Staff View
PUP Math Romina's proof to Ankur's challenge

Descriptive

TypeOfResource
MovingImage
Identifier (type = rbdil)
PM4_RominasProof
Genre (authority = RURes_RUResearchGenre)
Research data
Genre (authority = RURes_DataTypeOrMethodology)
Action research
Genre (authority = RURes_DataTypeOrMethodology)
Direct observation
Genre (authority = RURes_DataTypeOrMethodology)
Educational interventions (small 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)
Brian (Kenilworth, student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
Romina (student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
Jeff (student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = corporate)
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
Critical thinking in children--New Jersey--Case studies
Subject (authority = Grade range)
Topic
9-12
Subject (authority = rbdil_gradeLevel)
Topic
10
Subject (authority = NCTM Content)
Topic
Number and operations
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
Ankur's challenge
Subject (authority = rbdil_mathTools)
Topic
Unifix cubes
Subject (authority = rbdil_setting)
Topic
Informal learning
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Direct reasoning
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Reasoning by cases
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Controlling for variables
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Recognizing a pattern
Subject (authority = rbdil_topic)
Topic
Drawings
Subject (authority = rbdil_topic)
Topic
Representations
Subject (authority = rbdil_topic)
Topic
Organized lists
Subject (authority = rbdil_schoolType)
Topic
Public school
Subject (authority = rbdil_studentGender)
Topic
Mixed
Subject (authority = rbdil_studentEthnicity)
Topic
Mixed
Subject (authority = rbdil_cameraView)
Topic
Student view
Subject (authority = LCSH)
Topic
Learning, Psychology of--Case studies
Subject (authority = rbdil_topic)
Topic
Combinations
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.)
Abstract (type = summary)
In this edited and narrated episode from the Private Universe Project in Mathematics, five tenth-grade students consider two different problems. FIRST PROBLEM STATEMENT: “Choosing from two colors of Unifix® cubes, red and yellow, how many total combinations exist for towers 5 tall, that each contains two red? Convince us that you have found them all.” SECOND PROBLEM STATEMENT (Ankur’s Challenge): “How many towers can you build four tall, selecting from cubes available in three different colors of Unifix® cubes, so that the resulting towers contain at least one of each color?” During the session Ankur and Michael work together at one end of the table and Jeff, Romina, and Brian work at the other end. Ankur and Michael use binary notation to solve the first problem. While waiting for Jeff, Romina, and Brian to complete the first tower problem of five-tall with a choice of two colors, Ankur poses a new question about towers four tall with a selection of three colors: “How many with at least one of each color?” Romina develops a notation that she calls “ones, zeroes, and Xs” to represent the three colors in the problem. First at the table and then at the chalkboard, Romina presents her reasoning to the others as she works to convince them that there thirty-six total towers that meet Ankur’s criteria. She shows them her representation to justify the six possible arrangements for two “1s” in the four positions of the tower. She fills the blank positions with “X0” or “0X” for the other two colors. She then explains that the resulting twelve towers would be multipied by three to account for the three different colors of cubes available.
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. (1998). PUP Math Romina's proof to Ankur's challenge [video].
Note (type = available formats)
Resource vailable in QuickTime and Flash digital video formats.
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
OriginInfo
DateCreated (encoding = w3cdtf)
1998-01-09
Place
PlaceTerm (type = text)
Cambridge, MA
Publisher
Annenberg Learner
CopyrightDate (encoding = w3cdtf)
1998-01-09
Extension
DescriptiveEvent
Type
Related publication
Label
Ed.D. dissertation references the video footage that includes PUP Math Romina's proof to Ankur's challenge
Detail
Available in electronic form in RUcore, the Rutgers Community Repository.
AssociatedObject
Type
Dissertation
Relationship
References
Name
Tracing beliefs and behaviors of a participant in a longitudinal study for the development of mathematical ideas and reasoning: a case study.
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001500001.ETD.000052894
Reference
http://hdl.rutgers.edu/1782.2/rucore10001500001.ETD.000052894
Detail
Dissertation available in digital format in the RUcore Rutgers Electronic Theses and Dissertations collection.
DateTime (encoding = w3cdtf)
2010
AssociatedEntity
Role
Author
Name
Steffero, Maria.
Affiliation
Rutgers Graduate School of Education
Place
New Brunswick, NJ
Extension
DescriptiveEvent
Type
Related publication
Label
Ed.D. dissertation references the video footage that includes PUP Math Romina's proof to Ankur's challenge
Place
New Brunswick, NJ
DateTime (encoding = w3cdtf)
1999
AssociatedEntity
Role
Author
Name
Muter, Ethel M.
Affiliation
Rutgers Graduate School of Education
AssociatedObject
Type
Dissertation
Relationship
References
Name
The development of student ideas in combinatorics and proof : a six year study
Identifier (type = lccn)
QA.M992 1999
Detail
Dissertation is available in hard copy in the Rutgers University Libraries collection.
Extension
DescriptiveEvent
Type
Related publication
Label
Workshops (web-based) utilize the video PUP Math Romina's proof to Ankur's challenge
AssociatedEntity
Role
Publisher
Name
Annenberg Learner
Reference
http://www.learner.org/about/
AssociatedEntity
Role
Creator
Name
Harvard-Smithsonian Center for Astrophysics
Identifier
http://www.cfa.harvard.edu
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
Tracing beliefs and behaviors of a participant in a longitudinal study for the development of mathematical ideas and reasoning : a case study.
Identifier (type = uri)
http://hdl.rutgers.edu/1782.2/rucore10001500001.ETD.000052894
RelatedItem (type = is referenced by)
TitleInfo
Title
The development of student ideas in combinatorics and proof : a six year study / by Ethel M. Muter.
Identifier (type = lccn)
QA.M992 1999
Name (type = corporate)
NamePart
Harvard-Smithsonian Center for Astrophysics
Role
RoleTerm (authority = marcrelator); (type = text)
Creator
TitleInfo
Title
PUP Math Romina's proof to Ankur's challenge
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000062055
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/T30P0Z85
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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
ContactInformationDate
2011-06-17
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Source

SourceTechnical
SourceType
Videotape
Duration
00:07:57
PictureQualities
Color
color
SignalFormat
NTSC (composite color)
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Technical

ContentModel
Video
Generation
Digital preservation master
PreservationLevel
full
System
MS Video
Duration
00:07:57
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)
1808711680
Checksum (METHOD = SHA1)
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MimeType (TYPE = container)
application/x-tar
FileSize (UNIT = bytes)
81920
Checksum (METHOD = SHA1)
03cbafd7c87ccd46a75889341d89aa9d94385eab
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