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Early algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 5 of 7: Ariel revisits his solution for the 120 step ladder

Descriptive

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Research data
Genre (authority = RURes_dataGenre)
Observational data
Genre (authority = RURes_dataLifecycle)
Repurposed data
Genre (authority = RURes_qualitativeMethod)
Educational interventions (small group)
Genre (authority = RURes_researchDataType)
Longitudinal data
Genre (authority = RURes_researchMethodology)
Qualitative research
Genre (authority = RURes_dataCollectionSetting)
School
Genre (authority = RURes_dataLifecycle)
Edited data
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
Ariel (student)
Subject
Name (authority = RBDIL_personal)
NamePart (type = personal)
James T. (student)
Subject
Name (authority = RBDIL_corporate)
NamePart (type = corporate)
Frank J. Hubbard Middle School (Plainfield, N.J.)
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B17B18-ALG-VAR-CLIP005
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
Communication
Subject (authority = NCTM Process)
Topic
Connections
Subject (authority = NCTM Process)
Topic
Representation
Subject (authority = Grade range)
Topic
6-8
Subject (authority = LCSH)
Topic
Mathematics education
Subject (authority = LCSH)
Topic
Critical thinking in children--New Jersey--Case studies
Subject (authority = LCSH)
Topic
Learning, Psychology of--Case studies
Subject (authority = LCSH)
Topic
Manipulatives (Education)--Case studies
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Topic
Work view
Subject (authority = rbdil_cameraView)
Topic
Student view
Subject (authority = rbdil_mathStrand)
Topic
Algebra
Subject (authority = rbdil_mathProblem)
Topic
Ladder problem
Subject (authority = rbdil_mathTools)
Topic
Cuisenaire rods
Subject (authority = rbdil_mathTools)
Topic
Color markers
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
Considering a simpler problem
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Recursive reasoning
Subject (authority = rbdil_representations)
Topic
Physical models
Subject (authority = rbdil_representations)
Topic
Mathematical expressions
Subject (authority = rbdil_studentGender)
Topic
Male
Subject (authority = rbdil_studentEthnicity)
Topic
Mixed
Subject (authority = rbdil_schoolType)
Topic
Public school
Subject (authority = RURes_subjectOfStudy)
Topic
Sample of human subjects
Subject (authority = rbdil_gradeLevel)
Topic
7
Subject (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Proportional reasoning
Subject
HierarchicalGeographic
Country
UNITED STATES
State
New Jersey
County
Union County
City
Plainfield (N.J.)
TargetAudience (authority = RURes_discipline)
Social science
TargetAudience (authority = RURes_domain)
Mathematics education
Note (type = supplementary materials)
Transcript and student work are also available.
Note (type = APA citation)
Robert B. Davis Institute for Learning. (2005). Early algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 5 of 7: Ariel revisits his solution for the 120 step ladder [video]. Retrieved from
Name (type = personal)
NamePart (type = family)
Francisco
NamePart (type = given)
John
Role
RoleTerm (authority = marcrelator); (type = text)
Researcher
Affiliation
Rutgers, the State University of New Jersey
Name (type = personal)
NamePart (type = family)
Baldev
NamePart (type = given)
Prashant V.
Role
RoleTerm (authority = marcrelator); (type = text)
Researcher
Affiliation
Rutgers, the State University of New Jersey
Name (type = personal)
NamePart (type = family)
Hahkioniemi
NamePart (type = given)
Markus
Affiliation
Rutgers, the State University of New Jersey
Role
RoleTerm (authority = marcrelator); (type = text)
Researcher
Subject (authority = rbdil_district)
Geographic
Plainfield Public Schools
Classification (authority = RUresearch); (edition = Data)
Abstract (type = summary)
In the fifth of seven clips from an after-school enrichment session in an urban middle school, Ariel, a 7th grade boy, continues his work on the Ladder Problem. Researcher John Francisco challenges Ariel to reexamine his solution for a ladder with 120 steps by comparing it with the procedure that he had written down as a general rule for finding the number of rods for ladders with even numbers of steps. The procedure that Ariel had articulated and followed for relatively small numbers had the following steps: (1) divide the number by two; (2) build a ladder with that number of steps with actual rods; (3) count the rods; then (4) double that number and subtract two from the product. Ariel insists that he is following his rule and explains that he divides 120 by 2 to find 60. He then refers to his earlier count of 20 for a ladder with 6 steps and multiplies that by 10 to get 200 for 60 steps. Ariel then refers to his rule and subtracts 2, for a result of 198. To find the number of rods for 120 steps, Ariel doubles 198, subtracts another 2, and insists that the result of 394 is the correct number. Despite the researcher' s attempts to get Ariel to follow his written procedure more closely, including an appeal to James, who briefly looks over Ariel's written solution, Ariel did not waver from this answer. Researcher Markus Hahkioniemi is interacting with James and researcher Prashant Baldev is observing.
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. Build a rod model to represent a 3-rung ladder.
How many rods did you use? 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 Ariel and James:
Compare your solution for a ladder with 120 steps with your rule.
Are you following the steps that you outlined?
Explain how you used your rule to find your solution.
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B17, Early algebra, investigating linear functions, Series 5 of 7, Ladder problem (student view), Grade 7, December 15, 2005, raw footage
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B18, Early algebra, investigating linear functions, Series 5 of 7, Ladder problem (student view), Grade 7, December 15, 2005, raw footage
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TitleInfo
Title
Urban, seventh-grade students building early algebra ideas in an informal after school program / by Prashant V. Baldev.
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QA.B175 2009
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New Brunswick, N.J.
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Robert B. Davis Institute for Learning
CopyrightDate
2005-12-15
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DescriptiveEvent
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Related publication
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Ed.D. dissertation references the video footage that includes Early algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 5 of 7: Ariel revisits his solution for the 120 step ladder.
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Rutgers, the State University of New Jersey, New Brunswick, NJ
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2009
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Baldev, Prashant V.
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Rutgers, the State University of New Jersey
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Urban, seventh-grade students building early algebra ideas in an informal after school program
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QA.B175 2009
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QA.B175 2009
Detail
Dissertation is available in paper format in the Rutgers University Libraries' dissertation collection
TitleInfo
Title
Early algebra, investigating linear functions, series 5 of 7, ladder problem, Clip 5 of 7: Ariel revisits his solution for the 120 step ladder
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doi:10.7282/T31Z434M
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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
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
2013-02-11
RightsEvent
Type
Permission or license
Label
Non-exclusive license to share the video presentation via RUcore
Place
New Brunswick, NJ
DateTime (qualifier = exact)
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
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Duration
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