8

1 Analytic found

TitleNight session, Pascal's identity, clip 4 of 7: An example of Pascal's identity

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...

9

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...

10

3 Analytics found

TitlePizza problems with four and five toppings, clip 2 of 6: Finding an answer

DescriptionIn the second of 6 clips, the four 11th grade students generate an exhaustive list of pizza options choosing from 4 toppings. They recognize that the 16 choices correspond to the fourth row of...

11

1 Analytic found

TitleRevisiting construction of large models to compare fractions, Clip 4 of 5: Alan reasons about the third model he constructed

DescriptionIn the fourth of five clips from this classroom session, the researcher, Amy Martino, returned to Alan and questioned him about the third model that he had built for finding the difference between one...

12

TitleEarly algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 7 of 7: Finding a general direct "rule" for the number of Unifix-cube towers, selecting from two colors, for any height.

DescriptionIn the final clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie responds to questions from researcher Carolyn Maher about problems that she and her classmates had...

13

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. ...

14

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...

15

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...

16

2 Analytics found

TitleEarly algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 2 of 7: Predicting the rods for odd and even numbers of steps

DescriptionIn the second of seven clips from an after-school enrichment session in an urban middle school, two 7th grade boys, Ariel and James, are exploring ideas about linear functions. In responding to...

17

2 Analytics found

TitleEarly algebra, investigating linear functions, series 5 of 7,ladder problem, Clip 3 of 7: Recording the procedures for ladders with odd and even numbers of steps

DescriptionIn the third of seven clips from an after-school enrichment session in an urban middle school, two 7th grade boys, Ariel and James, are exploring ideas about linear functions. When Ariel explains his...