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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 second clip in a series of nine from the first of seven interviews focusing on Early Algebraic Ideas about the binomial expansion, researcher, Carolyn A. Maher, asks Stephanie, an 8th grade...

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DescriptionIn the fourth of five clips from a single class session, we see two students, Jessica and Andrew, placing unit fractions, ranging from 1/10 to 1/2, on a number line segment with endpoints labelled 0...

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DescriptionIn this fifth of six clips, four 11th grade students reconsider Pascal's Triangle as it relates to the Pizza Problem and connect this problem with the Towers Problem. As the students summarize their...

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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 final clip the students generalize the exponential structure of the Pizza Problem and describe the relationship between two consecutive rows of Pascal’s Triangle with reference both to the...

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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 second of five clips, the four twelfth grade students employ various strategies to determine the number of shortest paths to the remaining two points, B and C, on the problem grid. Various...

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DescriptionIn the fifth of five clips, Romina, Brian and Michael, describe patterns and relationships identified in their solution to the Taxicab problem to Arthur Powell, a second researcher. The students...

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DescriptionIn the eighth clip in a series of nine from the fourth of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, Stephanie revisits her physical model...