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**Early algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 1 of 11: Stephanie revisits combinatorics notation for building towers [video]. ** Retrieved from

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 1 of 11: Stephanie revisits combinatorics notation for building towers

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

DescriptionIn the first clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie revisits her earlier exploration of particular algebraic ideas about binomial expansion with researchers Carolyn Maher and Robert Speiser. Stephanie reports that, in Interview Five, she had worked with Maher to use mathematical notation for selecting r items from a set with number n. In responding to questions from Speiser, Stephanie first writes the symbolic notation for selecting one item from a set of 4 and illustrates this by building Unifix towers 4-cubes tall, selecting from blue and green cubes, that have exactly one green cube. She then constructs towers 4-tall with exactly 2 green cubes, justifies her solution, and records the symbolic notation that corresponds to her set of six. She then builds towers 4-tall with exactly 3 green cubes, recording the corresponding notation, and finally towers to illustrate the cases for exactly four green cubes and for no green cubes (all blue).

The problems, as generated by Stephanie, in her explanation to Speiser:

Explain the meaning of the symbolic notation for selecting a particular number of items from a set of items.

Convince us that you have all possible towers, 4-cubes tall, selecting from blue and green cubes, for each of the following cases: exactly one green cube; exactly 2 green cubes, exactly 3 green cubes, exactly 4 green cubes and no green cubes.

Record each case in your solution using the appropriate combinatorics notation.

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-CLIP001

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 1 of 11: Stephanie revisits combinatorics notation for building towers

__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