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A New Twist on Fraction Equations

The authors introduce an activity involving “follow-up equations” to connect with ideas children have already expressed during fraction problem solving.

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Developing Skills for Exploring Children’s Thinking From Extensive One-on-One Work With Students

In this article, we share results from a field experience model in which junior-year methods classes were held in an elementary school and preservice teachers (PSTs) worked with a single student (a “Math Buddy") on mathematics for 30 minutes per day. We focus on the development of PSTs’ skills for exploring children’s thinking and the structures and tools that we used to support this development. Data sources include screencast recordings of interactions with Math Buddies and written reflections completed by PSTs. Although the responsiveness of interactions varied across individuals and interactions, in general, PSTs showed improvements in exploring children’s thinking. We share implications of these findings for similar field experience models and for practice-based approaches to teacher education generally.

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Formative Assessment through Think Alouds

We describe a formative assessment approach called whole-class think alouds, which foster evidence-based instructional practices and promote the goal of assessment to promote learning. They allow students to collaborate and orally communicate their problem solving.

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Keep Calm and Press for Reasoning

The questions that teachers ask to elicit student reasoning—often referred to as press for reasoning—help students explicate the concepts and principles that undergird their strategies. This article describes the term, addresses its benefits and challenges, and offers three routines.

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Linking Factors and Multiples to Algebraic Reasoning

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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Learning from the Unknown Student

Three instructional situations demonstrate the value of using an “unknown” student's work to allow the advancement of students' mathematical thinking as well as their engagement in the mathematical practice of critiquing the reasoning of others.

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Difference Not Deficit: Reconceptualizing Mathematical Learning Disabilities

Mathematical learning disability (MLD) research often conflates low achievement with disabilities and focuses exclusively on deficits of students with MLDs. In this study, the author adopts an alternative approach using a response-to-intervention MLD classification model to identify the resources students draw on rather than the skills they lack. Detailed diagnostic analyses of the sessions revealed that the students understood mathematical representations in atypical ways and that this directly contributed to the persistent difficulties they experienced. Implications for screening and remediation approaches are discussed.

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From Whole Numbers to Invert and Multiply

An instructional sequence used in a course for prospective teachers directly relates to Common Core State Standards for grades 3–6.

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An Unplanned Path

As a means of identifying potential new elementary school trailblazers, examine the significant points along the professional journeys of two teachers.

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Challenge Beginning Teacher Beliefs

Use these specific strategies to confront assumptions about teaching and learning mathematics.