Staff View
A28, Night Session, Pascal's Identity (presentation view), Grade 11, May 12, 1999, raw footage

Descriptive

Genre (authority = RURes_Genre)
Research data
Genre (authority = RURes_dataGenre)
Observational data
Genre (authority = RURes_dataLifecycle)
Raw data
Genre (authority = RURes_dataLifecycle)
Repurposed data
Genre (authority = RURes_researchDataType)
Longitudinal data
Genre (authority = RURes_dataCollectionSetting)
School
Genre (authority = RURes_researchMethodology)
Qualitative research
Genre (authority = RURes_qualitativeMethod)
Educational interventions (small group)
Subject
Name (authority = RBDIL_personal)
NamePart
Jeff (student)
Subject
Name (authority = RBDIL_personal)
NamePart
Romina (student)
Subject
Name (authority = RBDIL_personal)
NamePart
Michael A. (Kenilworth, student)
Subject
Name (authority = RBDIL_personal)
NamePart
Ankur (student)
Subject
Name (authority = RBDIL_personal)
NamePart
Brian (Kenilworth, student)
Subject
Name (authority = RBDIL_corporate)
NamePart
David Brearley High School (Kenilworth, N.J.)
Subject (authority = Grade range)
Topic
9-12
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
Number and operations
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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_cameraView)
Topic
Classroom view
Subject (authority = rbdil_mathStrand)
Topic
Combinatorics
Subject (authority = rbdil_mathProblem)
Topic
Pascal's identity
Subject (authority = rbdil_mathTools)
Topic
Calculator
Subject (authority = rbdil_setting)
Topic
Informal learning
Subject (authority = rbdil_gradeLevel)
Topic
11
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_forms of reasoning, strategies and heuristics)
Topic
Recursive reasoning
Subject (authority = rbdil_representations)
Topic
Pascal's triangle
Subject (authority = rbdil_studentGender)
Topic
Mixed
Subject (authority = rbdil_studentEthnicity)
Topic
Mixed
Subject (authority = rbdil_schoolType)
Topic
Public school
Subject (authority = rbdil_topic)
Topic
Combinations
Subject (authority = rbdil_topic)
Topic
Factorials
Subject (authority = rbdil_topic)
Topic
Coefficients
Subject (authority = rbdil_mathStrand)
Topic
Counting
TypeOfResource
MovingImage
TitleInfo
Title
A28, Night Session, Pascal's Identity (presentation view), Grade 11, May 12, 1999, raw footage
Identifier (type = rbdil)
A28-19990512-KNWH-PV-CLASS-GR11-CMB-TW10T-RAW
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000065130
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 this full-session, raw footage video, students have come to school in the evening for a night session. The group, made up of Jeff, Michael and Romina begin discussing the coefficients of the binomial expansion, specifically (a+b) to the 10th power. In attempting to explain why 45 is the coefficient of the third term in this expansion, the students refer to counting how many 10-tall towers have exactly two cubes of a specific color. As they are joined by another member, Ankur, they discuss the formula for “n choose x” using factorial notation and what the factorial symbol means. When asked to explain “why you multiply,” Ankur responds by making use of an analogy of counting the number of ways to arrange three different colors. They then investigate the reason for dividing n! by (n-x)! and x! when calculating “n choose x.” In explaining the specific example of “5 choose 2,” they use the analogies: of arranging five people on a line when you are concerned about the positions of only two of the people and counting the number of 5-tall towers having exactly two cubes of one color. They then discuss the notation for combinations, which they called “choose” notation, and how it relates to Pascal’s Identity (the addition rule for Pascal’s Triangle). Michael describes how the third row of Pascal’s Triangle can be written in “choose notation” (1 3 3 1 becomes “3 choose 0, “3 choose 1,” “3 choose 2,” and “3 choose 3”). He and the other students explain how the answers to the 3-topping pizza problem are related to row 3 of Pascal’s Triangle, and how a specific instance of Pascal’s Identity can be understood as generating specific 4-topping pizzas from 3-topping pizzas. The researcher then asks the students to write Pascal’s Triangle in this notation, including a general row (row n). The students then explain to Brian, a late-comer, the meaning of Pascal’s Identity (the addition rule for Pascal’s Triangle) in terms of operations on the pizzas that are represented by specific entries in Pascal’s Triangle. They write Pascal’s Identity in general form using standard notation.
Notes:
“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!].
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?
The n-topping pizza problem is: How many pizzas can be made when there are n different pizza toppings to choose from?
PhysicalDescription
Extent (unit = digital file(s))
1
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video/x-flv
TargetAudience (authority = RURes_discipline)
Social science
TargetAudience (authority = RURes_domain)
Mathematics education
Note (type = supplementary materials)
Transcript is also available.
Note (type = APA citation)
Robert B. Davis Institute for Learning. (1999). A28, Night Session, Pascal's Identity (presentation view), Grade 11, May 12, 1999, raw footage [video]. Retrieved from http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000065130
Name (type = personal)
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Maher
NamePart (type = given)
Carolyn Alexander
Affiliation
Rutgers, the State University of New Jersey
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Researcher
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Pantozzi
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Ralph S.
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Rutgers, the State University of New Jersey
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Kiczek
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Regina D.
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Rutgers, the State University of New Jersey
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Researcher
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Steencken
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Elena Perrone
Affiliation
Rutgers, the State University of New Jersey
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Researcher
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New Brunswick, NJ
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Robert B. Davis Institute for Learning
CopyrightDate
1999-05-12
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Title
To symbols from meaning: Students' investigations in counting / Elizabeth B. Uptegrove
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Night session, Pascal's identity, clip 1 of 7: thinking about the meaning of combinatorics notation
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Night session, Pascal's identity, clip 2 of 7: making sense of factorial notation and "why you multiply”
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Night session, Pascal's identity, clip 3 of 7: further explorations of factorials and combinations
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Night session, Pascal's identity, clip 4 of 7: An example of Pascal's identity
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Night Session, Pascal’s Identity, Clip 5 of 7: Another way to write Pascal’s Triangle
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Night Session, Pascal’s Identity, Clip 6 of 7: Examples of Pascal’s Identity in the notation for combinations
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Night Session, Pascal’s Identity, Clip 7 of 7: Generating and generalizing Pascal’s Identity
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Ed.D. dissertation references video footage that includes A28, Night Session, Pascal's Identity (presentation view), Grade 11. May 12, 1999, raw footage.
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Rutgers, the State University of New Jersey, New Brunswick, NJ
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2005
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To symbols from meaning: Students' investigations in counting
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Dissertation available in digital and paper formats in the Rutgers University Libraries' dissertation collection
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Rights

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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
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Copyright protected
Availability
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Open
Reason
Permission or license
Publication
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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
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
Place
New Brunswick, NJ
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