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Taxicab Problem, Clip 4 of 5: Explaining the Taxicab and Towers Isomorphism

Descriptive

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Title
Taxicab Problem, Clip 4 of 5: Explaining the Taxicab and Towers Isomorphism
Identifier (type = local)
A02A26-GMY-TAXI-CLIP004
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http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000054853
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English
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Research data
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Action research
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Direct observation
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Educational interventions (small group)
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Field research
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Longitudinal data
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Continuous monitoring
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David Brearley High School (Kenilworth, N.J.)
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Brian (Kenilworth, student)
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Romina (student)
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Jeff (student)
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Michael A. (Kenilworth, student)
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Mathematics education
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9-12
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Counting
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Taxicab
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Color markers
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Informal learning
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12
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Recognizing an isomorphism
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Critical thinking in children--New Jersey--Case studies
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Algebra
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Geometry
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Pascal's triangle
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Kenilworth Public Schools
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UNITED STATES
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New Jersey
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Union County
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Kenilworth (N.J.)
Abstract (type = summary)
In the fourth of five clips, the four twelfth grade students explain their conjecture that Pascal's Triangle can be used to predict the number of paths to any point in the Taxicab grid to Carolyn Maher, the researcher. Romina relates the building of Unifix Towers, when selecting from two colors, to the moves on the Taxi grid, which can be in either a horizontal or a vertical direction, and demonstrates that in each case there is a correspondence to the addition rule 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.
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Note (type = supplementary materials)
Transcript is also available.
Note (type = APA citation)
Robert B. Davis Institute for Learning. (2000). Taxicab Problem, Clip 4 of 5: Explaining the Taxicab and Towers Isomorphism. [video]. Retrieved fromhttp://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000054853
Note (type = available formats)
Available in QuickTime streaming and downloadable Flash digital video files.
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Maher
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Carolyn Alexander
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Rutgers, the State University of New Jersey
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New Brunswick, NJ
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Robert B. Davis Institute for learning
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2000-05-05
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A02, 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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Ph.D. dissertation references the video footage that includes Taxicab problem, clip 4 of 5.
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New Brunswick, NJ
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Dissertation available in digital and paper formats in the Rutgers University Libraries dissertation collection.
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So let's prove it!: emergent and elaborated mathematical ideas and reasoning in the discourse and inscriptions of learners engaged in a combinatorial task
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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/T3Q2402Q
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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
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Permission or license
Publication
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Robert B. Davis Institute for Learning
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732-932-7496, ext. 8262
Address
Rutgers Graduate School of Education
10 Seminary Place
New Brunswick, NJ 08901-1183
ContactInformationDate
2009-11-03
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Non-exclusive license to share the video presentation via RUcore.
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New Brunswick, NJ
DateTime
2009-11-03
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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.
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Role
Licensor
Name
Maher, Carolyn A.
Affiliation
Director, Robert B. Davis Institute for Learning, Rutgers Graduate School of Education
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