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*Inductive reasoning*in Subject2

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...

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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 second clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie continues her exploration of early algebraic ideas about binomial expansion with researchers Carolyn...

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DescriptionIn the third clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie continues a discussion of ideas about binomial expansion with researchers Carolyn Maher and Robert...

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DescriptionIn the fourth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie remembers that she had figured out the expanded algebraic expressions for (a+b) for powers up to 6. ...

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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 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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Date Created1997-04-27

DescriptionThis video comes from The Private Universe Project in Mathematics and includes narrative voice-over interspersed with footage of a task-based interview with Stephanie and researcher, Robert Speiser....

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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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DescriptionResearcher Amy Martino posed two related tasks to the students that highlighted the difference between additive and multiplicative reasoning. First, she asked the students: If we call the orange...