Staff View
Early algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 4 of 11: Developing the correspondence among towers, selecting from two colors, Pascal's Triangle, and the symbolic algebraic expansions of (a+b) squared and (a+b) cubed

Descriptive

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_qualitativeMethod)
Interviews (individual)
Genre (authority = RURes_researchDataType)
Longitudinal data
Genre (authority = RURes_researchMethodology)
Qualitative research
Genre (authority = RURes_dataCollectionSetting)
School
Subject (authority = LCSH)
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
Subject (authority = NCTM Process)
Topic
Connections
Subject (authority = NCTM Process)
Topic
Representation
Subject (authority = rbdil_mathStrand)
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
Direct reasoning
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Recursive reasoning
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Inductive reasoning
Subject (authority = rbdil_representations)
Topic
Physical models
Subject (authority = rbdil_representations)
Topic
Combinatorics notation
Subject (authority = rbdil_topic)
Topic
Combinations
Subject (authority = rbdil_cameraView)
Topic
Student view
Subject (authority = rbdil_cameraView)
Topic
Work view
Subject (authority = rbdil_studentGender)
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_representations)
Topic
Pascal's triangle
Subject (authority = rbdil_representations)
Topic
Mathematical expressions
Subject (authority = rbdil_topic)
Topic
Coefficients
Subject (authority = rbdil_topic)
Topic
Exponents
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 4 of 11: Developing the correspondence among towers, selecting from two colors, Pascal's Triangle, and the symbolic algebraic expansions of (a+b) squared and (a+b) cubed. [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 (type = host)
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 (type = rbdil)
B06-19960327-KNWH-SV-INT-GR8-ALG-BIEX-RAW
RelatedItem (type = host)
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-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 = 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 eleven from the sixth of seven interviews, 8th grader Stephanie remembers that she had figured out the expanded algebraic expressions for (a+b) for powers up to 6. When asked by researchers Carolyn Maher and Robert Speiser to connect these expressions to Pascal's Triangle and Unifix-cube towers that she had built by selecting from two colors, Stephanie developed a correspondence between the variables, a and b, and the colors of the cubes that allowed her to understand that the numbers in the Triangle referred to the coefficients in the expression and the number of towers in each case for the expressions (a+b) squared and (a+b) cubed. She also recognized that each exponent in the expanded expression referred to the number of cubes of a particular color in the corresponding Unifix-cube tower.
The problems as generated by Stephanie for her discussion with the researchers:
What is the expanded expression for (a+b) squared?
How does this relate to the Unifix-cube towers with two colors and to Pascal's Triangle?
Build a similar correspondence for (a+b) cubed with both the towers and the Triangle.
PhysicalDescription
Extent (unit = digital file(s))
1
InternetMediaType
video/x-flv
OriginInfo
Place
PlaceTerm (type = text)
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 4 of 11: Developing the correspondence among towers, selecting from two colors, Pascal's Triangle, and the symbolic algebraic expansions of (a+b) squared and (a+b) cubed.
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
AssociatedObject
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 4 of 11: Developing the correspondence among towers, selecting from two colors, Pascal's Triangle, and the symbolic algebraic expansions of (a+b) squared and (a+b) cubed
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000066052
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/T3959GB9
Back to the top

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
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
Back to the top

Source

SourceTechnical
SourceType
Videotape
Duration
00:06:50
Back to the top

Technical

ContentModel
Video
PreservationLevel
full
Generation
Digital preservation master
Duration
00:06:50
System
MS Video
Frame
Height
640
Width
480
Rate
29.97 fps
AspectRatio
4:3
Structure
interlaced
FormatColors
Color
BitRateReduction
Compression
CompressionType
uncompressed
Codec
CodecName
full frame uncompressed
CodecQuality
code regenerating
VideoSampling
SamplingSize
4:2:2
WordSize
3-byte
BitsPerSample
24-bit
SoundPresent
yes
Sound
Channels
NumberOfChannels
2
SoundField
stereo
Sampling
SamplingRate
44.1 kHz
BitsPerSample
16-bit
WordSize
3-byte
MimeType (TYPE = file)
application/pdf
MimeType (TYPE = container)
application/x-tar
FileSize (UNIT = bytes)
1030205440
Checksum (METHOD = SHA1)
49118184f6e29594601f8ee0501607e9f595a4a4
MimeType (TYPE = container)
application/x-tar
FileSize (UNIT = bytes)
573440
Checksum (METHOD = SHA1)
cb92dcd1faf6f29ca9e8fb5586497fa5388f9d57
Back to the top
Version 8.3.13
Rutgers University Libraries - Copyright ©2020