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Early algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 11 of 11: Extending ideas about generating towers 4-cubes tall selecting from green and blue cubes to towers 5-cubes tall with exactly 1 green cube and connecting to Fermat and Pascal [video]. Retrieved from https://doi.org/doi:10.7282/T36D5RSD

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 11 of 11:
Extending ideas about generating towers 4-cubes tall selecting from green and blue cubes to towers 5-cubes tall with exactly 1 green cube and connecting to Fermat and Pascal
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-03-27
Persistent URLhttps://doi.org/doi:10.7282/T36D5RSD
DescriptionIn the final 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 extend her ideas about how to build the Unifix-cube towers across cases for towers 4-cubes tall for particular cases when selecting from blue and green cubes to towers that are 5-cubes tall. She describes how the five towers, 5-cubes tall with exactly one green cube, would generate the single tower with five blue. Researcher Speiser concludes the session by pointing out the connections between Stephanie's thinking about the towers and the mathematical thinking of both Fermat and Pascal.

The problem proposed to Stephanie is:
How could you extend your thinking about towers 4-cubes tall, selecting from blue and green cubes, to towers that are 5-cubes tall?
Math ToolColor markers, Unifix cubes
Math StrandAlgebra
Math ProblemBinomial expansion
NCTM Grade Range6-8
NCTM Content StandardAlgebra
NCTM Process StandardProblem solving, Reasoning and proof, Communication, Connections, Representation
Forms of Reasoning, Strategies and HeuristicsReasoning by cases, Direct reasoning, Working backwards, Controlling for variables, Recognizing a pattern, Referencing a previous problem
Grade Level8
Student ParticipantsStephanie (student)
MediatorsMaher, Carolyn Alexander (Researcher), Speiser, R. (Robert) (Researcher)
CorporateHarding Elementary School (Kenilworth, N.J.)
SettingInformal learning
Student GenderFemale
Student EthnicityWhite
Camera ViewsStudent view, Work view
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-CLIP011
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 11 of 11: Extending ideas about generating towers 4-cubes tall selecting from green and blue cubes to towers 5-cubes tall with exactly 1 green cube and connecting to Fermat and Pascal.
   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