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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)

This study relates to two critical points in mathematical education in Israel and abroad which are the need to increase the importance of mathematical creativity when teaching mathematics and the necessity of developing tools to assess mathematical creativity that is needed to promote and develop creativity among schoolchildren. The study is also motivated by the observation that the issue of mathematical creativity as well as of creativity in mathematics education is not well explored. Characterizing the relationship between mathematical giftedness and mathematical creativity is still missing in the professional literature (e.g., Leikin, 2013; Sriraman, 2005). Since Krutetskii's (1976) seminal study of mathematical abilities, only a small number of studies have been done on the characterization of the mathematical abilities of gifted students which have left a large number of open questions (Leikin, 2009b, 2013). This research attempted to address this deficiency.This study employed Multiple Solution Tasks (i.e., tasks that explicitly require solving a mathematical problem in different ways - MSTs) in order to explore students' creativity in mathematics (Leikin & Lev, 2007; Leikin, 2013). This study examined the relationship between mathematical creativity, general giftedness and excellence in school mathematics. The study (which is a part of multidimensional examination of mathematical giftedness, e.g. Leikin, Leikin, Lev, Paz-Baruch & Waisman, 2013) attempted to get better understanding of the concept of mathematical giftedness from the point of view of mathematical creativity. This study had three main interrelated Goals: 1. To examine relationships between mathematical creativity, general giftedness and excellence in secondary school mathematics. 2. To explore creativity of adolescents with superior mathematical abilities. 3. To explore the power of different types of Multiple Solution Tasks (MSTs) for the identification of between-group differences related to mathematical creativity The research sample consisted of 184 students (16-18 years old) divided into four major experimental groups according to varying combinations of the levels of excellence in school mathematics (EM factor) and of general giftedness (G factor) (see Section 2.3). Additionally 7 students (16-18 years old) with superior mathematical abilities (S-MG) took part in the study.Data collection and analysis: The data was collected by means of written tests and individual interviews.The Test consisting of five MSTs – was designed for the purpose of this study (see Sections 2.2.1 and 2.2.2). To evaluate students' creativity the study employed a model for evaluation of mathematical creativity using MSTs (see Part 3 and Section 1.2.7; Leikin, 2009b, 2013). The students' solutions to the Test were analyzed with 5 criteria (correctness of the solutions, fluency, flexibility, originality and creativity). The quantitative analysis of the tests was performed in 2 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. Step B was directed towards the identification of specific characteristics of S-MG participants. At Step A we used MANOVA for G factor and EM factor with consequent ANOVAs and pair-wise comparisons (G vs. NG in EM and NEM groups and EM vs. NEM in G and NG groups, separately). (PsycInfo Database Record (c) 2022 APA, all rights reserved)

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)

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)

Mathematical talent is an intriguing human phenomenon. From the time of Poincare (1908/1952), who linked mathematical talent to mathematical creation, the relationship between mathematical talent and mathematical creativity has been at the heart of the discussion of mathematical talent. Analysis of the criteria used for empirical examination of mathematical talent shows that researchers connect mathematical talent to general giftedness, to mathematical achievement, or to mathematical creativity. This chapter discusses the developing mathematical talent in schoolchildren. It starts by discussing the components and complexities of mathematical talent and goes on to review several frameworks for its development. It briefly addresses characteristics of mathematical content and didactical principles directed at the development of mathematical talent. Finally, it briefly addresses the proficiency required for teaching the gifted and presents examples of mathematical problems and their solutions. (PsycInfo Database Record (c) 2024 APA, all rights reserved) (Source: chapter)