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Early 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 [video]. Retrieved from
https://doi.org/doi:10.7282/T35D8QN1
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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
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-03-27
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 Speiser. With continuing reference to combinatorics notation, Stephanie organizes the towers of successive heights, selecting from two colors, to show how they grow inductively, row by row. She then writes the first several rows of Pascal's Triangle onto her paper and places the actual towers for the first two rows so that they correspond to the positions on the Triangle. She shows how the positions in the triangle can be added to generate the numbers in the next row and reorganizes the towers to illustrate the numbers in each of the cases. Stephanie then tries to build a correspondence between the towers organized to illustrate the addition rule noticed in the written numbers on her paper and her physical organization of the towers according to an inductive process of adding one of each color to two copies of the shorter tower to generate each tower in the next row.
The problems as generated by Stephanie for her discussion with the researchers:
Arrange the towers of height 1, 2 and 3 in rows that show how each successive row could be generated by adding one cube of each color to copies of the tower in the shorter row.
How can the rows of the triangle be generated using addition? How could they be organized to illustrate this pattern?
Can the towers in each successive row correspond to the addition rule as well as the inductive pattern simultaneously?
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-CLIP003
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 3 of 11: Comparing towers, selecting from two colors, built inductively and corresponding to the addition rule of Pascal's Triangle.
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