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Early algebra, investigating linear functions, series 6 of 7, Museum problem, Clip 6 of 6: James summarizes and compares the Museum and Ladder problems
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Research data
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Observational data
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Longitudinal data
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School
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Qualitative research
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Educational interventions (small group)
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Frank J. Hubbard Middle School (Plainfield, N.J.)
Subject
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NamePart
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James T. (student)
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Sample of human subjects
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Mathematics education
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Learning, Psychology of--Case studies
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Critical thinking in children--New Jersey--Case studies
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6-8
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Algebra
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Problem solving
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Reasoning and proof
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Communication
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Connections
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Representation
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7
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Algebra
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Informal learning
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Public school
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Male
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Black
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Student view
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Manipulatives (Education)--Case studies
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Cuisenaire rods
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Color markers
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Direct reasoning
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Multiplicative reasoning
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Generalizing
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Mathematical expressions
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Linear equations
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Museum problem
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Geographic
Plainfield Public Schools
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HierarchicalGeographic
Country
UNITED STATES
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New Jersey
County
Union County
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Plainfield (N.J.)
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1
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Social science
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Mathematics education
Note
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Transcript and student work are also available.
Note
(type = APA citation)
Robert B. Davis Institute for Learning. (2005). Early algebra, investigating linear functions, series 6 of 7, Museum problem, Clip 6 of 6: James summarizes and compares the Museum and Ladder problems [video]. Retrieved from
Name
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Francisco
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John M.
Affiliation
University of Massachusetts at Amherst
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Researcher
Name
(type = personal)
NamePart
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Hähkiöniemi
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Markus
Affiliation
University of Jyväskylä
Role
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(type = text);
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Researcher
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New Brunswick, NJ
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Robert B. Davis Institute for Learning
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2005-12-15
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2005-12-15
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TitleInfo
Title
Urban, seventh-grade students building early algegra ideas in an informal after school program / by Prashant V. Baldev
Identifier
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QA.B175 2009
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TitleInfo
Title
B19, Early algebra, investigating linear functions, series 6 of 7, Museum problem (student view), Grade 7, December 15, 2005, raw footage.
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B19-20051215-PFLD-SV-IFML-GR7-ALG-VAR-RAW
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Title
B20, Early algebra, investigating linear functions, series 6 of 7, Museum problem (student view), Grade 7, December 15, 2005, raw footage.
Identifier
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B20-20051215-PFLD-SV-IFML-GR7-ALG-VAR-RAW
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DescriptiveEvent
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Related publication
Label
Ed.D. dissertation references the video footage that includes Early algebra, investigating linear functions, series 6 of 7, Museum problem, Clip 6 of 6: James summarizes and compares the Museum and Ladder problems
Place
Rutgers, the State University of New Jersey, New Brunswick, NJ
DateTime
(encoding = w3cdtf);
(qualifier = exact)
2009
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Author
Name
Baldev, Prashant V.
Affiliation
Rutgers, the State University of New Jersey
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Dissertation
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References
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Urban, seventh-grade students building early algegra ideas in an informal after school program
Identifier
(type = lccn)
QA.B175 2009
Reference
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QA.B175 2009
Detail
Dissertation is available in paper format in the Rutgers University Libraries' dissertation collection.
Identifier
(type = rbdil)
B19B20-ALG-VAR-CLIP006
Abstract
(type = summary)
In the last of six clips from an after-school enrichment session in an urban middle school,
James, a 7th grade boy completing a unit about linear functions, is asked by researcher Markus Hahkioniemi to summarize his solutions to the Museum and Ladder problems and to explain the meaning of the numbers 2 and 3 in the solutions for each problem. Researcher John Francisco joins the pair and asks James to repeat his summary and whether he thinks there is any connection between the two problems. James responds that, in each case, the procedure for finding the solution involves mutliplying by 3 and adding 2 even though the numbers represent different things in the two contexts.
The worksheet wording for the Museum Problem:
The Museum Problem - Version One
A museum gift shop is having a craft sale. The entrance fee is $2. Once inside, there is
a special discount table where each craft piece costs $3.
How could you represent the total amount that you would spend if you were to buy any number of craft pieces at the discount price?
The worksheet wording for the Ladder Problem:
A company makes ladders of different heights, from very short ones to very tall ones. The shortest ladder has only one rung, and looks like this (we could build a model of it with 5 light green Cuisenaire rods.) A two-rung ladder could be modeled using 8 light green rods, and looks like this. How could you represent the number of rods needed if you were to build a ladder with any number of rungs?
The questions as posed to James:
Describe again how you solved each problem.
For the Ladder Problem, what does the 3 represent? What does the 2 represent?
For the Museum Problem, what does each number represent?
Is there a connection between the two problems? If so - what is that connection?
James, a 7th grade boy completing a unit about linear functions, is asked by researcher Markus Hahkioniemi to summarize his solutions to the Museum and Ladder problems and to explain the meaning of the numbers 2 and 3 in the solutions for each problem. Researcher John Francisco joins the pair and asks James to repeat his summary and whether he thinks there is any connection between the two problems. James responds that, in each case, the procedure for finding the solution involves mutliplying by 3 and adding 2 even though the numbers represent different things in the two contexts.
The worksheet wording for the Museum Problem:
The Museum Problem - Version One
A museum gift shop is having a craft sale. The entrance fee is $2. Once inside, there is
a special discount table where each craft piece costs $3.
How could you represent the total amount that you would spend if you were to buy any number of craft pieces at the discount price?
The worksheet wording for the Ladder Problem:
A company makes ladders of different heights, from very short ones to very tall ones. The shortest ladder has only one rung, and looks like this (we could build a model of it with 5 light green Cuisenaire rods.) A two-rung ladder could be modeled using 8 light green rods, and looks like this. How could you represent the number of rods needed if you were to build a ladder with any number of rungs?
The questions as posed to James:
Describe again how you solved each problem.
For the Ladder Problem, what does the 3 represent? What does the 2 represent?
For the Museum Problem, what does each number represent?
Is there a connection between the two problems? If so - what is that connection?
TitleInfo
Title
Early algebra, investigating linear functions, series 6 of 7, Museum problem, Clip 6 of 6: James summarizes and compares the Museum and Ladder problems
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Robert B. Davis Institute for Learning Mathematics Education Collection
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Identifier
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doi:10.7282/T3CZ3545
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Rights
RightsDeclaration
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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.
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
10 Seminary Place
New Brunswick, NJ 08901-1183
ContactInformationDate
2009-11-03
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1/2-inch
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