M3: The Three-Mathematical Minds Model for the Identification of Mathematically Gifted Students

Persistent Link:
http://hdl.handle.net/10150/194533
Title:
M3: The Three-Mathematical Minds Model for the Identification of Mathematically Gifted Students
Author:
Sak, Ugur
Issue Date:
2005
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:
Views of giftedness have evolved from unilateral notions to multilateral conceptions. The primary purpose of this study was to investigate the psychological validity of the three-mathematical minds model (M3) developed by the author. The M3 is based on multilateral conceptions of giftedness to identify mathematically gifted students. Teachings of Poincare and Polya about mathematical ability as well as the theory of successful intelligence proposed by Sternberg (1997) provided the initial framework in the development of the M3. A secondary purpose was to examine the psychological validity of the three-level cognitive complexity model (C3) developed by the author. The C3 is based on studies about expertise to differentiate among gifted, above-average and average-below-average students at three levels.The author developed a test of mathematical ability based on the M3 and C3 with the collaboration of mathematicians. The test was administered to 291 middle school students from four different schools. The reliability analysis indicated that the M3 had a .72 coefficient as a consistency of scores. Exploratory factor analysis yielded three separate components explaining 55% of the total variance. The convergent validity analysis showed that the M3 had medium to high-medium correlations with teachers' ratings of students' mathematical ability (r = .45) and students' ratings of their own ability (r = .36) and their liking of mathematics (r = .35). Item-subtest-total score correlations ranged from low to high. Some M3 items were found to be homogenous measuring only one aspect of mathematical ability, such as creative mathematical ability, whereas some items were found to be good measures of more than one facet of mathematical ability.The C3 accounted for 41% of variance in item difficulty (R square = .408, p < .001). Item difficulty ranged from .02 to .93 with a mean of .29. The analysis of the discrimination power of the three levels of the C3 revealed that level-two and level-three problems differentiated significantly among three ability levels, but level-one problems did not differentiate between gifted and above average students. The findings provide partial evidence for the psychological validity of both the M3 and C3 for the identification of mathematically gifted students.
Type:
text; Electronic Dissertation
Keywords:
Gifted; Creative; mathematical ability; assessment; identification
Degree Name:
PhD
Degree Level:
doctoral
Degree Program:
Special Education & Rehabilitation; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Maker, June

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titleM3: The Three-Mathematical Minds Model for the Identification of Mathematically Gifted Studentsen_US
dc.creatorSak, Uguren_US
dc.contributor.authorSak, Uguren_US
dc.date.issued2005en_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.abstractViews of giftedness have evolved from unilateral notions to multilateral conceptions. The primary purpose of this study was to investigate the psychological validity of the three-mathematical minds model (M3) developed by the author. The M3 is based on multilateral conceptions of giftedness to identify mathematically gifted students. Teachings of Poincare and Polya about mathematical ability as well as the theory of successful intelligence proposed by Sternberg (1997) provided the initial framework in the development of the M3. A secondary purpose was to examine the psychological validity of the three-level cognitive complexity model (C3) developed by the author. The C3 is based on studies about expertise to differentiate among gifted, above-average and average-below-average students at three levels.The author developed a test of mathematical ability based on the M3 and C3 with the collaboration of mathematicians. The test was administered to 291 middle school students from four different schools. The reliability analysis indicated that the M3 had a .72 coefficient as a consistency of scores. Exploratory factor analysis yielded three separate components explaining 55% of the total variance. The convergent validity analysis showed that the M3 had medium to high-medium correlations with teachers' ratings of students' mathematical ability (r = .45) and students' ratings of their own ability (r = .36) and their liking of mathematics (r = .35). Item-subtest-total score correlations ranged from low to high. Some M3 items were found to be homogenous measuring only one aspect of mathematical ability, such as creative mathematical ability, whereas some items were found to be good measures of more than one facet of mathematical ability.The C3 accounted for 41% of variance in item difficulty (R square = .408, p < .001). Item difficulty ranged from .02 to .93 with a mean of .29. The analysis of the discrimination power of the three levels of the C3 revealed that level-two and level-three problems differentiated significantly among three ability levels, but level-one problems did not differentiate between gifted and above average students. The findings provide partial evidence for the psychological validity of both the M3 and C3 for the identification of mathematically gifted students.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectGifteden_US
dc.subjectCreativeen_US
dc.subjectmathematical abilityen_US
dc.subjectassessmenten_US
dc.subjectidentificationen_US
thesis.degree.namePhDen_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineSpecial Education & Rehabilitationen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorMaker, Juneen_US
dc.identifier.proquest1032en_US
dc.identifier.oclc137353601en_US
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