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## Backing up Moving and Forward in Fractional Understanding

A well-crafted opening problem can provide preassessment of students' fraction knowledge and assist teachers in determining next steps for instruction.

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## A fraction feast

Family time in the kitchen can lead to opportunities to explore fractions in real-life circumstances and tap into children's engagement in the harvest season. You might supplement the October problems by setting up a time for your students to talk with a professional chef or event planner about how they use fractions in their jobs.

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## Coaching through Focusing on Student Thinking

Why is it so crucial that coaches and teachers concentrate their interactions on students' mathematical reasoning?

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## Split It! Unpacking the Equipartitioning Learning Trajectory

Working with a mathematics coach and university researchers in a K-4 lesson study, teachers increase their understanding of student abilities in a fair-share sandwich problem.

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## Assessing Prospective Teachers' Analysis of Teaching: How Well Can They Link Teaching and Learning?

One goal in teacher education is to prepare prospective teachers (PTs) for a career of systematic re_ ection and learning from their own teaching. One important skill involved in systematic re_ ection, which has received little research attention, is linking teaching actions with their outcomes on student learning; such links have been termed hypotheses. We developed an assessment task to investigate PTs' ability to create such hypotheses, prior to instruction. PTs (N = 16) each read a mathematics lesson transcript and then responded to four question prompts. The four prompts were designed to vary along research-based criteria to examine whether different contexts in_ uenced PTs' enactment of their hypothesizing skills. Results suggest that the assessment did capture PTs' hypothesizing ability and that there is room for teacher educators to help PTs develop better hypothesis skills. Additional analysis of the assessment task showed that the type of question prompt used had only minimal effect on PTs' responses.

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## Contemporary Curriculum Issues: An algebraic-habits-of-mind perspective on elementary school

Although it is necessary to infuse courses and curricula with modern content, what is even more important is to give students the tools they will need in order to use, understand, and even make mathematics that does not yet exist. A curriculum organized around habits of mind tries to close the gap between what the users and makers of mathematics do and what they say (Cuoco, Goldenberg, and Mark 1996, p. 376).

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## Think-Pair-Show-Share to Increase Classroom Discourse

Anticipating and responding to learner variability can make using talk moves complex. The authors fuse Universal Design for Learning (UDL), differentiation, and talk moves into three key planning and pedagogy considerations.

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## Foster Fact Fluency with Number String Discussions

Talking about a structured series or string of basic fact problems is a strategy that presents collaborative opportunities for students to explore relationships among related reasoning strategies.