A HIERARCHICAL ORDERING OF AREA SKILLS BASED ON RULES, REPRESENTATIONS, AND SHAPES

Persistent Link:
http://hdl.handle.net/10150/187800
Title:
A HIERARCHICAL ORDERING OF AREA SKILLS BASED ON RULES, REPRESENTATIONS, AND SHAPES
Author:
Schnaps, Adam
Issue Date:
1984
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:
A hierarchy of skills in the measurement topic of area was validated on three-hundred and six students between grades six and nine. The hierarchy of skills was based on the rules underlying the individual skills. When a rule for one skill was considered a component of a rule for another skill, then the two skills were hypothesized to be hierarchically ordered. In addition, if a simple rule for a particular skill was replaced by a more complex rule, resulting in a different skill, then these two skills were hypothesized to be hierarchically ordered. The physical representations of the area tasks, as well as the shapes of the area figures were hypothesized as influencing the skill orderings. The use of Latent-class analysis revealed that seven of the nine skill orderings analyzed were hierarchically ordered based on difficulty level and not prerequisiteness. The other two skill orderings indicated equaprobable partial mastery classes. In addition to Latent-class analysis, the incorrect processes used by the students were coded and tabulated. The results revealed that (1) nonstandard shaped area problems were the most difficult for this sample, (2) the most frequent process associated with incorrect responses involved the addition of numbers shown in area problem figures, (3) the second most frequent process involved some form of multiplication, without regard to the area concepts inherent in the task, and (4) students beyond the sixth grade made more errors involving multiplication processes than errors involving addition processes. The study revealed that the use of rules, representations and shapes as the basis for a hierarchy does appear to have merit. In addition, process analysis revealed that students respond in a large variety of ways when they do not know the correct process for area tasks.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics -- Study and teaching (Elementary); Problem solving in children.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Educational Psychology; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Bergan, John R.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleA HIERARCHICAL ORDERING OF AREA SKILLS BASED ON RULES, REPRESENTATIONS, AND SHAPESen_US
dc.creatorSchnaps, Adamen_US
dc.contributor.authorSchnaps, Adamen_US
dc.date.issued1984en_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.abstractA hierarchy of skills in the measurement topic of area was validated on three-hundred and six students between grades six and nine. The hierarchy of skills was based on the rules underlying the individual skills. When a rule for one skill was considered a component of a rule for another skill, then the two skills were hypothesized to be hierarchically ordered. In addition, if a simple rule for a particular skill was replaced by a more complex rule, resulting in a different skill, then these two skills were hypothesized to be hierarchically ordered. The physical representations of the area tasks, as well as the shapes of the area figures were hypothesized as influencing the skill orderings. The use of Latent-class analysis revealed that seven of the nine skill orderings analyzed were hierarchically ordered based on difficulty level and not prerequisiteness. The other two skill orderings indicated equaprobable partial mastery classes. In addition to Latent-class analysis, the incorrect processes used by the students were coded and tabulated. The results revealed that (1) nonstandard shaped area problems were the most difficult for this sample, (2) the most frequent process associated with incorrect responses involved the addition of numbers shown in area problem figures, (3) the second most frequent process involved some form of multiplication, without regard to the area concepts inherent in the task, and (4) students beyond the sixth grade made more errors involving multiplication processes than errors involving addition processes. The study revealed that the use of rules, representations and shapes as the basis for a hierarchy does appear to have merit. In addition, process analysis revealed that students respond in a large variety of ways when they do not know the correct process for area tasks.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics -- Study and teaching (Elementary)en_US
dc.subjectProblem solving in children.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineEducational Psychologyen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorBergan, John R.en_US
dc.contributor.committeememberMiller, Anne J.en_US
dc.contributor.committeememberMishra, Shitala P.en_US
dc.contributor.committeememberAleamoni, Lawrence M.en_US
dc.contributor.committeememberRosser, Rosemary A.en_US
dc.identifier.proquest8500473en_US
dc.identifier.oclc693269303en_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.