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Early algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 3 of 9: Describing the volume of (a+b) cubed using math manipulatives.

Descriptive

Genre (authority = RURes_Genre)
Research data
Genre (authority = RURes_dataGenre)
Observational data
Genre (authority = RURes_dataLifecycle)
Edited data
Genre (authority = RURes_dataLifecycle)
Repurposed data
Genre (authority = RURes_researchDataType)
Longitudinal data
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School
Genre (authority = RURes_researchMethodology)
Qualitative research
Genre (authority = RURes_qualitativeMethod)
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 = 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
Subject (authority = NCTM Process)
Topic
Representation
Subject (authority = rbdil_gradeLevel)
Topic
8
Subject (authority = rbdil_mathStrand)
Topic
Algebra
Subject (authority = rbdil_mathTools)
Topic
Color markers
Subject (authority = rbdil_mathTools)
Topic
Base ten blocks
Subject (authority = rbdil_mathTools)
Topic
Algebra blocks
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Direct reasoning
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Constructing a physical model
Subject (authority = rbdil_mathProblem)
Topic
Construct volume model
Subject (authority = rbdil_representations)
Topic
Mathematical expressions
Subject (authority = rbdil_representations)
Topic
Drawings
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Topic
Physical models
Subject (authority = rbdil_topic)
Topic
Variables
Subject (authority = rbdil_topic)
Topic
Exponents
Subject (authority = rbdil_topic)
Topic
Area
Subject (authority = rbdil_topic)
Topic
Volume
Subject (authority = rbdil_setting)
Topic
Informal learning
Subject (authority = rbdil_schoolType)
Topic
Public school
Subject (authority = rbdil_cameraView)
Topic
Student view
Subject (authority = rbdil_cameraView)
Topic
Work view
Subject (authority = rbdil_studentGender)
Topic
Female
Subject (authority = rbdil_studentEthnicity)
Topic
White
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Constructing a pictorial model
TypeOfResource
MovingImage
Identifier (type = rbdil)
A66A67-ALG-BIEX-CLIP003
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 nine from the fourth of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, researcher Carolyn Maher presents Stephanie with base-ten materials, algebra blocks and other rectangular prisms; then asks her how she might use any of the manipulatives to explain volume in general and the volume of cube with side (a+b) in particular. Stephanie uses the small cubic unit and the 100 cubic unit "flat" from the base-ten materials to explain the numerical volume of the large 1000 cubic unit block. She was then asked how she might figure out the volume of the large block if it were to have a side of (a+b). Precision about language and issues of meaning with reference to geometric models that involve two and three dimensions are addressed directly in clip 4 and discussed in each subsequent clip in the series.
The problem as presented to Stephanie:
How could you use squared materials to show the cube 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 3 of 9: Describing the volume of (a+b) cubed using math manipulatives. [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
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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 3 of 9: Describing the volume of (a+b) cubed using math manipulatives.
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
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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 3 of 9: Describing the volume of (a+b) cubed using math manipulatives.
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000065478
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Robert B. Davis Institute for Learning Mathematics Education Collection
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rucore00000001201
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Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers University. Libraries)
NjR
Identifier (type = doi)
doi:10.7282/T3QR4W1X
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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

SourceTechnical
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Videotape
Duration
00:09:19
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