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*Reasoning by cases*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 one…Can you find a rod that has the number name one...

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DescriptionThe third of 6 clips focuses on the four 11th grade students as they map the numbers of pizza choices to the rows of Pascal’s Triangle and attempt to make sense of the addition rule with the...

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DescriptionIn the fourth of six clips, the four students develop the structural isomorphism between adding an additional pizza topping choice and the addition rule for successive rows of Pascal’s Triangle and...

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DescriptionIn the second of 6 clips, the four 11th grade students generate an exhaustive list of pizza options choosing from 4 toppings. They recognize that the 16 choices correspond to the fourth row of...

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DescriptionIn the sixth clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie first revisits her investigation of the number of duplicates that would be produced when building...

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DescriptionIn the final clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie responds to questions from researcher Carolyn Maher about problems that she and her classmates had...