RUcore: Rutgers University Community Repository
Early algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 9 of 11: Beginning to generalize mathematical expressions to generate cases for towers 4-cubes tall selecting from green and blue cubes
Descriptive
Genre
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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
Subject
(authority = NCTM Process)
Topic
Communication
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(authority = NCTM Process)
Topic
Connections
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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
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
Working backwards
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(authority = rbdil_forms of reasoning, strategies and heuristics)
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Controlling for variables
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(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Recognizing a pattern
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(authority = rbdil_representations)
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Pascal's triangle
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Topic
Combinations
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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
Subject
(authority = rbdil_schoolType)
Topic
Public school
Subject
(authority = RURes_subjectOfStudy)
Topic
Sample of human subjects
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Referencing a previous problem
Subject
(authority = rbdil_representations)
Topic
Mathematical expressions
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 9 of 11: Beginning to generalize mathematical expressions to generate cases for towers 4-cubes tall selecting from green and blue cubes. [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
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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
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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
TypeOfResource
MovingImage
Identifier
(type = rbdil)
B06B07-ALG-BIEX-CLIP009
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)
n the ninth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie is asked by researchers Carolyn Maher and Robert Speiser to describe mathematically how she has generated sets of Unifix-cube towers 4-cubes tall across cases. She first considers the case for all green cubes when generated from the set of cubes with three green cubes and one blue cube and determines that the single resulting tower could be calculated by multiplying four (representing the four towers with exactly 3 green cubes) by 1 (representing the tower formed by exchanging the single blue cube for a green in each tower) and dividing the product by 4 because the four resulting towers are all duplicates. Stephanie then begins to express her observations in writing to explain how the four towers with one blue cube were generated from the towers with two blue and two green cubes.
The problems as proposed to Stephanie are:
How can you determine the number of towers, 4 cubes tall, with four green cubes from your set of four towers with one blue cube and 3 green cubes?
How could you describe with numbers how the single tower with four green cubes is generated?
How could you describe with numbers how the set of our towers with one blue cube and 3 green cubes is generated from the set of towers with two green cubes and two blue cubes ?
The problems as proposed to Stephanie are:
How can you determine the number of towers, 4 cubes tall, with four green cubes from your set of four towers with one blue cube and 3 green cubes?
How could you describe with numbers how the single tower with four green cubes is generated?
How could you describe with numbers how the set of our towers with one blue cube and 3 green cubes is generated from the set of towers with two green cubes and two blue cubes ?
PhysicalDescription
Extent
(unit = digital file(s))
1
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OriginInfo
Place
PlaceTerm
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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 9 of 11: Beginning to generalize mathematical expressions to generate cases for towers 4-cubes tall selecting from green and blue cubes.
Place
Rutgers, the State University of New Jersey, New Brunswick, NJ
DateTime
(qualifier = exact)
2011
Detail
D
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
(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 9 of 11: Beginning to generalize mathematical expressions to generate cases for towers 4-cubes tall selecting from green and blue cubes
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Robert B. Davis Institute for Learning Mathematics Education Collection
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Identifier
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doi:10.7282/T3Z036ZZ
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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
00:08:36
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Statistical Profile