THE HEURISTICS UTILIZED BY FIFTH GRADE STUDENTS IN SOLVING VERBAL MATHEMATICS PROBLEMS IN A SMALL GROUP SETTING.

Persistent Link:
http://hdl.handle.net/10150/188045
Title:
THE HEURISTICS UTILIZED BY FIFTH GRADE STUDENTS IN SOLVING VERBAL MATHEMATICS PROBLEMS IN A SMALL GROUP SETTING.
Author:
DUNCAN, JAMES EDWIN.
Issue Date:
1985
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Specific to the recommendation of the National Council of Teachers of Mathematics (1980) to identify and analyze problem solving strategies and the settings in which the development of these strategies could be optimized, this study is a compilation of three case studies which describe what elementary school children say and do when solving verbal mathematics problems in small groups. Persuant to this goal, three four-member groups were selected and asked to reach a consensus within each group on the solution to a variety of routine and non-routine problems. In this relatively unstructured setting, transcriptions of verbal interactions, written records of all computations, and observer notes were compiled for each group. The resulting identification and description of the problem solving behaviors which occurred were analyzed in terms of two broad interactive functions by which children seek to understand verbal problems: the construction of mental representations or physical displays of the problems and the evaluations of these constructions. Representations, in this perspective, are constructed at two levels: a contextual level at which the problem situation is linguistically interpreted and a structural level at which a statement of a problem underlying mathematical structure is defined. Evaluations also occur which allow group members to monitor their understanding and direct the course of the problem solving effort. The findings indicate that intermediate aged children when solving problems in small groups display general patterns of behavior. These patterns of behavior include: the manner in which the groups approach and effectively isolate the contextual elements of a verbal problem, the propensity of groups to change the mode in which a problem is represented by utilizing manipulatives, diagrams, tables and other physical displays, and the manner in which groups monitor the course of problem solving and reach consensuses on solution proposals. Within this general pattern, however, specific subject and task variables characterize individual groups, affecting both the group interaction and the incidence of specific problem solving behaviors. These findings suggest practical classroom applications for group problem solving formats in the elementary school classroom. Additional research, however, must provide the link between group problem solving and individual performance.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics -- Study and teaching (Elementary); Word problems (Mathematics) -- Study and teaching (Elementary); Group problem solving -- Study and teaching (Elementary); Problem solving in children -- Study and teaching (Elementary)
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Elementary Education; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Larson, Carol

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleTHE HEURISTICS UTILIZED BY FIFTH GRADE STUDENTS IN SOLVING VERBAL MATHEMATICS PROBLEMS IN A SMALL GROUP SETTING.en_US
dc.creatorDUNCAN, JAMES EDWIN.en_US
dc.contributor.authorDUNCAN, JAMES EDWIN.en_US
dc.date.issued1985en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractSpecific to the recommendation of the National Council of Teachers of Mathematics (1980) to identify and analyze problem solving strategies and the settings in which the development of these strategies could be optimized, this study is a compilation of three case studies which describe what elementary school children say and do when solving verbal mathematics problems in small groups. Persuant to this goal, three four-member groups were selected and asked to reach a consensus within each group on the solution to a variety of routine and non-routine problems. In this relatively unstructured setting, transcriptions of verbal interactions, written records of all computations, and observer notes were compiled for each group. The resulting identification and description of the problem solving behaviors which occurred were analyzed in terms of two broad interactive functions by which children seek to understand verbal problems: the construction of mental representations or physical displays of the problems and the evaluations of these constructions. Representations, in this perspective, are constructed at two levels: a contextual level at which the problem situation is linguistically interpreted and a structural level at which a statement of a problem underlying mathematical structure is defined. Evaluations also occur which allow group members to monitor their understanding and direct the course of the problem solving effort. The findings indicate that intermediate aged children when solving problems in small groups display general patterns of behavior. These patterns of behavior include: the manner in which the groups approach and effectively isolate the contextual elements of a verbal problem, the propensity of groups to change the mode in which a problem is represented by utilizing manipulatives, diagrams, tables and other physical displays, and the manner in which groups monitor the course of problem solving and reach consensuses on solution proposals. Within this general pattern, however, specific subject and task variables characterize individual groups, affecting both the group interaction and the incidence of specific problem solving behaviors. These findings suggest practical classroom applications for group problem solving formats in the elementary school classroom. Additional research, however, must provide the link between group problem solving and individual performance.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics -- Study and teaching (Elementary)en_US
dc.subjectWord problems (Mathematics) -- Study and teaching (Elementary)en_US
dc.subjectGroup problem solving -- Study and teaching (Elementary)en_US
dc.subjectProblem solving in children -- Study and teaching (Elementary)en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineElementary Educationen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorLarson, Carolen_US
dc.contributor.committeememberBrown, Edwarden_US
dc.contributor.committeememberGoodman, Kennethen_US
dc.identifier.proquest8526310en_US
dc.identifier.oclc696632654en_US
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