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Early 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.
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Early 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. [video] Retrieved from https://doi.org/doi:10.7282/T3S75F55

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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.
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-04-17
Persistent URLhttps://doi.org/doi:10.7282/T3S75F55
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 encountered in the past, particularly when working with researcher Robert B. Davis. Specifically, they discussed investigating the Tower of Hanoi problem and finding a general rule for predicting the number of Unifix-cube towers selecting from two colors for particular heights. Finally, Stephanie is asked to consider 2 raised to the power zero. Researcher Steven Maher provides a rationale for the conclusion that 2 to the zero power must be one. Researcher Donna Weir is observing.
The problems posed to Stephanie are:
How might you predict the number of towers for any particular height?
How would you figure this out if you did not know the number of towers for the preceding height?
How could you represent your number for the towers of particular heights from towers one-cube high to towers of height n using exponents?
What about 2 to the zero power
Math ToolColor markers
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, Recognizing a pattern, Recursive reasoning, Generalizing, Referencing a previous problem
Grade Level8
Student ParticipantsStephanie (student)
MediatorsMaher, Carolyn Alexander (Researcher), Weir, M. Donna (Researcher), Maher, Steven (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 Captured1996-04-17
Local IdentifierB08B09-ALG-BIEX-CLIP007
Related Publication
   Type: Related publication
   Label: Ed.D. dissertation references the video footage that includes Early 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.
   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: B08, Early algebra ideas about binomial expansion, Stephanie's interview seven of seven (student view), Grade 8, April 17, 1996, raw footage.
   Identifier: B08-19960417-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
   Title: B09, Early algebra ideas about binomial expansion, Stephanie's interview seven of seven (work view), Grade 8, April 17, 1996, raw footage.
   Identifier: B09-19960417-KNWH-WV-INT-GR8-ALG-BIEX-RAW
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