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

allergy

陈旧

placebo-effect

Block Towers: From Concrete Objects to Conceptual Imaginationination of patterns and symbolic representations of the coefficients in the binomial expansion, using ideas from earlier explorations with towers in grades 3–5, she examined several fundamental recursive processes, including the addition rule in Pascal’s Triangle.

切碎

Block Towers: Co-construction of Proofo the original towers problem (building towers when selecting from two colors of Unifix cubes) and extensions (with more than two colors of cubes), using methods including controlling for variables, justification by cases, and inductive reasoning.

forager

Representations and Standard Notationdents can come to make sense of complex mathematical ideas was captured during the session that came to be referred to as the “Night Session,” since it took place on a weekday evening from 7:30 to 10:00 ..

进取心

Adults Reasoning Combinatoriallyr the course of the semester. From a perspective of conceptualizing reasoning in terms of solving open-ended problems, it was of interest to learn whether students in a liberal-arts college mathematics course could be successful in providing arguments to support their reasoning and in making connections in a problem-solving-based curriculum.

音的强弱

陪审团每个人

cloture

Representations and Connectionsade use of their understanding of the structure of those problems to form preliminary ideas about the meaning of Pascal’s Identity. We show how their development and use of a sophisticated general representation scheme helped them make these connections and generalize their knowledge.

instulate

So Let’s Prove It!soning through work on the Taxicab Problem. They display criteria and techniques for justifying claims and an awareness of the power of generalizing, particularly as an aid to respond to special cases.