351
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...
352
DescriptionIn the fourth of five clips, the four twelfth grade students explain their conjecture that Pascal's Triangle can be used to predict the number of paths to any point in the Taxicab grid to Carolyn...
353
DescriptionIn the third of five clips, the four twelfth grade students attempt to justify for themselves and then demonstrate the relationship that they have conjectured between the Taxicab problem and Pascal's...
354
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...
355
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...
356
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...
357
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...
358
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...
359
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...
360
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...
