead of the bounce heights. As a consequence, we can also model the total time of bouncing using an infinite geometric series.