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Shannon E. Bostiga, Michelle L. Cantin, Cristina V. Fontana and Tutita M. Casa

Use debate journals as an innovative way to encourage your students to construct mathematical arguments as well as examine and critique others' mathematical thinking.

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Angela T. Barlow, Alyson E. Lischka, James C. Willingham and Kristin S. Hartland

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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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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Christine Phelps-Gregory and Sandy M. Spitzer

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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James Hiebert, Dawn Berk, Emily Miller, Heather Gallivan and Erin Meikle

We investigated whether the mathematics studied in 2 content courses of an elementary teacher preparation program was retained and used by graduates when completing tasks measuring knowledge for teaching mathematics. Using a longitudinal design, we followed 2 cohorts of prospective teachers for 3 to 4 years after graduation. We assessed participants' knowledge by asking them to identify mathematics concepts underlying standard procedures, generate multiple solution strategies, and evaluate students' mathematical work. We administered parallel tasks for 3 mathematics topics studied in the program and one mathematics topic not studied in the program. When significant differences were found, participants always performed better on mathematics topics developed in the program than on the topic not addressed in the program. We discuss implications of these findings for mathematics teacher preparation.

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Jody Guarino

Postscript 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. In this article, classroom clocks are used as an effective tool to support student understanding of basic number, fraction, and geometry concepts.

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Katherine E. Lewis

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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Jessica H. Hunt, Beth MacDonald, Rachel Lambert, Trisha Sugita and Juanita Silva

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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Erin M. Meikle

For orchestrating whole-class discussions, note these suggestions to fine tune problem-solving techniques into cognitively challenging tasks.

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Edited by Anna F. DeJarnette and Stephen Phelps

A monthly set of problems is aimed at a variety of ability levels.