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TitleNight session, Pascal's identity, clip 1 of 7: thinking about the meaning of combinatorics notation

DescriptionThis is the first of seven clips from the night session. In it, Jeff, Michael, and Romina discuss the coefficients of the binomial expansion, specifically (a+b) to the 10th power. In attempting to...

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DescriptionThis is the second of seven clips from the night session. In it, Jeff, Michael, and Romina, along with Ankur (who has just arrived), use the analogy they call “people on a line” to investigate...

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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 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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DescriptionIn the third clip in a series of nine from the first of seven interviews focusing on Early Algebraic Ideas about the binomial expansion, Stephanie, an 8th grade student, reviews her conclusions about...

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

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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 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 focus on the...

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DescriptionThis is the sixth of seven clips from the night session. After Jeff draws Pascal’s Triangle in what the students call “choose” notation, the researcher asks the students to express an instance...

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TitleNight session, Pascal's identity, clip 3 of 7: further explorations of factorials and combinations

DescriptionThis is the third of seven clips from the night session. The four students (Ankur, Jeff, Michael, and Romina) investigate the reason for dividing n! by (n-x)! and x! when calculating “n choose...