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School mathematics mainly embraces algorithmic problem solving, pays less attention to strategic reasoning, and rarely contains insightful problem solving. Based on our previous research, we hypothesize that success in solving insight problems correlates strongly with general giftedness, while mathematical expertise is essential for strategy-based problem solving. Furthermore, we employ a phenomenon of greater ERP amplitudes in PO4/8 electrodes associated with insightful problem solving. In this study, 114 high school students (aged 16-18) with varying degrees of general giftedness and mathematical expertise were asked to solve mathematical problem of three distinct type: (1) function problems, whose solutions are memory-based; (2) area problems that necessitate strategic thinking; and (3) insight problems, that necessitate insight for their resolution. The problem solving process was accompanied by ERP recording. We demonstrate that variations in accuracy of solutions and reaction time for correct responses between tasks are influenced by students' general giftedness and mathematical expertise. Our ERP analyses partly supported our hypotheses regarding the relationship between PO electrode activation, insight-based problem solving processes, and participants' levels of giftedness and mathematical expertise.

In this paper we suggest that instruments of neuro-cognitive research enable the evaluation of giftedness in mathematics. We start with a literature review on the related topics presented so as to situate our suggestions within the existing research on giftedness and excellence in mathematics. This literature review allows us later to discuss our findings, which are based on neurocognitive data collected in a large-scale multidimensional examination of mathematical giftedness. Sampling procedure in the study was performed based on two orthogonal (in our view) characteristics: general giftedness (G) and excellence in mathematics (EM). In this paper we present findings that lead to a definition of the mathematically gifted population. We present selected results to provide evidence for our findings. In this paper we demonstrate three major findings: A. Effects of G and EM factors are task-dependent both in behavioral and neurophysiological measures' the EM factor has significant main effects on tasks that require implementation of knowledge familiar to students from school mathematics. By contrast, the G factor has a significant main effect on insight-based problems which are not part of the school mathematical curriculum and, thus, require original mathematical reasoning. B. Mathematical performance in gifted students who excel in mathematics (G-EM students) on insight-based tasks has specific characteristics in both behavioral and electrophysiological results. C. G-EM participants exhibited superior performance in all the tests, showing a constant neuroefficiency effect. Based on these observations we suggest that mathematically gifted students are those who are both generally gifted and excel in mathematics. (PsycINFO Database Record (c) 2016 APA, all rights reserved) (Source: journal abstract)

This paper presents part of a multidimensional examination of mathematical giftedness. The present study examined the memory mechanisms associated with general giftedness (G) and excellence in mathematics (E) in four groups of 10th–12th grade students (16–18 years old) varying in levels of G and E. The participants first underwent the Raven test for general ability evaluation and SAT-M—the mathematical excellence tests in order to design the study groups. Afterwards, the students were tested on a battery of three memory tests including tests for short-term (STM) and working memory (WM). The results reveal that the G factor is related to high STM for both phonological loop and phonological central executive mechanisms. It was also found that the E factor is associated with high visual–spatial memory (VSM), in particular with the visual central executive mechanism. An interaction effect was found between G and E factors regarding WM. The central executive mechanism appeared to be related to both G and E factors. In addition, gender differences were shown within the groups. Male participants performed better than their female counterparts on a phonological storage task and a phonological central executive mechanism task. The results can contribute to the theoretical knowledge regarding similarities and differences in memory mechanisms in G and E groups. (PsycInfo Database Record (c) 2020 APA, all rights reserved) (Source: journal abstract)

Super-gifted individuals are considered to be very rare. This paper addresses one part of a larger body of research aimed at characterization of super-giftedness in mathematics. The research population consists of three groups of students who excel in mathematics: Super-gifted in mathematics (S-MG), generally gifted students who excel in school mathematics (G-EM) and students who excel in school mathematics but are not identified as generally gifted (NG-EM). Fifty-six male students who comprised these groups performed a battery of cognitive tests: memory, speed of information processing, visual perception, and attention. We found that the between-group differences are task depended and that S-MG students can be characterized by superior performance on Working Memory test (WM – span, WM – total score) and the accuracy of Pattern-recognition, which was an indicator of visual perception. (PsycINFO Database Record (c) 2016 APA, all rights reserved) (Source: journal abstract)

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)

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)

Previous studies on intelligence have demonstrated that higher abilities are associated with lower brain activation, indicating a higher neural efficiency. In other words, more able individuals use fewer brain resources. However, it is unclear whether the neural efficiency phenomenon also appears for mathematical performance, which is influenced by both domain-general giftedness and domain-specific competencies. Therefore, this study examined the effects of general giftedness (G) and excellence in mathematics (EM) on performance and brain activation while solving learning-based mathematical tasks that required translation from graphical to symbolic representations of functions. Overall, 118 high school students (aged 16–18) participated in the present study and were divided according to G and EM using a 2 × 2 study design. Participants worked on a function task requiring translation between symbolic and graphical representations of functions. Analyses of the behavioral data revealed positive effects of both G and EM on the accuracy of solutions and an interaction effect of both factors on reaction times, reflecting a positive effect of EM only among the gifted individuals. EEG analyses focused on oscillatory activity in the theta and alpha frequency bands and showed a significant effect of EM in the upper alpha band (10–12 Hz) event-related desynchronization (ERD) for both graphical and symbolic representations. Specifically, higher (compared to lower) EM was associated with a larger alpha ERD, indicating a higher level of brain activity. This stands in contrast with the neural efficiency phenomenon. These findings suggest that the neural efficiency phenomenon cannot be generalized to higher-order mathematical demands in high-performing individuals. Several explanations for this limitation are offered. (PsycInfo Database Record (c) 2023 APA, all rights reserved) (Source: journal abstract)

In order to achieve the present study’s goal—to understand better the phenomenon of mathematical giftedness—we performed a multidimensional examination of the mental processing in students who exhibited mathematical expertise (EM) at the secondary school level. The study included participants from the three groups: students who excelled in school mathematics but were not identified as generally gifted (NG-EM), generally gifted excelling in mathematics (G-EM) students, and students with superior performance in mathematics (S-MG). The research integrated three salient dimensions of mental processing: domain-general cognitive traits, domain-specific (mathematical) creativity, and neuro-cognitive functioning expressed in event-related potentials (ERPs) when solving mathematical problems. In the three study dimensions, we found four types of characteristics of S-MG students: accumulative, G-related, unique and unraveling. This paper defines and exemplifies the characteristics of the four types. (PsycINFO Database Record (c) 2017 APA, all rights reserved) (Source: journal abstract)