How would your students respond to the Raffle Scenario in figure 1? What information about your students' knowledge would help you plan instruction for statistical issues related to the Raffle Scenario? This article highlights students' thinking and instructional implications from two studies that examined upper-elementary students' written and oral explanations as they responded to survey situations.
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Victoria R. Jacobs and Julie Kusiak
The results of a year–long exploration of first graders' tool use. Article also showcases instructional activities designed to link tool use with quantitative understanding.
Victoria R. Jacobs and Randolph A. Philipp
Teachers demonstrated four categories of reasoning when deciding how to respond to students.
Victoria R. Jacobs and Randolph A. Philipp
How did Misha solve the problems in figure 1, and what mathematical understandings do her strategies reflect? Misha's written work provides a rich context in which prospective and practicing teachers can discuss issues of mathematics, teaching, and learning. These discussions might include conversations about the similarities and differences between Misha's two strategies, what she must have understood about place value to generate these strategies, and what type of instruction likely preceded and should follow this problem-solving effort.
Victoria R. Jacobs and Rebecca C. Ambrose
Honoring students' solution approaches helps teachers capitalize on the power of story problems. No more elusive train scenarios!
Victoria R. Jacobs, Tom R. Bennett, and Cathy Bullock
Explains the use of books in Spanish to teach mathematics, presents examples and book-selection guidelines, and describes a searchable database of appropriate literature.
Katherine Baker, Naomi A. Jessup, Victoria R. Jacobs, Susan B. Empson, and Joan Case
Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.
Victoria R. Jacobs, Heather A. Martin, Rebecca C. Ambrose, and Randolph A. Philipp
Avoid three common instructional moves that are generally followed by taking over children's thinking.
Victoria R. Jacobs, Rebecca C. Ambrose, Lisa Clement, and Dinah Brown
Victoria R. Jacobs, Lisa L. C. Lamb, and Randolph A. Philipp
The construct professional noticing of children's mathematical thinking is introduced as a way to begin to unpack the in-the-moment decision making that is foundational to the complex view of teaching endorsed in national reform documents. We define this expertise as a set of interrelated skills including (a) attending to children's strategies, (b) interpreting children's understandings, and (c) deciding how to respond on the basis of children's understandings. This construct was assessed in a cross-sectional study of 131 prospective and practicing teachers, differing in the amount of experience they had with children's mathematical thinking. The findings help to characterize what this expertise entails; provide snapshots of those with varied levels of expertise; and document that, given time, this expertise can be learned.
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