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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 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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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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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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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...