Staff View
Building large models to show equivalence, a generalization, Clip 3 of 3: Generating multiple models by doubling

Descriptive

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MovingImage
Genre (authority = RURes_Genre)
Research data
Genre (authority = RURes_dataGenre)
Observational data
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Edited data
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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 (large group)
Subject
Name (authority = RBDIL_corporate)
NamePart (type = corporate)
Conover Road (Colts Neck, N.J.)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
Alan (student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
Andrew (student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
Brian F. (Colts Neck, student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
Danielle (student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
David (student)
Subject
Name (authority = RBDIL_personal)
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Erik (student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
James (student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
Jessica (student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
Kimberly (student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
Meredith (student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
Michael (Colts Neck, student)
Subject (authority = RURes_subjectOfStudy)
Topic
Sample of human subjects
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 = Grade range)
Topic
3-5
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
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Topic
Connections
Subject (authority = NCTM Process)
Topic
Representation
Subject (authority = rbdil_gradeLevel)
Topic
4
Subject (authority = rbdil_mathStrand)
Topic
Fractions
Subject (authority = rbdil_setting)
Topic
Classroom
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Topic
Public school
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Mixed
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White
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Classroom view
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Presentation view
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Side view
Subject (authority = LCSH)
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Manipulatives (Education)--Case studies
Subject (authority = rbdil_topic)
Topic
Operations with fractions
Subject (authority = rbdil_mathTools)
Topic
Cuisenaire rods
Subject (authority = rbdil_mathProblem)
Topic
Fraction as number
Subject (authority = rbdil_mathProblem)
Topic
Comparing fractions
Subject (authority = rbdil_mathProblem)
Topic
Equivalent fractions
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
Reasoning by upper and lower bounds
Subject (authority = rbdil_representations)
Topic
Physical models
Subject (authority = rbdil_district)
Geographic
Colts Neck Township Schools
Subject
HierarchicalGeographic
Country
UNITED STATES
State
New Jersey
County
Monmouth County
City
Colts Neck (N.J. : Township)
Classification (authority = RUresearch); (edition = Data)
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. (1993). Building large models to show equivalence, a generalization, Clip 3 of 3: Generating multiple models by doubling [video]. Retrieved from
Name (type = personal)
NamePart (type = family)
Maher
NamePart (type = given)
Carolyn Alexander
Role
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Researcher
Affiliation
Rutgers, the State University of New Jersey
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Place
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New Brunswick, NJ
Publisher
Robert B. Davis Institute for Learning
CopyrightDate (encoding = w3cdtf); (qualifier = exact)
1993-10-11
RelatedItem (type = is referenced by)
TitleInfo
Title
The development of mathematical reasoning in elementary school students' exploration of fraction ideas / by Dina Yankelewitz
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http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000054787
RelatedItem (type = is referenced by)
TitleInfo
Title
A study of fourth-grade students' explorations into comparing fractions / by Suzanne Loveridge Reynolds
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QA.R465 2005
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TitleInfo
Title
A94, Building large models to show equivalence, a generalization (classroom view), Grade 4, October 11, 1993, raw footage.
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A94-19931011-CNCR-CV-CLASS-GR4-FRC-CMPRF-RAW
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Title
A95, Building large models to show equivalence, a generalization (presentation view), Grade 4, October 11, 1993, raw footage.
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A95-19931011-CNCR-PV-CLASS-GR4-FRC-CMPRF-RAW
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TitleInfo
Title
A96, Building large models to show equivalence, a generalization (side view), Grade 4, October 11, 1993, raw footage.
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A96-19931011-CNCR-SIV-CLASS-GR4-FRC-CMPRF-RAW
Extension
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Related publication
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Ed.D. dissertation references the video footage that includes Building large models to show equivalence, a generalization, Clip 3 of 3: Generating multiple models by doubling
Place
Rutgers, the State University of New Jersey, New Brunswick, NJ
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Author
Name
Yankelewitz, Dina
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Rutgers, the State University of New Jersey
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References
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The development of mathematical reasoning in elementary school students' exploration of fraction ideas
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000054787
Reference
http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000054787
Detail
Dissertation available in digital format in the Rutgers University Libraries' dissertation collection.
DateTime (encoding = w3cdtf); (qualifier = exact)
2009
Extension
DescriptiveEvent
Type
Related publication
Label
Ed.D. dissertation references the video footage that includes Building large models to show equivalence, a generalization, Clip 3 of 3: Generating multiple models by doubling
Place
Rutgers, the State University of New Jersey, New Brunswick, NJ
DateTime (encoding = w3cdtf); (qualifier = exact)
2008
AssociatedEntity
Role
Author
Name
Reynolds, Suzanne Loveridge
Affiliation
Rutgers, the State University of New Jersey
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Type
Dissertation
Relationship
References
Name
A study of fourth-grade students' explorations into comparing fractions
Identifier (type = lccn)
QA.R465 2005
Reference (type = physical)
QA.R465 2005
Detail
Dissertation is available in paper format in the Rutgers University Libraries' dissertation collection.
Identifier (type = rbdil)
A94A95A96-FRC-CMPRF-CLIP003
Abstract (type = summary)
In the third clip researcher Carolyn Maher asked David to share the theory that he had formulated with the class. David, with some assistance from Erik, said that Meredith had originally built a model using a train of one orange, one blue, and one black rod as one, and that the white rod was one twenty-fourth and the red rod was one twelfth. As David spoke, researcher Maher built the model that he had described at the overhead projector. The students then saw a discrepancy in David’s model, and Alan and Erik showed the contradiction in David’s model. Alan and Erik stated that the reds couldn’t be twelfths and the whites couldn’t be twenty-fourths. The researcher asked Andrew and Jessica to share the model that they had built with the class. Referring to the twenty-four centimeter-long model that he had replicated on his desk Andrew explained the model to the class. The researcher asked Andrew if one brown was called one third. Andrew and Jessica clarified that he had considered two brown rods placed end to end to be one third. The researcher asked Andrew and Jessica to build the model using large Cuisenaire rods at the front of the room. They did so, and repeated their justification for their solution three times to different groups of students. The researcher asked David if Andrew and Jessica’s model was linked in any way to the theory that he had tested. David and Erik responded that it did, since they had thought that the white rods would be forty-eighths and that the red rods would be twenty-fourths, just as Andrew’s model had shown. Alan and Erik then noted that there was a relationship between the two larger models that had been built and that everything was basically doubled. The researcher continued Alan’s direct train of thought by describing the models that had been built, saying that one model contained an orange and red train and the other a train of two orange rods and a purple rod. She asked the class if the models were related in any way. Alan repeated that it was basically just doubled. The researcher pointed out that the first model (composed of the orange and red train) that James had built did not contain any purple rods. Alan responded in a manner that indicated that he had misunderstood the question that the researcher had posed. James then explained why the smallest model that had been built did not contain a purple rod. James showed that Alan’s pattern could be used to show that the second model was twice the length of the first. Alan then continued his original train of thought, explaining again that the third model was twice the length of the second. The researcher then repeated her question. She asked how the second model was double the length of the first and Kimberly explained :“Well, they used a purple and the red, two reds make a purple, so now if they have a purple, they doubled the red”. The researcher asked the class to predict what the third model should look like if there indeed was a doubling pattern inherent in the models. Danielle stated that the train would be composed of four orange rods and two purple rods, and Erik and Alan confirmed that that was the case. The researcher continued to question the students about this pattern. She asked them to predict what the next model would look like. Brian said that the length of the train would equal forty-eight white rods. The researcher pointed out that the third model that had been built was that length. Brian conceded that he was mistaken. Andrew predicted the length of the next model, saying that the train would be composed of eight orange and two brown rods. Alan challenged Andrew’s reasoning by using an argument he had used in previous sessions (that you can’t third it). Erik said that one could third it by using a train. Andrew predicted that the thirds would be three brown rods and that the fourths would be three dark greens. David repeated Erik’s argument, saying that thirds could be made using trains of rods. Alan then concluded by saying he meant you couldn’t third it by using only one rod
The researcher asked if a model could be built that was bigger than the one Andrew had described. Erik described what it would like if it was doubled. With that, The researcher closed the session, and asked the students to think and write about the question: Is there a biggest model?
TitleInfo
Title
Building large models to show equivalence, a generalization, Clip 3 of 3: Generating multiple models by doubling
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http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000067470
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Robert B. Davis Institute for Learning Mathematics Education Collection
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Identifier (type = doi)
doi:10.7282/T3FB51J2
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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.
RightsEvent
Type
Permission or license
Label
Non-exclusive license to share the video presentation via RUcore.
Place
New Brunswick, NJ
DateTime
11/3/2009
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
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
732-932-8848
Address
Rutgers Graduate School of Education
10 Seminary Place
New Brunswick, NJ 08901-1183
ContactInformationDate
2009-11-03
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Source

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1/2-inch
Duration
00:17:53
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