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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...

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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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TitleFraction problems, Sharing and Number Lines, Clip 2 of 5: Equal shares, 3 candy bars for 25 students

DescriptionIn this second of five clips from a single class session, the students consider how 3 candy bars could have been equally distributed among their class of 25. The students had worked on this problem...

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Date Created2006-05-12

DescriptionResearchers Carolyn Maher and Liz Uptegrove conduct a group interview with Romina, Angela and Magda as young professionals who have been participants in a long-term study on development of...

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Date Created1999-05-18

DescriptionThis video comes from an interview conducted by researcher Carolyn Maher with Romina as an 11th grader and participant of a long-term study on development of mathematical thinking and reasoning in...

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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 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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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...