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Early algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 4 of 10: Investigating the "doubling pattern" for unifix towers of increasing heights.

Descriptive

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Research data
Genre (authority = RURes_dataGenre)
Observational data
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Edited data
Genre (authority = RURes_dataLifecycle)
Repurposed data
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Longitudinal data
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School
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Qualitative research
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Interviews (individual)
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A68A69-ALG-BIEX-CLIP004
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)
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 (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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Topic
Connections
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Topic
Representation
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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 = 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
Tree diagrams
Subject (authority = LCSH)
Topic
Manipulatives (Education)--Case studies
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 fourth 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. Using combinatorics notation, researcher Carolyn Maher records as Stephanie reviews the total number of towers 4-tall selecting from red and yellow cubes. In each of the five cases for n equal height 4 and r equal the number of red cubes from zero to 4, Stephanie indicates the number of towers and then adds the numbers from the subtotals to find the total. She then revisits the totals for towers one, two and three cubes high and notes that the totals double for each additional cube. Maher asks Stephanie to begin with the two, one-tall towers and to generate towers two-cubes tall by adding either a red or a yellow cube above the original base. From these four, Stephanie then generates the 8 towers that are 3 cubes tall and justifies her solution by referring to the tree diagram that she has drawn. She posits that, on the basis of her findings, this doubling pattern will continue.
The problems as presented to Stephanie:
Based on your combinatorics notation, what is the total number of Unifix Towers that are four-cubes tall?
What are the total numbers for towers that are: one-cube tall, two-cubes tall and three-cubes tall?
What would you predict as the total for towers 5-cubes tall?
If there are exactly two towers one-cube tall, how can you generate towers that are 2-cubes tall? Three cubes tall? Why does this pattern work? Do you think that it would continue for towers 4-cubes tall and taller?
PhysicalDescription
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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 4 of 10, Investigating the "doubling pattern" for unifix towers of increasing heights [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 (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.
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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
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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 4 of 10: Investigating the "doubling pattern" for unifix towers of increasing heights.
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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A case study: the development of Stephanie's algebraic reasoning
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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 4 of 10: Investigating the "doubling pattern" for unifix towers of increasing heights.
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000064503
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Robert B. Davis Institute for Learning Mathematics Education Collection
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Location
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NjR
Identifier (type = doi)
doi:10.7282/T3WQ02R3
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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
ContactInformationDate
2009-11-03
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Duration
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