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Early algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 2 of 7: Generating Unifix-cube towers 4-tall from exactly two to exactly three red cubes and from exactly three yellow cubes to the tower with all four yellow cubes.

Descriptive

Identifier (type = rbdil)
B08B09-ALG-BIEX-CLIP002
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
Genre (authority = RURes_dataCollectionSetting)
School
Genre (authority = RURes_researchMethodology)
Qualitative research
Genre (authority = RURes_qualitativeMethod)
Interviews (individual)
Subject
Name (authority = RBDIL_personal)
NamePart
Stephanie (student)
Subject
Name (authority = RBDIL_corporate)
NamePart
Harding Elementary School (Kenilworth, N.J.)
Subject (authority = RURes_subjectOfStudy)
Topic
Sample of human subjects
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_cameraView)
Topic
Work view
Subject (authority = rbdil_cameraView)
Topic
Student view
Subject (authority = rbdil_gradeLevel)
Topic
8
Subject (authority = rbdil_mathStrand)
Topic
Algebra
Subject (authority = rbdil_mathProblem)
Topic
Binomial expansion
Subject (authority = rbdil_mathTools)
Topic
Unifix cubes
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Reasoning by cases
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Direct reasoning
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Recognizing a pattern
Subject (authority = rbdil_representations)
Topic
Physical models
Subject (authority = rbdil_topic)
Topic
Combinations
Subject (authority = rbdil_setting)
Topic
Informal learning
Subject (authority = rbdil_schoolType)
Topic
Public school
Subject (authority = rbdil_studentGender)
Topic
Female
Subject (authority = rbdil_studentEthnicity)
Topic
White
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Reasoning by contradiction
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Controlling for variables
Subject (authority = rbdil_representations)
Topic
Combinatorics notation
TypeOfResource
MovingImage
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 second clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie first predicts the number of Unifix-cube towers with exactly three red cubes to be generated from the six towers with two red and two yellow cubes. In response to questions from researchers Carolyn Maher and Donna Weir, Stephanie predicts and then builds twelve towers from the six and identifies the four sets of three duplicate towers to produce the four unique towers with exactly three red cubes. Stephanie notes that the six towers with two of each color would be multiplied by 2 because of the two possible positions for the third red cube and the resulting 12 would be divided by 3 to account for the duplicates. She then focuses on the four towers with exactly one red cube and recognizes that each of these would produce a single tower with all four cubes yellow. Since the four would be the same, there would be only one such tower. Stephanie concludes by noting that this same process would produce a single tower with four red cubes from the four that she has built with exactly three red cubes.

The problems posed to Stephanie are:
Predict the number of towers with exactly three red cubes that would be generated from the six towers with two red and two yellow.
Confirm your prediction by building the towers and eliminating duplicates. How would you describe this process with numbers?
Predict the number of towers that would be produced moving from three of one color to all four of that color. How can you confirm that prediction?
PhysicalDescription
Extent (unit = digital file(s))
1
InternetMediaType
video/x-flv
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 seven of seven, Clip 2 of 7: Generating Unifix-cube towers 4-tall from exactly two to exactly three red cubes and from exactly three yellow cubes to the tower with all four yellow cubes. [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
Name (type = personal)
NamePart (type = family)
Weir
NamePart (type = given)
M. Donna
Affiliation
Rutgers, the State University of New Jersey
Role
RoleTerm (authority = marcrelator); (type = text)
Researcher
OriginInfo
CopyrightDate
1996-04-17
Place
PlaceTerm (type = text)
New Brunswick, NJ
Publisher
Robert B. Davis Institute for Learning
RelatedItem (type = host)
TitleInfo
Title
B08, Early algebra ideas about binomial expansion, Stephanie's interview seven of seven (student view), Grade 8, April 17, 1996, raw footage.
Identifier (type = rbdil)
B08-19960417-KNWH-SV-INT-GR8-ALG-BIEX-RAW
RelatedItem (type = host)
TitleInfo
Title
B09, Early algebra ideas about binomial expansion, Stephanie's interview seven of seven (work view), Grade 8, April 17, 1996, raw footage.
Identifier (type = rbdil)
B09-19960417-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 seven of seven, Clip 2 of 7: Generating Unifix-cube towers 4-tall from exactly two to exactly three red cubes and from exactly three yellow cubes to the tower with all four yellow cubes.
Place
Rutgers, the State University of New Jersey, New Brunswick, NJ
DateTime (qualifier = exact)
2011
AssociatedEntity
Role
Author
Name
Aboelnaga, Eman Y. (Eman Yousry)
Affiliation
Rutgers, the State University of New Jersey
AssociatedObject
Type
Dissertation
Relationship
References
Name
A case study: the development of Stephanie's algebraic reasoning
Identifier (type = global)
http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000057485
Reference (type = digital)
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 seven of seven, Clip 2 of 7: Generating Unifix-cube towers 4-tall from exactly two to exactly three red cubes and from exactly three yellow cubes to the tower with all four yellow cubes.
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000065430
RelatedItem (type = host)
TitleInfo
Title
Robert B. Davis Institute for Learning Mathematics Education Collection
Identifier (type = local)
rucore00000001201
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers University. Libraries)
NjR
Identifier (type = doi)
doi:10.7282/T34J0CXH
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Rights

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
RightsDeclaration (AUTHORITY = 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
ContactInformationDate
2012-09-12
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Source

SourceTechnical
SourceType
Videotape
Duration
00:07:32
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Checksum (METHOD = SHA1)
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