1

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...

2

1 Analytic found

TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 1 of 11: Stephanie revisits combinatorics notation for building towers

DescriptionIn the first clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie revisits her earlier exploration of particular algebraic ideas about binomial expansion with...

3

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. ...

4

TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 6 of 11: Generating towers 3-cubes tall, selecting from blue and green cubes, from towers with exactly one blue cube to towers with exactly two blue cubes

DescriptionIn the sixth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie is challenged by researchers Carolyn Maher and Robert Speiser to consider how the eight Unifix-cube...

5

TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 5 of 11: Developing the correspondence between towers 4-cubes tall, selecting from two colors, Pascal's Triangle and the symbolic algebraic expansion of (a+b) to the 4th power

DescriptionIn the fifth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie responds to questions from researchers Carolyn Maher and Robert Speiser about the correspondence...

6

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...

7

1 Analytic found

TitleEarly Algebra Ideas About Binomial Expansion, Stephanie's Interview Six of Seven: Clip 7 of 11: Generating towers 4-cubes tall, selecting from blue and green cubes, from towers with exactly one green cube to towers with exactly two green cubes.

DescriptionIn the seventh clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie is asked by researchers Carolyn Maher and Robert Speiser to consider how the Unifix-cube towers...

8

1 Analytic found

TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 10 of 11:
Developing mathematical expressions for generating the number of towers 4-cubes tall selecting from green and blue cubes for exactly 2 green cubes, exactly 3 green cubes, and for 4 green cubes

DescriptionIn the tenth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie works with researchers Carolyn Maher and Robert Speiser to synthesize her ideas about how to build the...

9

1 Analytic found

TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 9 of 11: Beginning to generalize mathematical expressions to generate cases for towers 4-cubes tall selecting from green and blue cubes

Descriptionn the ninth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie is asked by researchers Carolyn Maher and Robert Speiser to describe mathematically how she has...

10

TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 8 of 11: Working backwards from towers 4-cubes tall selecting from blue and green cubes, with exactly two green cubes, to towers with exactly one green cube

DescriptionIn the eighth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie is asked by researchers Carolyn Maher and Robert Speiser to revisit her set of six Unifix cube towers...