Early algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 9 of 10: Relating coefficients of the binomial expansion to Pascal's Triangle and to unifix cube towers, selecting from two colors.
Descriptive
Genre
(authority = RURes_Genre)
Research data
Genre
(authority = RURes_dataGenre)
Observational data
Genre
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Edited data
Genre
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Repurposed data
Genre
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Longitudinal data
Genre
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School
Genre
(authority = RURes_researchMethodology)
Qualitative research
Genre
(authority = RURes_qualitativeMethod)
Interviews (individual)
TypeOfResource
MovingImage
Identifier
(type = rbdil)
A68A69-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 = Grade range)
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 = NCTM Content)
Subject
(authority = NCTM Process)
Subject
(authority = NCTM Process)
Topic
Reasoning and proof
Subject
(authority = NCTM Process)
Subject
(authority = NCTM Process)
Subject
(authority = NCTM Process)
Subject
(authority = rbdil_cameraView)
Subject
(authority = rbdil_cameraView)
Subject
(authority = rbdil_mathStrand)
Subject
(authority = rbdil_mathProblem)
Subject
(authority = rbdil_mathTools)
Subject
(authority = rbdil_setting)
Subject
(authority = rbdil_gradeLevel)
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
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)
Subject
(authority = rbdil_representations)
Topic
Combinatorics notation
Subject
(authority = rbdil_studentGender)
Subject
(authority = rbdil_studentEthnicity)
Subject
(authority = rbdil_schoolType)
Subject
(authority = rbdil_topic)
Subject
(authority = RURes_subjectOfStudy)
Topic
Sample of human subjects
Subject
(authority = LCSH)
Topic
Manipulatives (Education)--Case studies
Subject
(authority = rbdil_mathProblem)
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
Recognizing an isomorphism
Subject
(authority = rbdil_representations)
Subject
(authority = rbdil_topic)
Subject
(authority = rbdil_topic)
Subject
(authority = rbdil_topic)
Subject
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Geographic
Kenilworth Public Schools
Classification
(authority = RUresearch);
(edition = Data)
Abstract
(type = summary)
In the ninth 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 refers to written work that Stephanie had completed in an earlier interview where she had recorded the binomial (a + b) expanded to successive powers from one to five. Stephanie maps the coefficients for each expansion to the corresponding row of Pascal's Triangle and recognizes that there is also a correspondence to unifix towers built to the same height, when selecting from two colors. She then provides an explanation of the correspondence between particular terms in one of the expansions with the corresponding unifix-cube towers.
The problems as presented to Stephanie:
Compare the coefficients from successive powers of the binomial expansion to the rows of Pascal's Triangle.
Can the various terms of any given power of the expansion be shown to correspond to towers of different heights, selecting from two colors?
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 9 of 10: Relating coefficients of the binomial expansion to Pascal's Triangle and to unifix cube towers, selecting from two colors. [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
Place
PlaceTerm
(type = text)
New Brunswick, NJ
Publisher
Robert B. Davis Institute for Learning
RelatedItem
(type = host)
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
(type = rbdil)
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
Label
Ed.D. dissertation references the video footage that includes Early algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 9 of 10: Relating coefficients of the binomial expansion to Pascal's Triangle and to unifix cube towers, selecting from two colors.
Place
Rutgers, the State University of New Jersey, New Brunswick, NJ
DateTime
(qualifier = exact)
2011
AssociatedEntity
Name
Aboelnaga, Eman Y. (Eman Yousry)
Affiliation
Rutgers, the State University of New Jersey
AssociatedObject
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 five of seven, Clip 9 of 10: Relating coefficients of the binomial expansion to Pascal's Triangle and to unifix cube towers, selecting from two colors.
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000064508
RelatedItem
(type = host)
TitleInfo
Title
Robert B. Davis Institute for Learning Mathematics Education Collection
Identifier
(type = local)
rucore00000001201
Location
PhysicalLocation
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(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Location
PhysicalLocation
(authority = marcorg);
(displayLabel = Rutgers University. Libraries)
NjR
Identifier
(type = doi)
doi:10.7282/T3DR2TFX
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