RUcore: Rutgers University Community Repository
PUP Math Towers of Hanoi
Descriptive
TypeOfResource
MovingImage
Identifier
(type = rbdil)
PM4_TowersOfHanoi
Genre
(authority = RURes_RUResearchGenre)
Research data
Genre
(authority = RURes_DataTypeOrMethodology)
Action research
Genre
(authority = RURes_DataTypeOrMethodology)
Direct observation
Genre
(authority = RURes_DataTypeOrMethodology)
Educational interventions (large group)
Genre
(authority = RURes_DataTypeOrMethodology)
Field research
Genre
(authority = RURes_DataTypeOrMethodology)
Longitudinal data
Genre
(authority = RURes_directObservationMethodology)
Continuous monitoring
Genre
(authority = RURes_subjectOfStudy)
Defined population
Genre
(authority = RURes_RUResearchGenre)
Derived or repurposed data
Genre
(authority = RURes_RUResearchGenre)
Observational data
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Amy-Lynn (student)
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Ankur (student)
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Brian (Kenilworth, student)
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Jeff (student)
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Matt (student)
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Michael A. (Kenilworth, student)
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Michelle I. (student)
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Michelle R. (student)
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Milin (student)
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Robert (student)
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = personal)
Romina (student)
Subject
Name
(authority = RBDIL_personal)
NamePart
(type = corporate)
Stephanie (student)
Subject
Name
(authority = RBDIL_corporate)
NamePart
(type = corporate)
Harding Elementary School (Kenilworth, N.J.)
Subject
(authority = lcsh)
Topic
Mathematics education
Subject
(authority = lcsh)
Topic
Critical thinking in children--New Jersey--Case studies
Subject
(authority = Grade range)
Topic
6-8
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
Connections
Subject
(authority = NCTM Process)
Topic
Representation
Subject
(authority = NCTM Process)
Topic
Communication
Subject
(authority = rbdil_gradeLevel)
Topic
6
Subject
(authority = rbdil_mathStrand)
Topic
Algebra
Subject
(authority = rbdil_mathProblem)
Topic
Towers of Hanoi
Subject
(authority = rbdil_mathTools)
Topic
Towers of Hanoi (game)
Subject
(authority = rbdil_setting)
Topic
Classroom
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Considering a simpler problem
Subject
(authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Recognizing a pattern
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_topic)
Topic
Representations
Subject
(authority = rbdil_topic)
Topic
Physical models
Subject
(authority = rbdil_topic)
Topic
Function tables
Subject
(authority = rbdil_schoolType)
Topic
Public school
Subject
(authority = rbdil_studentGender)
Topic
Mixed
Subject
(authority = rbdil_studentEthnicity)
Topic
Mixed
Subject
(authority = rbdil_cameraView)
Topic
Work view
Subject
(authority = rbdil_cameraView)
Topic
Student view
Subject
(authority = rbdil_cameraView)
Topic
Teacher view
Subject
(authority = LCSH)
Topic
Manipulatives (Education)--Case studies
Subject
(authority = LCSH)
Topic
Learning, Psychology of--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.)
Abstract
(type = summary)
This video comes from The Private Universe Project in Mathematics and includes excerpts from interviews as well as narrative voice-over, interspersed with footage of students engaged with problem solving. A class of Kenilworth sixth graders investigate the Tower of Hanoi problem that was posed by researcher, Robert B. Davis. He tells the students about an order of monks in the city of Hanoi, who were concerned about when the world was going to end, and so they made a puzzle like this which has 100 disks in it [illustrates a model of the discs]. Davis explains how the monks were very focused on working to solve that puzzle. When they have it done, that is supposed to be when the world ends. The students were challenged to find out when the world would end and began by moving discs of the tower model according to the rules described and clarified by the researcher. The students speculate as to the outcome and then explore cases for the number of moves required for towers built with certain number of rings. They record, share and check their findings. Inserted in the clip is a description of the solution to the problem by mathematician Fern Hunt. The episode returns to show the students' problem solving. Working from simpler cases, they notice a pattern for the number of moves up to five rings that is shared by Michelle as 31; for six rings, by Brian as 63; and for 10 rings by Ankur as 1023. The students offer conjecture for the number of moves for 100 rings and offer as a conjecture 2 to the 100th power as a solution for the number of moves. In dealing with larger moves, the students struggle with the algebra of exponents. Inserted in the clip is an interview that took place seven years later. It was conducted by mathematician Gary Davis and former student, Matt, who viewed the video, revisited the problem, and reflected on the students’ problem solving. Matt comments on the remainder of the video that shows the exploration of the students guided by researcher Robert B. Davis.
PhysicalDescription
Extent
(unit = digital file(s))
1
InternetMediaType
video/quicktime
InternetMediaType
video/x-flv
Note
(type = supplementary materials)
Transcript is also available.
Note
(type = APA citation)
Smithsonian Astrophysical Observatory. (1993).PUP Math Towers of Hanoi [video].
Note
(type = available formats)
Resource vailable in QuickTime and Flash digital video formats.
OriginInfo
DateCreated
(encoding = w3cdtf)
1993-10-29
Place
PlaceTerm
(type = text)
Cambridge, MA
Publisher
Annenberg Learner
CopyrightDate
(encoding = w3cdtf)
1993-10-29
Extension
DescriptiveEvent
Type
Related publication
Label
Workshops (web-based) utilize the video PUP Math Towers of Hanoi
AssociatedEntity
Role
Publisher
Name
Annenberg Learner
Reference
http://www.learner.org/about/contactus.html
Detail
Annenberg Learner, part of the Annenberg Foundation,
Advancing Excellent Teaching in American Schools
Annenberg Learner uses media and telecommunications to advance excellent teaching in American schools.
Advancing Excellent Teaching in American Schools
Annenberg Learner uses media and telecommunications to advance excellent teaching in American schools.
AssociatedEntity
Role
Creator
Name
Harvard-Smithsonian Center for Astrophysics
Reference
http://www.cfa.harvard.edu/
AssociatedObject
Type
Workshop
Relationship
References
Name
Private Universe Project in Mathematics Workshops
Reference
http://www.learner.org/workshops/pupmath/about/overview.html
Extension
DescriptiveEvent
Type
Related publication
Label
Ed.D. dissertation references the video footage that includes PUP Math Towers of Hanoi
DateTime
2007
AssociatedEntity
Role
Author
Name
Mayansky, Elmira.
Affiliation
Rutgers Graduate School of Education
AssociatedObject
Type
Dissertation
Relationship
References
Name
An analysis of the pedagogy of Robert B. Davis : young children working on the Tower of Hanoi problem
Identifier
(type = lccn)
QA.M467 2007
Detail
Dissertation is available in hard copy in the Rutgers University Libraries collection.
RelatedItem
(type = host)
TitleInfo
Title
Private Universe Project in Mathematics Workshops. Cambridge, MA: Annenberg Learner.
Identifier
(type = uri)
http://www.learner.org/workshops/pupmath/index.html
RelatedItem
(type = is referenced by)
TitleInfo
Title
An analysis of the pedagogy of Robert B. Davis : young children working on the Tower of Hanoi problem / by Elmira Mayansky
Identifier
(type = lccn)
QA.M467 2007
Name
(type = corporate)
NamePart
Harvard-Smithsonian Center for Astrophysics
Role
RoleTerm
(authority = marcrelator);
(type = text)
Creator
Name
(type = personal)
NamePart
(type = family)
Davis
NamePart
(type = given)
Robert B. (Robert Benjamin)
NamePart
(type = date)
1926-
Role
RoleTerm
(authority = marcrelator);
(type = text)
Researcher
TitleInfo
Title
PUP Math Towers of Hanoi
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000062052
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/T3S46R6P
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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
Published
RightsEvent
Type
Permission or license
Label
Non-exclusive license to share the video presentation via RUcore.
Place
Cambridge, MA
DateTime
(encoding = w3cdtf);
(qualifier = exact)
2011-06-17
AssociatedEntity
Role
Licensee
Name
Thomas Bonnenfant
Affiliation
Section Manager, Contracts and Grants, Smithsonian Astrophysical Observatory
RightsHolder
(type = corporate)
Name
Smithsonian Astrophysical Observatory
Role
Copyright holder
Address
60 Garden St.
Cambridge, MA 02138
Cambridge, MA 02138
ContactInformationDate
2011-06-17
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Source
SourceTechnical
SourceType
Videotape
Duration
00:20:14
PictureQualities
Color
color
SignalFormat
NTSC (composite color)
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Technical
ContentModel
Video
Generation
Digital preservation master
PreservationLevel
full
System
MS Video
Duration
00:20:14
Frame
Height
640
Width
480
Rate
29.97 fps
AspectRatio
4:3
Structure
interlaced
SignalFormat
NTSC (composite color)
SoundSampling
SamplingRate
44.1 kHz
BitsPerSample
16-bit
WordSize
3-byte
VideoSampling
SamplingSize
4:2:2
WordSize
3-byte
BitsPerSample
24-bit
SoundPresent
yes
Sound
Channels
NumberOfChannels
2
SoundField
stereo
FormatColors
Color
Note
Uncompressed video. Video codec name: full frame uncompressed. Video codec quality: code regenerating. Sound sampling rate 44.1 kHz; bits per sample, 16-bit, word size, 3-byte.
MimeType
(TYPE = file)
application/pdf
MimeType
(TYPE = container)
application/x-tar
FileSize
(UNIT = bytes)
2147483647
Checksum
(METHOD = SHA1)
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MimeType
(TYPE = container)
application/x-tar
FileSize
(UNIT = bytes)
133120
Checksum
(METHOD = SHA1)
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Statistical Profile