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Courtney Starling and Ian Whitacre

Introduce your students to a fun and innovative game to encourage precise communication

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Ian Whitacre, Robert C. Schoen, Zachary Champagne and Andrea Goddard

Instructional activities designed to encourage relational thinking in primary-grades classrooms can give students advantages when they reason about subtraction.

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Lisa L. Lamb, Jessica Pierson Bishop, Randolph A. Philipp, Bonnie P. Schappelle, Ian Whitacre and Mindy Lewis

Research on how students make sense of and use the minus sign indicates that students struggle to understand the multiple meanings of this symbol. Teachers can support students in developing a robust understanding of each interpretation.

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Jessica Pierson Bishop, Lisa L. Lamb, Randolph A. Philipp, Ian Whitacre and Bonnie P. Schappelle

Reasoning about integers provides students with rich opportunities to look for and make use of structure.

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Jessica Pierson Bishop, Lisa L. Lamb, Randolph A. Philipp, Ian Whitacre, Bonnie P. Schappelle and Melinda L. Lewis

We identify and document 3 cognitive obstacles, 3 cognitive affordances, and 1 type of integer understanding that can function as either an obstacle or affordance for learners while they extend their numeric domains from whole numbers to include negative integers. In particular, we highlight 2 key subsets of integer reasoning: understanding or knowledge that may, initially, interfere with one's learning integers (which we call cognitive obstacles) and understanding or knowledge that may afford progress in understanding and operating with integers (which we call cognitive affordances). We analyzed historical mathematical writings related to integers as well as clinical interviews with children ages 6-10 to identify critical, persistent cognitive obstacles and powerful ways of thinking that may help learners to overcome obstacles.