# M?: THE THREE-MATHEMATICAL MINDS MODEL FOR THE IDENTIFICATION OF MATHEMATICALLY GIFTED STUDENTS

Abstract (Summary)

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, 12 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. 13
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School:The University of Arizona

School Location:USA - Arizona

Source Type:Master's Thesis

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