Staff View
From Taxicabs to Towers: An Analysis of Problem-Solving Strategies

Descriptive

TypeOfResource
Text
TitleInfo (id = T-1)
Title
From Taxicabs to Towers: An Analysis of Problem-Solving Strategies
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/Analytic.an.i.45
Abstract
Problem solving is a cornerstone to the mathematical learning experience that makes possible students' application of creative strategies and logical reasoning while working to complete particular tasks. This analytic is a detailed overview of various problem-solving strategies employed by four twelfth-grade students - Brian, Jeff, Michael, and Romina - when solving the Taxicab Problem, a challenging mathematical task involving combinatorial reasoning and ideas from coordinate geometry. Each clip presents a different focus and its respective contribution to the high school students' Taxicab Problem solution. Among these highlighted problem-solving tactics are peer discussion, solving a simpler problem, pattern discovery, drawing a diagram as a representation, and building isomorphisms. The analytic was developed as an interactive instructional tool not only for K-12 teachers who may wish to integrate a problem solving unit, but also for mathematics teacher educators as a starting point to begin discussing methods to develop insightful problem-solving experiences in the classroom. Classroom teachers and teacher education students can use the Questions to Consider at the end of each video clip to reflect on the effectiveness and significance of the showcased strategies used by the students in solving the Taxicab Problem.

Taxicab 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.

References

Dienes, Z.D. (2002). Zoltan Dienes' six-stage theory of learning mathematics. In Some Thoughts on Mathematics. Retrieved from http://www.zoltandienes.com/?page_id=226

Greer, B. & Harel, G. (1998). The role of isomorphisms in mathematical cognition. Journal of Mathematics Behavior. 17(1), 5-24.

Powell, A. B. (2003). "So let's prove it!": Emergent and elaborated mathematical ideas and reasoning in the discourse and inscriptions of learners engaged in a combinatorial task. (Doctoral dissertation). Retrieved from Rutgers University Community Repository. (UMI Number: 3092981).

Uptegrove, E.B. & Maher, C. A. (2004). Students building isomorphisms. In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education. (Vol. 4, p. 353-360). Bergen, Norway.
Genre (authority = RULIB)
Student collaboration
Genre (authority = RULIB)
Student elaboration
Genre (authority = RULIB)
Student engagement
Genre (authority = RULIB)
Student model building
Genre (authority = RULIB)
Student reasoning
Genre (authority = RULIB)
Student representation
RelatedItem (type = host)
TitleInfo
Title
RBDIL Analytics
Identifier (type = local)
rucore00000002136
Name (id = NAME-1); (type = personal)
NamePart (type = family)
Leyva
NamePart (type = given)
Luis
DisplayForm
Luis Leyva
Role
RoleTerm (authority = RULIB)
Creator
Affiliation
Rutgers University
Name (id = NAME-2); (type = personal)
NamePart (type = family)
Maher
NamePart (type = given)
Carolyn A.
DisplayForm
Carolyn A. Maher
Role
RoleTerm (authority = RULIB)
Publisher
Affiliation
Rutgers University
OriginInfo
DateOther (qualifier = exact); (type = created)
2011-08-04T19:24:02-05:00
OriginInfo
DateOther (qualifier = exact); (type = modified)
2012-05-15T10:37:53-05:00
OriginInfo
DateOther (qualifier = exact); (type = published)
2012-05-15T10:37:53-05:00
OriginInfo
DateCreated (encoding = w3cdtf); (qualifier = exact)
2012-05-15
Identifier (type = doi)
doi:10.7282/T3MS3RRQ
Back to the top

Rights

Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
Note
RightsHolder
Name (TYPE = personal); (ID = R-NAME_0001)
Luis Leyva
Role
Author
ContactInformation
ContactInformationDate
2012-05-15T10:40:13-05:00
Back to the top

Technical

ContentModel
Analytic
PreservationLevel
full
Generation
born digital source
MimeType (TYPE = file)
application/xml
FileSize (UNIT = bytes)
28009
CreatingApplication
CreatingApplicationName
RUAnalytic Tool
CreatingApplicationVersion
0.9
CreatingApplicationDateCreated
2012-05-15T10:37:53-05:00
Note
Generated using the RUanalytic tool export function.
Back to the top
Version 8.4.8
Rutgers University Libraries - Copyright ©2022