Following recent research linking executive functioning to children 's skills, this thesis explores the relationship between children's inhibition effciency and mathematical ability. This relationship was initially explored using six Stroop task variants containing verbal, numerical or pictorial stimuli. The results indicated that, in the numerical variants only, children of lower mathematical abilty possess less effcient inhibition mechanisms, compared to children of higher mathematical ability. Thus, it is proposed that low-abilty mathematicians may possess a domain-specifc problem with the inhibition of numerical information. The increased interference scores of the lowability mathematicians, however, were only evident under those conditions which also required a degree of switching between temporary strategies. A series of experiments also examined children's ability to inhibit prepotent responses and switch between strategies whilst performing mental arithmetic. The aim of these experiments was to provide a more naturalistic and appropriate exploration of the hypothesized relationship between mathematical abilty and inhibition effciency. These results also indicated that low-ability mathematicians possess fewer executive resources to cope with increased inhibition demands. A further systematic manipulation of switching and inhibition demands revealed that the low-abilty mathematicians experienced a particular difculty when both types of inhibitory demands (i.e. inhibiting a prepotent response and inhibiting an established strategy)were present. This suggests that their reduction in inhibition effciency stems from the amount of demands, rather than the type of demands placed on the executive system. Furthermore, the results indicated that inhibition effciency may be a specifc element of mathematical ability rather than an element of intellectual ability in general. The final study involved a group of low-abilty mathematicians and examined the disturbing impact of irrelevant information on their arithmetic word problem solving abilty. This study revealed that irrelevant numerical (IN) information has a more detrimental impact on performance than irrelevant verbal (IV) information. It is proposed that it is more difcult to inhibit IN information, as it appears more relevant to intentions, and thus, enters WM with a higher level of activations. In sum, the results indicate that low-abilty mathematicians have a reduced domainspecific working memory capacity, characterized by ineffcient inhibition mechanisms.

Recent theories in numerical cognition suggest that humans are equipped with a mental system that supports the representation and processing of symbolic and nonsymbolic magnitudes, called the Approximate Number System (ANS). Prior research also suggests that the acuity of the ANS can predict individuals’ mathematical ability. However, results from research within the field has proven to be inconsistent with one another which raises questions about the reliability and validity of methods used to measure the ANS. The present study attempts to replicate the results found in studies suggesting that ANS acuity correlates with mathematical ability. The study also investigates the reliability and validity of different task that have been used to measure the ANS, and also presents a new method of measuring the ANS with an adaptive method. The results show that two tasks correlate significantly with mathematical ability, and multiple regression analyses show that ANS acuity can predict mathematical ability when controlling for general intelligence. Furthermore, the results also further highlight the issue of methodological flaws in previous studies.

MSc Research Project. July 2013. / This study focuses on understanding the strategies used by a sample of high ability and low ability Grade 2 learners drawn from two government primary schools in Gauteng, with emphasis on more concrete or more abstract strategies learners use to solve early number problems. This study takes place against the backdrop of poor performance in South African schools more especially across the foundation phase and also amidst claims that learners remain largely dependent on concrete strategies for solving problems. The theoretical background for this study is drawn from Sfard’s (1992) “Dual Nature of Mathematical Conceptions” and also Sfard’s (1992) theory of reification. I used on a wide range of literature on strategies for counting, addition, subtraction within my analysis of nine videos of high ability learners and 9 videos of low ability learners with the aim of examining the strategies these learners use when dealing with early number concepts. My findings pointed to the limited use of higher levels of abstraction in solving early number problems. Whilst there is progression from the concrete to the abstract levels of conception this is not happening at a pace and depth that is required for Foundation Phase learners in order for them to effectively engage with more challenging and complicated arithmetic in the Intermediate Phase.

Magister Educationis - MEd / The twenty-first century society demands a high level of mathematical literacy. This drove Korean educators to evaluate their students using international mathematics tests such as TIMSS, PISA and IMO. In these tests, Korean students ranked highly among the participating countries. Korean students, however, had done poorly in the application of mathematics in daily life situations as well as in their interest in mathematics in comparison to those of other countries. Based on these observations, the present study was an investigation on the contexts which Korean grade 8 to 10 students would prefer to deal with mathematics, in order to improve these weak points and thus increase their mathematical power. The aim of the study was to investigate mathematical literacy in connection with the relevance of mathematics and mathematical modelling. The study paid more attention to mathematics education in real life situations. / South Africa

by Lee Fong Lok. / Chinese title: / Bibliography: leaves 103-111 / Thesis (M.A.Ed.)--Chinese University of Hong Kong

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Thesis (MA)--University of Montana, 2009. / Contents viewed on November 30, 2009. Title from author supplied metadata. Includes bibliographical references.

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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.

A confirmatory approach based on a multidimensional model (Douglas, Roussos, & Stout, 1996; Shealy & Stout, 1993; Stout & Roussos, 1995) was used to identify sources of differential item functioning (DIF) and differential bundle functioning (DBF) for boys and girls on the British Columbia Principles of Mathematics Exam for grade 12 (PME12). Data consisted of a total of 9404 examinees; 4335 girls and 5069 boys. There were 45 multiple choice items in the exam. Analyses were completed in two stages. In stage 1, patterns present in the gender DIF research in mathematics were identified. Stage 2 was the statistical confirmation of these patterns. Sources of gender DIF were confirmed for the content areas: polynomial, quadratic relations, logarithms and exponents. Items tapping higher cognitive levels dealing with patterns and relation, word problems, and items containing visuals were also confirmed as a source of DIF. Exploratory analyses indicated that computation items for which no equations are provided may be a source of DIF along with trigonometry items. This study contributes to an increased understanding of sources of gender DIF that may assist test developers to ensure that mathematics items measure the construct that they are intended to measure and that the test as a whole measures that which it purports to measure. The findings of this research provide an additional source of information about the differential performance of boys and girls that may be used to develop guidelines and test construction principles for reducing gender DIF in mathematics. This research also contributes to a greater understanding of gender differences in mathematics learning and achievement.