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Early algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 2 of 7: Explaining the meaning of area of a square with concrete materials [video]. Retrieved from https://doi.org/doi:10.7282/T3SF2V35

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 2 of 7: Explaining the meaning of area of a square with concrete materials
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-02-07
Persistent URLhttps://doi.org/doi:10.7282/T3SF2V35
DescriptionIn the second clip in a series of seven from the third of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, the researcher, Carolyn Maher, asks how she would explain her ideas about area of squares to her younger sister. When Stephanie indicates that she would revisit basic ideas about units and square units, Maher offers her base-ten blocks from which Stephanie selects and uses a cubic unit and a square "flat" composed of 100 cubic units. When asked how she would represent a square with side length "a", Stephanie selects from a set of plastic shapes one that most closely approximates a square, noting that the side has no marked units and so can be considered to represent the general case.
The problem as presented to Stephanie:
How could you use squared concrete materials to explain about the area of a square to someone who has not studied area?
Math ToolBase ten blocks, Algebra blocks
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 HeuristicsDirect reasoning, Substituting numbers for variables, Considering a simpler problem, Constructing a physical model
Grade Level8
Student ParticipantsStephanie (student)
MediatorsMaher, Carolyn Alexander (Researcher)
CorporateHarding Elementary School (Kenilworth, N.J.)
SettingInformal learning
Student GenderFemale
Student EthnicityWhite
Camera ViewsWork view, Student 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 Captured1996-02-07
Local IdentifierA64A65-ALG-BIEX-CLIP002
Related Publication
   Type: Related publication
   Label: Ed.D. dissertation references the video footage that includes Early algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 2 of 7: Explaining the meaning of area of a square with concrete materials
   Date: 2011
   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: A64, Early algebra ideas about binomial expansion, Stephanie's interview three of seven (student view), Grade 8, February 7, 1996, raw footage.
   Identifier: A64-19960207-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
   Title: A65, Early algebra ideas about binomial expansion, Stephanie's interview three of seven (work view), Grade 8, February 7, 1996, raw footage.
   Identifier: A65-19960207-KNWH-WV-INT-GR8-ALG-BIEX-RAW