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*Reasoning by contradiction*in Subject1

DescriptionDuring this clip, the students discuss a task that had been posed by Erik: If I call the blue rod one, what rod will I call one half? A lively discussion centering on the definition of one half...

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DescriptionIn the first clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie revisits her earlier exploration of particular algebraic ideas about binomial expansion with...

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DescriptionIn the second clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie first predicts the number of Unifix-cube towers with exactly three red cubes to be generated from the...

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DescriptionIn the first clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie revisits her earlier exploration of how to generate Unifix-cube towers across cases with researchers...

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DescriptionResearcher Amy Martino led a whole class discussion that focused on solutions to the task: I'm going to call the orange and light green together oneā¦Can you find a rod that has the number name one...

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DescriptionIn the first clip in a series of six from the second of seven interviews in which 8th grade Stephanie explores Early Algebraic Ideas about Binomial Expansion, the researcher, Carolyn A. Maher, asks...

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Date Created1995-11-08

DescriptionIn the fifth clip in a series of nine from the first of seven interviews focusing on Early Algebraic Ideas about the binomial expansion researcher Carolyn Maher asks Stephanie to multiply (x + y)(x +...

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DescriptionAmy Martino leads a whole class discussion during which they talk about ways of writing number sentences for two problems: 1) How many one sixths are in one? and 2) How many one twelfths are in one?...

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Date Created1993

DescriptionResearcher Amy Martino asked the students to assign a number name to the white rod when the orange rod was called ten. After discussing the problem with their partners, the students joined in a whole...

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DescriptionResearcher Carolyn Maher leads a whole class discussion after the students' exploration of the problem: Which is larger, one fourth or one ninth, and by how much? Several students described their...