Titlebook: Combinatorics and Reasoning; Representing, Justif Carolyn A. Maher,Arthur B. Powell,Elizabeth B. Upt Book 2010 Springer Science+Business Me

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cipher

Towers: Schemes, Strategies, and Argumentsld their solution to the shirts and jean problem (which was to determine how many outfits could be formed from three different shirts and two different pairs of jeans and to provide a convincing argument of the solution). In their effort to make sense of the components of the problem and to monitor

山頂可休息

Hyaluronic-Acid

Making Pizzas: Reasoning by Cases and by Recursion fifth grades. In this chapter, we discuss five sessions during which these students worked to make sense of the pizza problems. These problems presented new challenges and required the students to adapt the representations and solution strategies that they had previously formed to meet the needs of

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紀(jì)念

Representations and Connections we observe a different cohort of students also exploring the towers and pizza problems. In the five sessions discussed here, spanning December 1997 through March 1998, the five students in this cohort were reintroduced to the towers and pizza problems, which they last explored in elementary school

morale

Representations and Standard Notationr own increasingly sophisticated and abstract representations. In this chapter, we see how one group built on those ideas in order to derive, explain, and record Pascal’s Identity (the addition rule for Pascal’s Triangle) using standard mathematical notation. This remarkable demonstration of how stu

跳脫衣舞的人

So Let’s Prove It!orics – the towers problems and the pizza problems. In this chapter, we see how students just finishing high-school work on another isomorphic problem, demonstrating the application of techniques and ways of thinking that they developed throughout their previous years in the study. We further addres