Giftedness In Mathematics Research Articles

(Lack of) neural efficiency related to general giftedness and mathematical excellence: An EEG study

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.

Effects of Dynamic Geometry Software on Students’ Geometric Thinking Regarding Probability of Giftedness in Mathematics

Gifted students have potential to improve countries and this potential can be revealed and developed in schools where they spend most of their times with other regular students. However, these classrooms have some limitations for them; hence, they need some differentiated activities. Usage of dynamic geometry in mathematics lessons could be an opportunity to provide differentiated activities. Therefore, the aim of this study is to explore effects of mathematics lessons integrated with dynamic geometry activities on students' van Hiele geometric thinking levels controlling their probability for mathematical giftedness. Participants of the study were fifty-three fifth graders from a private school in Marmaris, Turkey. These students were grouped in terms of their probability of mathematical giftedness. Seven dynamic geometry activities about properties of line segments, triangles and quadrilaterals were developed and implemented in classrooms with tablets. Van Hiele geometric thinking level test was administered to the participants as pre-test and post-test. Results showed that dynamic geometry activities help students to move from geometric thinking level about recognizing shapes with visual clues to higher level about geometrical properties of shapes, namely relationship among shapes and their properties. Moreover, interaction between their probability for mathematical giftedness and improvements in geometric thinking levels were found. This study may contribute both to the gifted education and mathematics education fields by exploring the improvements in geometric thinking level and differentiated opportunities for gifted students. As a suggestion, a more comprehensive experimental study with larger samples so as to obtain generalize the findings could be conducted as a further study.

Prospective teachers constructing dynamic geometry activities for gifted pupils: Connections between the frameworks of Krutetskii and van Hiele

The Swedish educational system has, so far, accorded little attention to the development of gifted pupils. Moreover, up to date, no Swedish studies have investigated teacher education from the perspective of mathematically gifted pupils. Our study is based on an instructional intervention, aimed to introduce the notion of giftedness in mathematics and to prepare prospective teachers (PTs) for the needs of the gifted. The data consists of 10 dynamic geometry software activities, constructed by 24 PTs. We investigated the constructed activities for their qualitative aspects, according to two frameworks: Krutetskii’s framework for mathematical giftedness and van Hiele’s model of geometrical thinking. The results indicate that nine of the 10 activities have the potential to address pivotal abilities of mathematically gifted pupils. In another aspect, the analysis suggests that Krutetskii’s holistic description of mathematical giftedness does not strictly correspond with the discrete levels of geometrical thinking proposed by van Hiele.

A Proposed Model for Understanding and Supporting Creativity and Mathematical Talent Development

Research on education has been focused on creativity and talent development in order to better understand underlying concepts and suggest teaching practices that lead students to a higher level for best utilization of their potentials. Giftedness in mathematics is a major focus for many researchers because of the importance of mathematics in scientific development and innovation. Creativity, on the other hand, is considered not only as a major component of giftedness, but also as the essence of mathematics that should be fostered for all students. This research study further analyzed creativity and giftedness in mathematics, and synthesized rational support of a proposed model to better understand and support creativity and mathematical talent development in general education schools; it also discussed preliminary requirements for effective use of the proposed model based on teachers' perspectives. The major purpose is to contribute to enhancing school trends toward nurturing creativity for all students and meeting the needs of gifted mathematics students, utilizing broad conceptions of creativity and giftedness, and internalizing positive beliefs about student capability for success in mathematics.

Expertise, giftedness and insight in mathematics

Absence epilepsy (AE) and nocturnal frontal lobe epilepsy (NFLE) are system epilepsies of the sleep–wake system.1. Absence epilepsy is a well-known idiopathic childhood epilepsy. The spike–wake pattern of absence epilepsy and the non–rapid eye movement (NREM) sleep-related burst-firing mode of the corticothalamic system share the same functional structures in the brain. Absences occur when vigilance decreases, during the transition from waking to NREM sleep, whereas they are inhibited by wakefulness and rapid eye movement sleep. The sensory stimuli reaching the brain during the transition state [cyclic alternating pattern (CAP) A1 phase] elicit “reactive” slow-wave responses and may activate spike–wave responses, whereas those arriving in other states (CAP 2 or 3 NREM sleep) evoke “regular” desynchronization–arousal responses and do not trigger spike–waves.In other words, in terms of states and functions, absence epilepsy seems to be linked to the periods of initiation and shifts toward NREM sleep.2. Autosomal dominant nocturnal frontal lobe epilepsy, the genetic variation of NFLE, is underlain by mutations of the nicotinic acetylcholine receptor system.The acetylcholine receptor (AChE) gene mutations render the cholinergic ascending arousal system oversensitive to arousals during NREM sleep, resulting in arousal-linked seizure fragments and full-blown seizures with different degrees of behavioral manifestations, from plain arousal behaviors to alarm reactions with hypermotor features. The semiology and the occurrence pattern of seizures can be explained by an increased propensity to arousal and a dissociation between the partially activated brain and a sleeping (dysfunctional) dorsofrontal cortical system. The clinical semiology of the genetic variations and the sporadic cases does not differ.Therefore, NFLE seems to be linked to the epileptically facilitated cholinergic arousal system, underlain by a genetic or a suspected genetic origin.Arousal parasomnia (AP) manifests behaviors similar to those of NFLE, caused by a nonepileptic mechanism. The two conditions (AP and NFLE) show a familial clustering, with patients and families suffering in both conditions and probably sharing the pathomechanisms related to a dissociation background.We can see that NFLE and AP (the epileptic and nonepileptic counterparts) may both be linked to a disorder of the frontal part of the ascending arousal system.

Advancements in research on creativity and giftedness in mathematics education: introduction to the special issue

Creativity and giftedness in mathematics education research are topics of an increased interest in the education community during recent years. This introductory paper to the special issue on Mathematical Creativity and Giftedness in Mathematics Education has a twofold purpose: to offer a brief historical perspective on the study of creativity and giftedness, and to place an emphasis on the added value of the present volume to the research in the field. The historical overview addresses the development of research and practice in creativity and giftedness with specific attention to creativity and giftedness in mathematics. We argue that this special issue makes a significant contribution to bridging domain-general theories of creativity and giftedness with theories in mathematics education with special attention given to nurturing these phenomena in the process of mathematics teaching and learning.

The Curious Transformation of Boy to Computer

The Curious Transformation of Boy to Computer

Visual Processing in Generally Gifted and Mathematically Excelling Adolescents

Little empirical data are available concerning the cognitive abilities of gifted individuals in general and especially those who excel in mathematics. We examined visual processing abilities distinguishing between general giftedness (G) and excellence in mathematics (EM). The research population consisted of 190 students from four groups of 10th- to 12th-grade students who differed in their G and EM levels. The students performed a battery of visual processing tests: visual-spatial memory, visual speed of information processing (SVIP), visual perception (VP), and visual attention (VA). The results demonstrate that EM type has a significant effect on the Backward Corsi-Span, whereas G type has a main effect on the Pattern-Recognition test and d2-CP (concentration performance) and d2-E (number of errors) scores in the attention test. SVIP and the fluctuation rate in VA tests (d2-FR) were associated with both G and EM types. The current study identified two different components of visual processing that were accordingly termed Visual-Serial and Pattern-Recall. It seems that G-EM students can be characterized by superior performance on Visual-Serial processing.

Does solving insight-based problems differ from solving learning-based problems? Some evidence from an ERP study

We asked: “What are the similarities and differences in mathematical processing associated with solving learning-based and insight-based problems?” To answer this question, the ERP research procedure was employed with 69 male adolescent subjects who solved specially designed insight-based and learning-based tests. Solutions of insight-based problems were not related to the learning experience but rather to an “Aha!” moment. As learning-based problems, we employed tasks that require comparing the areas of geometric figures. The analysis was performed through the lens of mathematical performance in students who differed in the combination of levels of general giftedness (G) and excellence in school mathematics (EM). Alongside a quantitative analysis of the effects of EM and G factors on accuracy, reaction time, strength of the electrical potentials and their topographical distribution, we performed a qualitative comparison of the differences in the effects of EM and G factors associated with the two types of tests. We demonstrate that an analysis of the behavioral measures is insufficient and even misleading and argue that neurocognitive analysis is crucial for the understanding of the distinctions between mathematical processing associated with solving different types of problems. Analysis of the electrical potentials evoked when solving the two types of problems demonstrated that excellence in school mathematics affects learning-based problem solving but does not affect insight-based problem solving. Based on the observation of the increased activation of PO4–PO8 electrode site as related to G and EM factors, we further hypothesize that the ability to solve insight-based problems is a specific personal aptitude related mainly to general giftedness, while experience-based problem solving by experts involves insight-related components at the stage of problem understanding.

Brain activity associated with logical inferences in geometry: focusing on students with different levels of ability

Mathematical processing associated with solving short geometry problems requiring logical inference was examined among students who differ in their levels of general giftedness (G) and excellence in mathematics (EM) using ERP research methodology. Sixty-seven male adolescents formed four major research groups designed according to various combinations of G and EM factors, while another group of seven students were considered to be ‘super mathematically gifted’ (S-MG). EM and G factors affected behavioral measures similarly: EM and G students were more accurate than their non-EM and non-G counterparts respectively. At the same time, G and EM factors affected electrophysiological measures differently, with significant interaction between G and EM factors associated with absolute ERP amplitudes at some of the solution stages. S-MG students exhibited significantly lower absolute ERP amplitude values, which we attribute to a neural efficiency effect in this research group. Based on the differences revealed, we suggest that our research demonstrates that G and EM factors are interrelated individual traits which are different in nature. Since the accuracy and strength of electrical potentials associated with solving the problems appeared to be of an accumulative nature, we argue that S-MG is an extreme expression of combined EM and G factors. Taking it one step further, we suggest that ability grouping in school mathematics must take into account both EM and G factors.

Social and Emotional Characteristics and Early Childhood Mathematical and Literacy Giftedness

Research has demonstrated mixed results regarding differences in social and emotional characteristics between gifted and typical populations. The purpose of this secondary analysis of data from the Early Childhood Longitudinal Study: Birth Cohort (ECLS-B) is to investigate the affective characteristics of early mathematics and literacy ability among preschool children using a logistic regression analysis. Specifically, parents and childcare providers were asked a series of questions relating to socially maladaptive behaviors, concentration, empathy, worry, and friendship of a nationally representative sample of children born in 2002. The results of the study demonstrate that childcare providers and parents of preschool children ( M age = 53 months) have different patterns of observations of social and emotional characteristics of children, and that concentration and socially maladaptive behaviors were significant predictors of early giftedness in literacy. There were no social or emotional predictors of early giftedness in mathematics found in this study.

Giftedness and Aesthetics

Giftedness in mathematics has been characterized by exceptional attributes including strong mathematical memory, formalizing perception, generalization, curtailment, flexibility, and elegance. Focusing on the last attribute, this study examined the following: (a) the criteria which expert mathematicians and mathematically gifted students fleshed out to identify their own most preferred mathematics problem-solving approaches and (b) the extent to which students perceived expert mathematicians’ preferences for one approach over the others as aesthetically pleasing. The findings suggested that: (a) unlike expert mathematicians who saw beauty in mathematics as an exhaustive consequence of simplicity and originality, mathematically gifted students found mathematical elegance only in approaches that were efficient in terms of time and number of steps to solve the problems and (b) although expert mathematicians considered mathematically gifted students’ most preferred approaches to be the least “beautiful,” mathematically gifted students, showing no enthusiasm, considered expert mathematicians’ most preferred approaches to be no more attractive than their own approaches.

Speed of information processing in generally gifted and excelling-in-mathematics adolescents

A considerable amount of recent evidence suggests that speed of information processing (SIP) may be related to general giftedness as well as contributing to higher mathematical ability. To date, no study has examined SIP associated with both general giftedness (G) and excellence in mathematics (EM). This paper presents a part of more extensive research aimed at a multidimensional examination of mathematical giftedness, which is a complex function of the G factor and EM factor. The research population consisted of four groups of 10th–11th grade students who differed in their G level and EM level. 190 participants performed five SIP tests: Visual-matching, Cross-out of numbers, Digit-symbol, Symbol-search and Simple arithmetic exercises. We found that the G–EM group outperformed the three other study groups on all five tests. The findings reveal that between-group differences in performance on Cross-out of numbers and Simple arithmetic exercises tests are associated with both G and EM factors, whereas especially the G factor had an effect on students’ scores on Digit-symbol, Symbol-search and Visual-matching tests. In addition, we found gender differences on the Digit-symbol and Symbol-search tests. The results of this study suggest that EM and G factors are interrelated but represent different traits with respect to the SIP.

BRAIN ACTIVITY ASSOCIATED WITH TRANSLATION BETWEEN GRAPHICAL AND SYMBOLIC REPRESENTATIONS OF FUNCTIONS IN GENERALLY GIFTED AND EXCELLING IN MATHEMATICS ADOLESCENTS

In this study, we examine the impact and the interplay of general giftedness (G) and excellence in mathematics (EM) on high school students’ mathematical performance associated with translations from graphical to symbolic representations of functions, as reflected in cortical electrical activity (by means of ERP—event-related potentials—methodology). We report on findings of comparative data analysis based on 75 right-handed male high school students (16 – 18 years old) divided into four research groups designed by a combination of EM and G factors. Effects of EM factor appeared at the behavioral and electrophysiological levels. The fifth group of participants included 9 students with extraordinary mathematical abilities (S-MG: super mathematically gifted). We found that in EM participants, the G factor has no impact on the performance associated with translation between representations of the functions. The highest overall electrical activity is found in excelling in mathematics students who are not identified as generally gifted (NG-EM students). This increased electrical activity can be an indicator of increased cognitive load in this group of students. We identified accumulative and unique characteristics of S-MG at the behavioral and electrophysiological levels. We explain the findings by the nature of the tasks used in the study. We argue that a combination of the ERP techniques along with more traditional educational research methods enables obtaining reliable measures on the mental processing involved in learning mathematics and mathematical problem solving.

Empirical Investigations of Creativity and Giftedness in Mathematics: An International Perspective

The idea for this book originated at the first joint meeting of the Korean Mathematical Society and the American Mathematical Society, held in Seoul, South Korea, on December 16–20, 2009. Contributing authors from Sweden, Norway, Turkey, Israel, Iran, China, Canada, South Korea, and the United States provide international perspectives on creativity and giftedness in mathematics education. The vast majority of the book is comprised of reports from empirical studies. In this respect, the book is not theory driven, per se. Instead, the focus is on reporting findings from studies in an attempt to elucidate the relationship between giftedness and creativity in mathematics. In this review, I provide a brief synopsis of each chapter (except Chapter 1, which outlines the book) and discuss the relevance of the work to the literature on mathematical creativity and giftedness. The overview of the chapters is followed by general remarks on the state of mathematics education research on creativity and giftedness and final thoughts about the contribution of this book to the field.

Memory abilities in generally gifted and excelling-in-mathematics adolescents

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 (16–18years 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.

Modeling children’s mathematical gift by neural networks and logistic regression

The purpose of the paper was to extract important features of children’s mathematical gift by using neural networks and logistic regression, in order to create a model that will assist teachers in elementary schools to recognize mathematically gifted children in an early stage, therefore enabling further development and realization of that gift. The initial model was created on the basis of a theoretical background and heuristical knowledge on giftedness in mathematics, including five components: (1) mathematical competencies, (2) cognitive components of gift, (3) personal components that contribute gift development, (4) environmental factors, and (5) efficiency of active learning and exercising methods, as well as grades and out-of-school activities of pupils in the fourth year of elementary school. The three neural network classification algorithms were tested in order to extract the important variables for detecting mathematically gifted children. The best neural network model was selected on the basis of a 10-fold cross-validation procedure. The model was also investigated by the logistic regression. Important predictors detected by two methods were compared and analyzed. The results show that both methods extract similar set of variables as the most important, including grades in mathematics, mathematical competencies of a child regarding numbers and calculating, but also grades in the literature, and environmental factors.

Mathematically gifted and talented learners: theory and practice

There is growing recognition of the special needs of mathematically gifted learners. This article reviews policy developments and current research and theory on giftedness in mathematics. It includes a discussion of the nature of mathematical ability as well as the factors that make up giftedness in mathematics. The article is set in the context of current developments in Mathematics Education and Gifted Education in the UK and their implications for Science and Technology. It argues that early identification and appropriate provision for younger mathematically promising pupils capitalizes on an intellectual resource which could provide future mathematicans as well as specialists in Science or Technology. Drawing on a Vygotskian framework, it is suggested that the mathematically gifted require appropriate cognitive challenges as well as attitudinally and motivationally enhancing experiences. In the second half of this article we report on an initiative in which we worked with teachers to identify mathematically gifted pupils and to provide effective enrichment support for them, in a number of London Local Authorities. A number of significant issues are raised relating to the identification of mathematical talent, enrichment provision for students and teachers’ professional development.

Are Giftedness and Creativity Synonyms in Mathematics?

At the K-12 level one assumes that mathematically gifted students identified by out-of-level testing are also creative in their work. In professional mathematics, “creative” mathematicians constitute a very small subset within the field. At this level, mathematical giftedness does not necessarily imply mathematical creativity but the converse is certainly true. In the domain of mathematics, are the words creativity and giftedness synonyms? In this article, the constructs of mathematical creativity and mathematical giftedness are developed via a synthesis and analysis of the general literature on creativity and giftedness. The notions of creativity and giftedness at the K-12 and professional levels are compared and contrasted to develop principles and models that theoretically “maximize” the compatibility of these constructs. The relevance of these models is discussed with practical considerations for the classroom. The paper also significantly extends ideas presented by Usiskin (2000).

Identification of Mathematically Gifted Children in New Zealand

A popular way of identifying mathematically gifted children in New Zealand is to select those ranked at or above the 90th percentile on a mathematics multiple-choice test, the Progressive Achievement Test (PAT). Giftedness in mathematics can properly be defined as the ability to solve difficult mathematical problems. We therefore compared the performance of sixty-six children on a published problem-solving test and the PAT. Receiver Operating Characteristic analysis showed that, independent of any chosen percentile, the PAT's accuracy at identifying mathematically gifted children was 78 per cent. Such a degree of accuracy will lead to many mathematically gifted children being overlooked, or many being mistakenly identified as gifted. Use of the PAT for this purpose is therefore not recommended.