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Early algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 4 of 11: Developing the correspondence among towers, selecting from two colors, Pascal's Triangle, and the symbolic algebraic expansions of (a+b) squared and (a+b) cubed
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
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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
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(authority = NCTM Process)
Topic
Communication
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(authority = NCTM Process)
Topic
Connections
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(authority = NCTM Process)
Topic
Representation
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Topic
Algebra
Subject
(authority = rbdil_mathProblem)
Topic
Binomial expansion
Subject
(authority = rbdil_mathTools)
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
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(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Inductive reasoning
Subject
(authority = rbdil_representations)
Topic
Physical models
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(authority = rbdil_representations)
Topic
Combinatorics notation
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(authority = rbdil_topic)
Topic
Combinations
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Student view
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Work view
Subject
(authority = rbdil_studentGender)
Topic
Female
Subject
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Topic
White
Subject
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Topic
Public school
Subject
(authority = RURes_subjectOfStudy)
Topic
Sample of human subjects
Subject
(authority = rbdil_representations)
Topic
Pascal's triangle
Subject
(authority = rbdil_representations)
Topic
Mathematical expressions
Subject
(authority = rbdil_topic)
Topic
Coefficients
Subject
(authority = rbdil_topic)
Topic
Exponents
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 4 of 11: Developing the correspondence among towers, selecting from two colors, Pascal's Triangle, and the symbolic algebraic expansions of (a+b) squared and (a+b) cubed. [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
(type = host)
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
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MovingImage
Identifier
(type = rbdil)
B06B07-ALG-BIEX-CLIP004
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 fourth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie remembers that she had figured out the expanded algebraic expressions for (a+b) for powers up to 6. When asked by researchers Carolyn Maher and Robert Speiser to connect these expressions to Pascal's Triangle and Unifix-cube towers that she had built by selecting from two colors, Stephanie developed a correspondence between the variables, a and b, and the colors of the cubes that allowed her to understand that the numbers in the Triangle referred to the coefficients in the expression and the number of towers in each case for the expressions (a+b) squared and (a+b) cubed. She also recognized that each exponent in the expanded expression referred to the number of cubes of a particular color in the corresponding Unifix-cube tower.
The problems as generated by Stephanie for her discussion with the researchers:
What is the expanded expression for (a+b) squared?
How does this relate to the Unifix-cube towers with two colors and to Pascal's Triangle?
Build a similar correspondence for (a+b) cubed with both the towers and the Triangle.
The problems as generated by Stephanie for her discussion with the researchers:
What is the expanded expression for (a+b) squared?
How does this relate to the Unifix-cube towers with two colors and to Pascal's Triangle?
Build a similar correspondence for (a+b) cubed with both the towers and the Triangle.
PhysicalDescription
Extent
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1
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video/x-flv
OriginInfo
Place
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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 4 of 11: Developing the correspondence among towers, selecting from two colors, Pascal's Triangle, and the symbolic algebraic expansions of (a+b) squared and (a+b) cubed.
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 4 of 11: Developing the correspondence among towers, selecting from two colors, Pascal's Triangle, and the symbolic algebraic expansions of (a+b) squared and (a+b) cubed
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Robert B. Davis Institute for Learning Mathematics Education Collection
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doi:10.7282/T3959GB9
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Rights
RightsDeclaration
(AUTHORITY = rbdil1_v1);
(ID = rbdil1_v1)
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
00:06:50
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