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TitleNight session, Pascal's identity, clip 2 of 7: making sense of factorial notation and "why you multiply"
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...
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...
DescriptionResearchers Carolyn Maher and John Francisco conduct a group interview with Romina and Jeff as second-year college students who have been participants in a long-term study on development of...
TitleBuilding Towers, Selecting from Two Colors for Guess My Tower, Clip 1 of 5: The Meaning of "At Least"
DescriptionIn the first of five clips, Milin and Michelle I, two fifth grade students are attempting to find all possible towers three cubes tall when selecting from two colors as the sample space for Question 1...
TitleBuilding Towers, Selecting from two colors for Guess My Tower, Clip 3 of 5: Milin introduces an inductive argument
DescriptionIn clip three of five, Milin, a fifth grade student, shares his inductive argument for building towers up to 3 cubes tall with researcher Carolyn Maher and his partner, Michelle I. Michelle in turn...
TitleBuilding Towers, Selecting from two colors for Guess My Tower, Clip 4 of 5: Stephanie and Matt Rebuild the Argument
DescriptionIn clip 4 of 5, fifth grade student Matt shares his understanding of Milin’s inductive argument with Robert and Michelle R. who, up to this point, found twelve, four-tall towers. Stephanie...
TitleBuilding Towers, Selecting from two colors for Guess My Tower, Clip 5 of 5: Sharing with the Group
DescriptionIn this final clip, an exuberant Stephanie presents her understanding of the “doubling rule” to the group of students ( Matt, Michelle I, Michelle R, Milin and Robert) who assembled around a...
DescriptionIn the second of five clips, the four twelfth grade students employ various strategies to determine the number of shortest paths to the remaining two points, B and C, on the problem grid. Various...
DescriptionIn the first of five clips, four twelfth grade students develop their initial strategies for approaching the Taxicab Problem. They determine the shortest distances to the three given points: A, B and...
TitleTaxicab problem, clip 5 of 5: extending the taxicab correspondence to pizza with toppings and binary notation
DescriptionIn the fifth of five clips, Romina, Brian and Michael, describe patterns and relationships identified in their solution to the Taxicab problem to Arthur Powell, a second researcher. The students...