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Night Session, Pascal’s Identity, Clip 5 of 7: Another way to write Pascal’s Triangle

Descriptive

TypeOfResource
MovingImage
TitleInfo
Title
Night Session, Pascal’s Identity, Clip 5 of 7: Another way to write Pascal’s Triangle
Identifier (type = rbdil)
A28-CMB-TW10T-CLIP005
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000055284
Language
LanguageTerm (authority = ISO 639-3:2007)
English
Genre (authority = RURes_RUResearchGenre)
Research data
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
Jeff (student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
Romina (student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
Michael A. (Kenilworth, student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
Ankur (student)
Subject
Name (authority = RBDIL_corporate)
NamePart (type = corporate)
David Brearley High School (Kenilworth, N.J.)
Subject (authority = lcsh)
Topic
Mathematics education
Subject (authority = lcsh)
Topic
Learning, Psychology of--Case studies
Subject (authority = Grade range)
Topic
9-12
Subject (authority = NCTM Content)
Topic
Number and operations
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
Counting
Subject (authority = rbdil_mathStrand)
Topic
Combinatorics
Subject (authority = rbdil_mathProblem)
Topic
Pascal's identity
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Direct reasoning
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Inductive reasoning
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Referencing a previous problem
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Recognizing a pattern
Subject (authority = rbdil_topic)
Topic
Pascal's triangle
Subject (authority = rbdil_topic)
Topic
Representations
Subject (authority = rbdil_topic)
Topic
Combinations
Subject (authority = rbdil_gradeLevel)
Topic
11
Subject (authority = rbdil_setting)
Topic
Informal learning
Subject (authority = rbdil_cameraView)
Topic
Classroom view
Subject (authority = rbdil_studentGender)
Topic
Mixed
Subject (authority = rbdil_studentEthnicity)
Topic
Mixed
Subject (authority = rbdil_mathProblem)
Topic
Towers
Subject (authority = rbdil_district)
Geographic
Kenilworth Public Schools
Subject
HierarchicalGeographic
Country
UNITED STATES
State
New Jersey
County
Union County
City
Kenilworth (N.J.)
Abstract (type = summary)
This is the fifth of seven clips from the night session. The students (Ankur, Jeff, Michael, and Romina) have been discussing Pascal’s Triangle. The researcher rewrites row 3 of Pascal’s Triangle in what the students call “choose” notation (1 3 3 1 becomes “3 choose 0, “3 choose 1,” “3 choose 2,” and “3 choose 3”). The researcher then asks the students to write more rows of Pascal’s Triangle in this notation, including a general row (row n). As the students work on this task, they describe connections between Pascal’s Triangle and the binomial expansion and between the n-th row of Pascal’s Triangle and the answer to the n-tall towers problem.
Notes:
The n-tall towers problem is: How many towers n cubes tall is it possible to make when there are two colors of cubes to choose from?
“Choose” notation is the notation for counting the number of combinations; “n choose r” gives the number of ways of selecting subsets containing r objects from a set containing n objects. When counting combinations, the order of selection is irrelevant. “n choose r” is equal to n!/[(n – r)!r!].
PhysicalDescription
Extent (unit = digital file(s))
1
InternetMediaType
video/x-flv
Note (type = supplementary materials)
Transcript is also available.
Note (type = APA citation)
Robert B. Davis Institute for Learning. (1999). Night Session, Pascal’s Identity, Clip 5 of 7: Another way to write Pascal’s Triangle. [video]. Retrieved from http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000055284/rucore00000001201.Video.000055284
Name (type = personal)
NamePart (type = family)
Maher
NamePart (type = given)
Carolyn Alexander
Role
RoleTerm (authority = marcrelator); (type = text)
Researcher
Affiliation
Rutgers, the State University of New Jersey
Name (type = personal)
NamePart (type = family)
Kiczek
NamePart (type = given)
Regina D.
Role
RoleTerm (authority = marcrelator); (type = text)
Researcher
Name (type = personal)
NamePart (type = family)
Steencken
NamePart (type = given)
Elena Perrone
Role
RoleTerm (authority = marcrelator); (type = text)
Researcher
OriginInfo
Place
PlaceTerm (type = text)
New Brunswick, NJ
Publisher
Robert B. Davis Institute for learning
CopyrightDate
1999-05-12
RelatedItem (type = host)
TitleInfo
Title
A28, Night session, Pascal's identity, grade 11, May 12, 1999, raw footage
Identifier (type = rbdil)
A28-19990512-KNWH-PV-CLASS-GR11-CMB-TW10T-RAW
RelatedItem (type = is referenced by)
TitleInfo
Title
To symbols from meaning: students' investigations in counting / by Elizabeth Uptegrove
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000055263
RelatedItem (type = host)
TitleInfo
Title
Robert B. Davis Institute for Learning Mathematics Education Collection
Identifier (type = local)
rucore00000001201
Extension
DescriptiveEvent
Type
Dissertation
Label
Ed.D. dissertation references the video footage that includes Night Session, Pascal’s Identity, Clip 5 of 7: Another way to write Pascal’s Triangle
Place
New Brunswick, NJ
Detail
Dissertation available in digital and paper formats in the Rutgers University Libraries dissertation collection.
AssociatedEntity
Role
Author
Name
Uptegrove, Elizabeth B.
Affiliation
Rutgers Graduate School of Education
AssociatedObject
Type
Dissertation
Relationship
References
Name
To symbols from meaning: students' investigations in counting.
Identifier (type = global)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000055263
Detail
Dissertation available in digital and paper formats in the Rutgers University Libraries dissertation collection.
Genre (authority = RURes_dataGenre)
Observational data
Genre (authority = RURes_dataLifecycle)
Edited data
Genre (authority = RURes_dataLifecycle)
Repurposed data
Genre (authority = RURes_researchDataType)
Longitudinal data
Genre (authority = RURes_researchMethodology)
Qualitative research
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School
Genre (authority = RURes_qualitativeMethod)
Educational interventions (small group)
TargetAudience (authority = RURes_discipline)
Social science
TargetAudience (authority = RURes_domain)
Mathematics education
Classification (authority = RUresearch); (edition = Data)
Identifier (type = doi)
doi:10.7282/T3GH9HT0
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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 (ID = CRH-1); (type = corporate)
Name
Robert B. Davis Institute for Learning
Role
Copyright holder
Telephone
732-932-7496, ext. 8262
Address
Rutgers Graduate School of Education
10 Seminary Place
New Brunswick, NJ 08901-1183
ContactInformationDate
2009-11-03
RightsEvent (ID = RE-1); (AUTHORITY = rulib)
Type
Permission or license
Label
Non-exclusive license to share the video presentation via RUcore.
Place
New Brunswick, NJ
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 (ID = AE-1); (AUTHORITY = rulib)
Role
Licensor
Name
Maher, Carolyn A.
Affiliation
Director, Robert B. Davis Institute for Learning, Rutgers Graduate School of Education
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Format
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1/2-inch
Duration
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PictureQualities
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color
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Duration
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