5

1 Analytic found

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...

6

1 Analytic found

TitlePUP Math Pascal's addition

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....

7

1 Analytic found

TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 4 of 11: Developing the correspondence among towers, selecting from two colors, Pascal's Triangle, and the symbolic algebraic expansions of (a+b) squared and (a+b) cubed

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. ...

8

1 Analytic found

TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 3 of 11: Comparing towers, selecting from two colors, built inductively and corresponding to the addition rule of Pascal's Triangle

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...

9

TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 2 of 11: Stephanie rebuilds Unifix towers 1-cube, 2-cubes, 3-cubes and 4-cubes tall, selecting from two colors

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...

10

1 Analytic found

TitleFractions, Grade 4, Clip 2 of 4: Additive vs. multiplicative reasoning

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...

11

1 Analytic found

TitleFractions, Grade 4, Clip 4 of 4: Designing a new rod set

DescriptionResearcher Amy Martino posed two related tasks to the students. In this clip, the students work on designing a rod that can be called one half when the blue rod is called one. Erik and Alan discuss...

12

1 Analytic found

TitleNight Session, Pascal’s Identity, Clip 7 of 7: Generating and generalizing Pascal’s Identity

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...

13

2 Analytics found

TitlePizza problems with four and five toppings, clip 5 of 6: Explaining solutions

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...

14

3 Analytics found

TitleBuilding Towers, Selecting from two colors for Guess My Tower, Clip 5 of 5: Sharing with the Group

Date Created1993-02-26

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...