RUcore: Rutgers University Community Repository
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
Descriptive
Genre
(authority = RURes_Genre)
Research data
Genre
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Observational data
Genre
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Edited data
Genre
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Repurposed data
Genre
(authority = RURes_qualitativeMethod)
Interviews (individual)
Genre
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Longitudinal data
Genre
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Qualitative research
Genre
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School
Subject
(authority = LCSH)
Topic
Mathematics education
Subject
(authority = LCSH)
Topic
Critical thinking in children--New Jersey--Case studies
Subject
(authority = LCSH)
Topic
Learning, Psychology of--Case studies
Subject
(authority = LCSH)
Topic
Manipulatives (Education)--Case studies
Subject
(authority = Grade range)
Topic
6-8
Subject
(authority = NCTM Content)
Topic
Algebra
Subject
(authority = NCTM Process)
Topic
Problem solving
Subject
(authority = NCTM Process)
Topic
Reasoning and proof
Subject
(authority = NCTM Process)
Topic
Communication
Subject
(authority = NCTM Process)
Topic
Connections
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(authority = NCTM Process)
Topic
Representation
Subject
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Topic
Algebra
Subject
(authority = rbdil_mathProblem)
Topic
Binomial expansion
Subject
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Topic
Color markers
Subject
(authority = rbdil_mathTools)
Topic
Unifix cubes
Subject
(authority = rbdil_setting)
Topic
Informal learning
Subject
(authority = rbdil_gradeLevel)
Topic
8
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Direct reasoning
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Recursive reasoning
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Inductive reasoning
Subject
(authority = rbdil_representations)
Topic
Physical models
Subject
(authority = rbdil_representations)
Topic
Combinatorics notation
Subject
(authority = rbdil_topic)
Topic
Combinations
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Topic
Student view
Subject
(authority = rbdil_cameraView)
Topic
Work view
Subject
(authority = rbdil_studentGender)
Topic
Female
Subject
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Topic
White
Subject
(authority = rbdil_schoolType)
Topic
Public school
Subject
(authority = RURes_subjectOfStudy)
Topic
Sample of human subjects
Subject
(authority = rbdil_representations)
Topic
Pascal's triangle
TargetAudience
(authority = RURes_discipline)
Social science
TargetAudience
(authority = RURes_domain)
Mathematics education
Note
(type = APA citation)
Robert B. Davis Institute for Learning. (1996). 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
Note
(type = supplementary materials)
Transcript and student work are also available.
Name
(type = personal)
NamePart
(type = family)
Maher
NamePart
(type = given)
Carolyn Alexander
Affiliation
Rutgers, the State University of New Jersey
Role
RoleTerm
(authority = marcrelator);
(type = text)
Researcher
Name
(type = personal)
NamePart
(type = family)
Speiser
NamePart
(type = given)
R. (Robert)
Role
RoleTerm
(authority = marcrelator);
(type = text)
Researcher
Affiliation
Rutgers, the State University of New Jersey
RelatedItem
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TitleInfo
Title
B06, Early algebra ideas about binomial expansion, Stephanie's interview six of seven (student view), Grade 8, March 27, 1996, raw footage.
Identifier
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B06-19960327-KNWH-SV-INT-GR8-ALG-BIEX-RAW
RelatedItem
(type = host)
TitleInfo
Title
B07, Early algebra ideas about binomial expansion, Stephanie's interview six of seven (work view), Grade 8, March 27, 1996, raw footage.
Identifier
(type = rbdil)
B07-19960327-KNWH-WV-INT-GR8-ALG-BIEX-RAW
RelatedItem
(type = is referenced by)
TitleInfo
Title
A case study : the development of Stephanie's algebraic reasoning / by Eman Y. Aboelnaga.
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000057485
TypeOfResource
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Identifier
(type = rbdil)
B06B07-ALG-BIEX-CLIP003
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Stephanie (student)
Subject
Name
(authority = RBDIL_corporate)
NamePart
(type = corporate)
Harding Elementary School (Kenilworth, N.J.)
Subject
(authority = rbdil_district)
Geographic
Kenilworth Public Schools
Subject
HierarchicalGeographic
Country
UNITED STATES
State
New Jersey
County
Union County
City
Kenilworth (N.J.)
Classification
(authority = RUresearch);
(edition = Data)
Abstract
(type = summary)
In 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?
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?
PhysicalDescription
Extent
(unit = digital file(s))
1
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OriginInfo
Place
PlaceTerm
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New Brunswick, NJ
Publisher
Robert B. Davis Institute for Learning
CopyrightDate
(qualifier = exact)
1996-03-27
Extension
DescriptiveEvent
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.
Place
Rutgers, the State University of New Jersey, New Brunswick, NJ
DateTime
(qualifier = exact)
2011
Detail
D
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Author
Name
Aboelnaga, Eman Y. (Eman Yousry)
Affiliation
Rutgers, the State University of New Jersey
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Dissertation
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Name
A case study: the development of Stephanie's algebraic reasoning
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000057485
Reference
(type = digital)
http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000057485
Detail
issertation available in digital format in the Rutgers University Libraries' dissertation collection
TitleInfo
Title
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
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Robert B. Davis Institute for Learning Mathematics Education Collection
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doi:10.7282/T35D8QN1
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Rights
RightsDeclaration
(AUTHORITY = rbdil1_v1);
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The 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.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
Publication
Status
Unpublished
RightsHolder
(type = corporate)
Name
Robert B. Davis Institute for Learning
Role
Copyright holder
Telephone
732-932-7496 ext. 8112
Address
Rutgers Graduate School of Education
10 Seminary Place
New Brunswick, NJ 08901-1183
10 Seminary Place
New Brunswick, NJ 08901-1183
ContactInformationDate
2012-09-12
RightsEvent
Type
Permission or license
Label
Non-exclusive license to share the video presentation via RUcore
DateTime
2009-11-03
Detail
Non-exclusive license to digitize and make openly available the videos and other collection resources of the Institute is on file in the office of the RUcore Collections Manager.
AssociatedEntity
Role
Licensor
Name
Maher, Carolyn A.
Affiliation
Director, Robert B. Davis Institute for Learning, Rutgers Graduate School of Education
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Source
SourceTechnical
SourceType
Videotape
Duration
00:11:27
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Statistical Profile