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Early algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 6 of 10: Connecting the combinatorics notation for tower choices when selecting from two colors to the first 5 rows of Pascal's Triangle.
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
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Longitudinal data
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School
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Qualitative research
Genre
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Interviews (individual)
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MovingImage
Identifier
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A68A69-ALG-BIEX-CLIP006
Subject
Name
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NamePart
(type = personal)
Stephanie (student)
Subject
Name
(authority = RBDIL_corporate)
NamePart
(type = corporate)
Harding Elementary School (Kenilworth, N.J.)
Subject
(authority = Grade range)
Topic
6-8
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
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Topic
Algebra
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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
Subject
(authority = NCTM Process)
Topic
Representation
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Topic
Work view
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Topic
Student view
Subject
(authority = rbdil_mathStrand)
Topic
Algebra
Subject
(authority = rbdil_mathProblem)
Topic
Towers
Subject
(authority = rbdil_mathTools)
Topic
Color markers
Subject
(authority = rbdil_setting)
Topic
Informal learning
Subject
(authority = rbdil_gradeLevel)
Topic
8
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Direct reasoning
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Constructing a pictorial model
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Referencing a previous problem
Subject
(authority = rbdil_representations)
Topic
Mathematical expressions
Subject
(authority = rbdil_representations)
Topic
Drawings
Subject
(authority = rbdil_representations)
Topic
Combinatorics notation
Subject
(authority = rbdil_studentGender)
Topic
Female
Subject
(authority = rbdil_studentEthnicity)
Topic
White
Subject
(authority = rbdil_schoolType)
Topic
Public school
Subject
(authority = rbdil_topic)
Topic
Combinations
Subject
(authority = RURes_subjectOfStudy)
Topic
Sample of human subjects
Subject
(authority = LCSH)
Topic
Manipulatives (Education)--Case studies
Subject
(authority = rbdil_mathProblem)
Topic
Binomial expansion
Subject
(authority = rbdil_mathProblem)
Topic
Explore Pascal's triangle
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Recognizing a pattern
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Making conjectures
Subject
(authority = rbdil_representations)
Topic
Pascal's triangle
Subject
(authority = rbdil_representations)
Topic
Tree diagrams
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 sixth clip in a series of ten from the fifth of seven interviews, 8th grader Stephanie continues her exploration of Early Algebraic Ideas about Binomial Expansion. Researcher Carolyn Maher asks Stephanie to represent towers one-cube tall using the combinatorics notation introduced earlier for n choose r, and records this in a form that is the first row of Pascal's Triangle. As Stephanie continues to develop this correspondence for towers 2 and 3-cubes tall, she recognizes the addition property of the triangle. Using this pattern to predict the entries for the 4th row of the triangle, Stephanie recognizes that the predicted entries correspond correctly to the numbers of towers that she had built for each case. She uses this representation and the recognized pattern to predict the entries in the 5th row.
The problems as presented to Stephanie:
Does the number of towers in each case for n equal 1 to 3-cubes tall and r equal to the number of red cubes from zero to n, when selecting from two colors, match the corresponding entry in each of the first 3 rows of Pascal's Triangle?
How can this representation be used to predict rows 4 and 5 in the Triangle and the corresponding number of towers 4 and 5-cubes tall?
?
The problems as presented to Stephanie:
Does the number of towers in each case for n equal 1 to 3-cubes tall and r equal to the number of red cubes from zero to n, when selecting from two colors, match the corresponding entry in each of the first 3 rows of Pascal's Triangle?
How can this representation be used to predict rows 4 and 5 in the Triangle and the corresponding number of towers 4 and 5-cubes tall?
?
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 five of seven, Clip 6 of 10: Connecting the combinatorics notation for tower choices when selecting from two colors to the first 5 rows of Pascal's Triangle. [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
1996-03-13
Place
PlaceTerm
(type = text)
New Brunswick, NJ
Publisher
Robert B. Davis Institute for Learning
RelatedItem
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TitleInfo
Title
A68, Early algebra ideas about binomial expansion, Stephanie's interview five of seven (student view), Grade 8, March 13, 1996, raw footage.
Identifier
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A68-19960313-KNWH-SV-INT-GR8-ALG-BIEX-RAW
RelatedItem
(type = host)
TitleInfo
Title
A69, Early algebra ideas about binomial expansion, Stephanie's interview five of seven (work view), Grade 8, March 13, 1996, raw footage.
Identifier
(type = rbdil)
A69-19960313-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 five of seven, Clip 6 of 10: Connecting the combinatorics notation for tower choices when selecting from two colors to the first 5 rows of Pascal's Triangle.
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
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Dissertation
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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
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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 five of seven, Clip 6 of 10: Connecting the combinatorics notation for tower choices when selecting from two colors to the first 5 rows of Pascal's Triangle.
Identifier
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http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000064505
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Robert B. Davis Institute for Learning Mathematics Education Collection
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rucore00000001201
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NjR
Identifier
(type = doi)
doi:10.7282/T31G0K7D
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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
732-932-8848
Address
Rutgers Graduate School of Education
10 Seminary Place
New Brunswick, NJ 08901-1183
10 Seminary Place
New Brunswick, NJ 08901-1183
ContactInformationDate
2009-11-03
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Source
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Videotape
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1/2-inch
Duration
00:06:44
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Statistical Profile