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Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 1 of 9: Explaining that (a+b) squared = (a squared + 2ab + b squared), algebraically and geometrically

Descriptive

Genre (authority = RURes_Genre)
Research data
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Observational data
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Edited data
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Repurposed data
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Longitudinal data
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School
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Qualitative research
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Interviews (individual)
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 = RURes_subjectOfStudy)
Topic
Human sample
Subject (authority = LCSH)
Topic
Mathematics education
Subject (authority = LCSH)
Topic
Learning, Psychology of--Case studies
Subject (authority = LCSH)
Topic
Critical thinking in children--New Jersey--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
Subject (authority = NCTM Process)
Topic
Representation
Subject (authority = rbdil_gradeLevel)
Topic
8
Subject (authority = rbdil_mathStrand)
Topic
Algebra
Subject (authority = rbdil_mathProblem)
Topic
Binomial expansion
Subject (authority = rbdil_mathTools)
Topic
Color markers
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Direct reasoning
Subject (authority = rbdil_representations)
Topic
Mathematical expressions
Subject (authority = rbdil_representations)
Topic
Drawings
Subject (authority = rbdil_topic)
Topic
Variables
Subject (authority = rbdil_topic)
Topic
Exponents
Subject (authority = rbdil_topic)
Topic
Area
Subject (authority = rbdil_topic)
Topic
Distributive property
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Informal learning
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Public school
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Topic
Student view
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Topic
Work view
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Topic
Female
Subject (authority = rbdil_studentEthnicity)
Topic
White
TypeOfResource
MovingImage
Identifier (type = rbdil)
A66A67-ALG-BIEX-CLIP001
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 first clip in a series of nine from the fourth of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, Stephanie explains the conclusions that she has justified in earlier interviews. In response to the researcher, Carolyn Maher, Stephanie firsts writes out the expanded form of (a+b) squared. She then explains that she had used geometric drawings to illustrate the meaning of the square with side a, first by substituting the value 3 for a and drawing a 3 by 3 array within a square and then representing a square with side (a+b) by sectioning her drawing into four parts.
The problem as presented to Stephanie:
Explain your conclusions about the square of the quantity (a+b).
PhysicalDescription
InternetMediaType
video/quicktime
InternetMediaType
video/x-flv
Extent (unit = digital file(s))
1
TargetAudience (authority = RURes_discipline)
Social science
TargetAudience (authority = RURes_domain)
Mathematics education
Note (type = supplementary materials)
Transcript and student work are also available.
Note (type = APA citation)
Robert B. Davis Institute for Learning. (1996). Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 1 of 9: Explaining that (a+b) squared = (a squared + 2ab + b squared), algebraically and geometrically [video]. Retrieved from
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
OriginInfo
CopyrightDate (qualifier = exact)
1996-02-21
Place
PlaceTerm (type = text)
New Brunswick, NJ
Publisher
Robert B. Davis Institute for Learning
RelatedItem (type = host)
TitleInfo
Title
A66, Early algebra ideas about binomial expansion, Stephanie's interview four of seven (student view), Grade 8, February 21, 1996, raw footage.
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A66-19960221-KNWH-SV-INT-GR8-ALG-BIEX-RAW
RelatedItem (type = host)
TitleInfo
Title
A67, Early algebra ideas about binomial expansion, Stephanie's interview four of seven (work view), Grade 8, February 21, 1996, raw footage.
Identifier (type = rbdil)
A67-19960221-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
Extension
DescriptiveEvent
Type
Related publication
Label
Ed.D. dissertation references the video footage that includes Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 1 of 9: Explaining that (a+b) squared = (a squared + 2ab + b squared), algebraically and geometrically
Place
New Brunswick, NJ
DateTime (qualifier = exact)
2011
AssociatedEntity
Role
Author
Name
Aboelnaga, Eman Y. (Eman Yousry)
Affiliation
Rutgers, the State University of New Jersey
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Type
Dissertation
Relationship
References
Name
A case study : the development of Stephanie's algebraic reasoning
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000057485
Reference
http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000057485
Detail
Dissertation available in digital format in the Rutgers University Libraries' dissertation collection.
TitleInfo
Title
Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 1 of 9: Explaining that (a+b) squared = (a squared + 2ab + b squared), algebraically and geometrically
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000065476
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Robert B. Davis Institute for Learning Mathematics Education Collection
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rucore00000001201
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Identifier (type = doi)
doi:10.7282/T3G73CK5
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Rights

RightsHolder (type = corporate)
Name
Robert B. Davis Institute for Learning
Role
Copyright holder
Telephone
732-932-8848
Address
Rutgers Graduate School of Education
10 Seminary Place
New Brunswick, NJ 08901-1183
ContactInformationDate
2009-11-03
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
RightsEvent
Type
Permission or license
Label
Non-exclusive license to share the video presentation via RUcore.
Place
New Brunswick, NJ
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

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Videotape
Duration
00:02:01
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