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Taxicab problem, clip 2 of 5: investigating the number of shortest paths.

Descriptive

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MovingImage
TitleInfo (ID = T-1)
Title
Taxicab problem, clip 2 of 5: investigating the number of shortest paths.
Identifier (type = local)
A02A26-GMY-TAXI-CLIP002
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000054818
Language
LanguageTerm (authority = ISO 639-3:2007)
English
Genre (authority = RURes_RUResearchGenre)
Research data
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Action research
Genre (authority = RURes_DataTypeOrMethodology)
Direct observation
Genre (authority = RURes_DataTypeOrMethodology)
Educational interventions (small group)
Genre (authority = RURes_DataTypeOrMethodology)
Field research
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Longitudinal data
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Continuous monitoring
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Defined population
Subject (ID = SBJ-1)
Name (authority = RBDIL_personal)
NamePart (type = personal)
Brian (Kenilworth, student)
Subject (ID = SBJ-2)
Name (authority = RBDIL_personal)
NamePart (type = personal)
Romina (student)
Subject (ID = SBJ-3)
Name (authority = RBDIL_personal)
NamePart (type = personal)
Jeff (student)
Subject (ID = SBJ-4)
Name (authority = RBDIL_personal)
NamePart (type = personal)
Michael A. (Kenilworth, student)
Subject (ID = SBJ-5)
Name (authority = RBDIL_corporate)
NamePart (type = corporate)
David Brearley High School (Kenilworth, N.J.)
Subject (ID = SBJ-6); (authority = lcsh)
Topic
Mathematics education
Subject (ID = SBJ-7); (authority = lcsh)
Topic
Critical thinking in children--New Jersey--Case studies
Subject (ID = SBJ-8); (authority = Grade range)
Topic
9-12
Subject (ID = SBJ-9); (authority = NCTM Content)
Topic
Algebra
Subject (ID = SBJ-209876543210); (authority = NCTM Content)
Topic
Data analysis and probability
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Topic
Geometry
Subject (ID = SBJ-22); (authority = NCTM Content)
Topic
Number and operations
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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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Counting
Subject (ID = SBJ-29); (authority = rbdil_mathStrand)
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Combinatorics
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Topic
Taxicab
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Topic
Color markers
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Graph paper
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Direct reasoning
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Representations
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Charts
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Topic
Organized lists
Subject (ID = SBJ-37); (authority = rbdil_topic)
Topic
Path diagrams
Subject (ID = SBJ-1); (authority = rbdil_topic)
Topic
Pascal's triangle
Subject (ID = SBJ-1); (authority = rbdil_gradeLevel)
Topic
12
Subject (ID = SBJ-1); (authority = rbdil_setting)
Topic
Informal learning
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Side view
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Work view
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Mixed
Subject (ID = SBJ-1); (authority = rbdil_studentEthnicity)
Topic
Mixed
Subject (ID = SBJ-1); (authority = rbdil_forms of reasoning, strategies and heuristics)
Topic
Considering a simpler problem
Subject (ID = SBJ-1); (authority = rbdil_district)
Geographic
Kenilworth Public Schools
Subject (ID = SBJ-1)
HierarchicalGeographic
Country
UNITED STATES
State
New Jersey
County
Union County
City
Kenilworth (N.J.)
Abstract (type = summary)
In the second of five clips, the four twelfth grade students employ various strategies to determine the number of shortest paths to the remaining two points, B and C, on the problem grid. Various patterns, invented notations, and color-coded diagrams are shared in an attempt to find a solution for the problem. As they calculate total numbers of routes for successively larger areas of the grid, the students conjecture about a possible relationship to the Towers Problem . When Romina calculates the numbers of shortest routes for the points where each shortest route has length 5, she makes the conjecture that the problem follows the pattern of Pascal's Triangle.

PROBLEM STATEMENT: The problem was presented to the students with an accompanying representation on a single (fourth) quadrant of a coordinate grid of squares with the “taxi stand” located at (0,0) and the three “pick-up” points A (blue), B(red) and C(green) at (1,-4), (4,-3) and (5,-5) respectively, implying that movement could only occur horizontally or vertically toward a point. The problem states that: A taxi driver is given a specific territory of a town, as represented by the grid. All trips originate at the taxi stand. One very slow night, the driver is dispatched only three times; each time, she picks up passengers at one of the intersections indicated on the map. To pass the time, she considers all the possible routes she could have taken to each pick-up point and wonders if she could have chosen a shorter route. What is the shortest route from the taxi stand to each point? How do you know it is the shortest? Is there more than one shortest route to each point? If not, why not? If so, how many? Justify your answers.
PhysicalDescription
Extent (unit = digital file(s))
1
InternetMediaType
video/quicktime
InternetMediaType
video/x-flv
TargetAudience (authority = Domain)
Education
Note (type = supplementary materials)
Transcript is also available.
Note (type = APA citation)
Robert B. Davis Institute for Learning. (2000). Taxicab problem, clip 2 of 5: investigating the number of shortest paths. [video]. Retrieved from http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000054818
Note (type = available formats)
Available in QuickTime streaming and downloadable Flash digital video files.
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NamePart (type = family)
Kiczek
NamePart (type = given)
Regina
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Researcher
OriginInfo
Place
PlaceTerm (type = text)
New Brunswick, NJ
Publisher
Robert B. Davis Institute for learning
CopyrightDate
2000-05-05
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NjNbRU
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Title
A02, Taxicab problem, full session, grade 12, May 5, 2000, raw footage
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A26,Taxicab problem: full session, grade 12, May 5, 2000, raw footage
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TitleInfo
Title
So let's prove it!: emergent and elaborated mathematical ideas and reasoning in the discourse and inscriptions of learners engaged in a combinatorial task / by Arthur B. Powell.
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http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000054821
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Robert B. Davis Institute for Learning Mathematics Education Collection
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rucore00000001201
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Type
Dissertation
Label
Ph.D. dissertation references the video footage that includes Taxicab problem, clip 2 of 5.
Place
New Brunswick, NJ
Detail
Dissertation available in digital and paper formats in the Rutgers University Libraries dissertation collection.
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Author
Name
Powell, Arthur B.
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QA 22 2009
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Rutgers Graduate School of Education
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References
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So let's prove it!: emergent and elaborated mathematical ideas and reasoning in the discourse and inscriptons of learners engaged in a combinatorial task .
Identifier (type = global)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000054821
Detail
Dissertation available in digital and paper formats in the Rutgers University Libraries dissertation collection.
Identifier (type = doi)
doi:10.7282/T3FJ2GNQ
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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
Unpublished
RightsHolder (ID = CRH-1); (type = corporate)
Name
Robert B. Davis Institute for Learning
Role
Copyright holder
Telephone
732-932-7496, ext. 8262
Address
Rutgers Graduate School of Education
10 Seminary Place
New Brunswick, NJ 08901-1183
ContactInformationDate
2009-11-03
RightsEvent (ID = RE-1); (AUTHORITY = rulib)
Type
Permission or license
Label
Non-exclusive license to share the video presentation via RUcore.
Place
New Brunswick, NJ
DateTime
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 (ID = AE-1); (AUTHORITY = rulib)
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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