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**Early 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 [video]. ** Retrieved from

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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

PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-03-27

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. When asked by researchers Carolyn Maher and Robert Speiser to connect these expressions to Pascal's Triangle and Unifix-cube towers that she had built by selecting from two colors, Stephanie developed a correspondence between the variables, a and b, and the colors of the cubes that allowed her to understand that the numbers in the Triangle referred to the coefficients in the expression and the number of towers in each case for the expressions (a+b) squared and (a+b) cubed. She also recognized that each exponent in the expanded expression referred to the number of cubes of a particular color in the corresponding Unifix-cube tower.

The problems as generated by Stephanie for her discussion with the researchers:

What is the expanded expression for (a+b) squared?

How does this relate to the Unifix-cube towers with two colors and to Pascal's Triangle?

Build a similar correspondence for (a+b) cubed with both the towers and the Triangle.

RightsThe video is protected by copyright. It is available for reviewing and use within the Video Mosaic Collaborative (VMC) portal. Please contact the Robert B. Davis Institute for Learning (RBDIL) for further information about the use of this video.

Date Captured1996-03-27

Local IdentifierB06B07-ALG-BIEX-CLIP004

Related Publication

__Type__: Related publication

__Label__: Ed.D. dissertation references the footage that includes Early 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.

__Date__: 2011

__Detail__: D

__Author__: Aboelnaga, Eman Y. (Eman Yousry) (Rutgers, the State University of New Jersey)

__Name__: A case study: the development of Stephanie's algebraic reasoning

__Reference__: http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000057485
Source

__Title__: B06, Early algebra ideas about binomial expansion, Stephanie's interview six of seven (student view), Grade 8, March 27, 1996, raw footage.

__Identifier__: B06-19960327-KNWH-SV-INT-GR8-ALG-BIEX-RAW

Source

__Title__: B07, Early algebra ideas about binomial expansion, Stephanie's interview six of seven (work view), Grade 8, March 27, 1996, raw footage.

__Identifier__: B07-19960327-KNWH-WV-INT-GR8-ALG-BIEX-RAW