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Early algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 5 of 7: Developing numerical representations for each case for the number of Unifix-cube towers 5-tall and 6-tall selecting from red and yellow cubes.
Descriptive Metadata
Rights Metadata
Source Metadata
Technical Metadata

Descriptive

Identifier (type = rbdil)
B08B09-ALG-BIEX-CLIP005
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_mathTools)
Topic
Color markers
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 fifth clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie and researcher Carolyn Maher extend their earlier investigation of how to represent the number of Unifix cube towers for cases from no red cubes to four red cubes for towers 4-cubes tall to towers 5-tall and then towers 6-tall, still selecting from red and yellow cubes.
For each case, Stephanie builds or imagines the actual towers and records the numerical expression that would calculate the number of towers. After completing her lists for towers 5-tall and 6-tall, Maher points out that, while the calculated results for each case correspond to the entries in Pascal's Triangle, they have been developed for towers of 5-cubes tall and 6-cubes tall based on patterns rather than a logical correspondence between the numbers and the towers. She challenges Stephanie to think about how to justify her conclusions. Researcher Donna Weir is observing.

The problems posed to Stephanie are:
How might the reasoning that you used for numerically representing Unifix-cube towers 4-cubes tall, when selecting from red and yellow cubes, for each case be helpful in determining the number of towers, 5-cubes tall, for each case?
Use similar reasoning to numerically represent the numbers of 6-tall towers in each case.
How could you justify your answers?
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 5 of 7: Developing numerical representations for each case for the number of Unifix-cube towers 5-tall and 6-tall selecting from red and 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 5 of 7: Developing numerical representations for each case for the number of Unifix-cube towers 5-tall and 6-tall selecting from red and 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 5 of 7: Developing numerical representations for each case for the number of Unifix-cube towers 5-tall and 6-tall selecting from red and yellow cubes.
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000065447
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/T3HQ3XQQ
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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
2009-11-03
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Source

SourceTechnical
SourceType
Videotape
Gauge
1/2-inch
Duration
00:07:43
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Technical

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interlaced
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Checksum (METHOD = SHA1)
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