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The study presented in this dissertation is part of a larger research project that searches for deep insights into the nature of mathematical giftedness. Mathematical giftedness (MG) is a complex construct which is ill-defined (Leikin, 2012). The larger research project aims to resolve the ambiguity in the field of MG and propose a solid definition of mathematical giftedness. It is of a multidimensional nature, as it examines and compares the mental activity of participants with varying levels of mathematical exceptionality in three salient dimensions: Cognition, Neuro-cognition and Mathematical creativity. The study presented in this dissertation focuses on the neuro-cognitive dimension of the larger research project. This study aimed to: 1. Design and validate research instrument for ERP (Event Related Potentials) procedure on the upper secondary level of mathematics. 2. Search for the relationship of general giftedness (G factor) and excellence in school mathematics (EM factor) to problem solving performance as reflected in (1) Behavioral measures: Accuracy of responses (Acc) and Reaction time for correct responses (RTc) and (2) Electrophysiological measures: Amplitudes, latencies, and scalp topographies of brain electrical activity identified with Event-Related Brain Potentials (ERP) procedure. 3. Examine specific behavioral and electrophysiological characteristics of students with superior mathematical performance (S-MG).To achieve the study aims, a special sampling procedure was conducted based on the distinction between general giftedness (G factor) and excellence in school mathematics (EM factor). The research sample included 200 right-handed male 10th and 11th grade high school students (16-18 years old) who were divided into 4 major sub-groups that varied in combinations of their degree of general giftedness and excellence in school mathematics. The fifth research group consisted of 9 students with superior mathematical performance (S-MG). We report herein the findings of the comparative data analysis (See Section 2.2). Research tests were designed to employ the Event Related Potentials (ERP) research procedure. The tests were innovative in terms of the complexity of the tasks and the item design, which was based on Polya's model of problem-solving strategies. Since translations between representations are among the key indicators of mathematics understanding, the tests were initially designed to examine different types of translations (e.g., from graphical/pictorial to symbolic, from verbal to symbolic, from symbolic to graphical representations). Of the 9 initially designed tests 3 proved to be insufficiently reliable (Alpha Cronbach lower than 0.6). Thus, we collected data using 6 of the 9 tests. Furthermore, 4 of these 6 tests allowed for between-test comparisons and thus were chosen for the report in this study (see Part 3 for tool design). Scalp EEG data were continuously recorded using a 64-channel BioSemi ActiveTwo system (BioSemi, Amsterdam, The Netherlands) and ActiveView recording software. The ERP waveforms were time-locked to the onsets (appearance on the screen) of S1, S2 (and S3 if it existed).Data analysis: Both behavioral and electrophysiological analyses were performed in two steps: Step A focused on the similarities and differences in the four major groups of participants - G-EM, NG-EM, G-NEM and NG-NEM (with ANOVA examinations as the main type of statistical test employed). Step B was directed at identifying specific characteristics of the S-MG participants. (PsycInfo Database Record (c) 2022 APA, all rights reserved)
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This study represents part of more extensive research aimed at a multidimensional examination of mathematical giftedness. This study aimed to:1. Examine the link between cognitive abilities and General giftedness (G), Excellence in Mathematics (EM) and gender. The cognitive abilities that were examined include: memory, attention, speed of information processing and visual perception.2. Examine differences and similarities in cognitive abilities of excelling in mathematics students who vary in their degree of general giftedness (S-MG, G-EM, and NG-EM), as reflected in memory, speed of information processing, attention and visual perception.3. Examine the cognitive profiles of students from four study groups according to memory, speed of information processing, attention and visual perception traits.4. Identify cognitive components that can predict General giftedness (G) and Excellence in mathematics (EM). The cognitive components (determined after factor analysis) that were examined include: STM_WM, Pattern-recall, Visual serial processing and Numeric processing. Population and sampling procedure: The sampling procedure included 1200 10th -11th grade students who undergo a battery of general intelligence (Raven's Advanced Progressive Matrix Test (RPMT)) and mathematical ability (Scholastic Assessment Test in Mathematics, (SAT-M)) tests. After completion of this procedure, a sample of 200 students was selected. These students were subdivided into four experimental groups, determining the research population by a combination of EM and G factors:G-EM group: students who are identified as generally gifted and excelling in mathematics;G-NEM group: students who are identified as generally gifted but do not excel in mathematics;NG-EM group: students excelling in mathematics who are not identified as generally gifted; NG-NEM group: students who are identified as being neither generally gifted nor excelling in mathematics.Students from G groups are mainly chosen from classes for gifted students (IQ>130) or with Raven score above 27. Students who are sampled as EM are those that study mathematics at high level (HL) with SAT-M scores higher than 26 and math score above 90.Another study group participated in this study are super-mathematically-gifted (S-MG). These students satisfied all criteria for the G-EM group and additionally displayed exceptional achievements in mathematics: membership in national Olympiad teams (in mathematics or computer sciences) or studying university mathematics courses parallel with their high school studies, and attaining scores above 95.The study findings are reported based on 190 students divided into four study groups and 7 S-MG students who fully completed the cognitive tasks. The cognitive abilities that were examined include: memory, speed of information processing (SIP), attention and visual perception. Data Analysis: In chapters 3.1-3.3 multivariate analysis of variance tests (MANOVA) were used to compare the cognitive abilities (memory, speed of information processing, attention and visual perception) of participants from the four study groups.In chapter 3.4 non-parametric tests were used for the analysis of the between-group in all cognitive tests between S-MG, G-EM and NG-EM students.In chapter 3.5 non-hierarchical K-means cluster analysis was conducted to identify the cognitive profile of participants'. Thereafter, a structural equation modeling (SEM) was used in order to determine which cognitive categories can predict general giftedness (G) and excellence in mathematics (EM). (PsycInfo Database Record (c) 2022 APA, all rights reserved)
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- Entre 2000 y 2026 (2)