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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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DescriptionIn the fourth clip in a series of ten from the fifth of seven interviews, 8th grader Stephanie continues her exploration of Early Algebraic Ideas about Binomial Expansion. Using combinatorics...

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DescriptionIn the third clip in a series of ten from the fifth of seven interviews, 8th grader Stephanie continues her exploration of Early Algebraic Ideas about Binomial Expansion. She is revisiting the...

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DescriptionIn the second clip in a series of ten from the fifth of seven interviews, 8th grader Stephanie continues her exploration of Early Algebraic Ideas about Binomial Expansion. She is revisiting the...

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DescriptionIn this full-session, raw footage video, students have come to school in the evening for a night session. The group, made up of Jeff, Michael and Romina begin discussing the coefficients of the...

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DescriptionThis is the fifth of seven clips from the night session. The students (Ankur, Jeff, Michael, and Romina) have been discussing Pascal’s Triangle. The researcher rewrites row 3 of Pascal’s...

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DescriptionThis is the last of seven clips from the night session. The students (Ankur, Jeff, Michael, and Romina) explain to Brian, a late-comer, the meaning of Pascal’s Identity (the addition rule for...

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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 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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