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Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison and James Hiebert

In our March editorial (Cai et al., 2018), we considered the problem of isolation in the work of teachers and researchers. In particular, we proposed ways to take advantage of emerging technological resources, such as online archives of student data linked to instructional activities and indexed by learning goals, to produce a professional knowledge base (Cai et al., 2017b, 2018). This proposal would refashion our conceptions of the nature and collection of data so that teachers, researchers, and teacher-researcher partnerships could benefit from the accumulated learning of ordinarily isolated groups. Although we have discussed the general parameters for such a system in previous editorials, in this editorial, we present a potential mechanism for accumulating learning into a professional knowledge base, a mechanism that involves collaboration between multiple teacher-researcher partnerships. To illustrate our ideas, we return once again to the collaboration between fourth-grade teacher Mr. Lovemath and mathematics education researcher Ms. Research, who are mentioned in our previous editorials(Cai et al., 2017a, 2017b).

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Jennifer Suh

Post Script items are designed as rich “grab and go” resources that any teacher can quickly incorporate into their classroom repertoire with little effort and maximum impact. This article shares ideas for using a clothesline number line to build understanding of number relationships across the elementary grades.

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Hope A. Walter

Meaningful dialogue supports metacognition and teaches students how to discuss, debate, and reevaluate situations in a respectful manner.

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Corey Webel, Erin Krupa and Jason McManus

Contextual tasks such as the Milk problem and the Cupcake problem can illuminate operations with fractions, but not all visual models align with the standards.

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Kimberly Morrow-Leong

Comparing two fractions gives a context for exploring students' flexibility with and understanding of mathematical ideas.

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Sarah Quebec Fuentes

Each month, this section of the Problem Solvers department showcases students' in-depth thinking and discusses the classroom results of using problems presented in previous issues of Teaching Children Mathematics. The October 2014 problem scenario offers students an opportunity to divide whole chocolate bars into fractional amounts to gain understanding of the partitioning of a whole into different fractional amounts, on comparing these amounts, and on the ability to develop and defend their thinking.

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Emily R. Fagan, Cheryl Rose Tobey and Amy R. Brodesky

Start with a strategic process to gather and interpret evidence of students' mathematical understandings and misconceptions; then aim your teaching to address identified needs.

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Janet B. Andreasen and Jessica H. Hunt

To meet diverse student needs, use an approach that is situated in understanding fractions.

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Lara Kikosicki and Debbie Prekeges

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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Nicole Pitsolantis and Helena P. Osana

Three specific sites, or points in real time, during problem solving gave fifth and sixth graders conceptual understanding, procedural skill, and the ability to justify their mathematical thinking about fractions.