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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)
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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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Entre 2000 y 2026
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Entre 2010 y 2019
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Entre 2010 y 2019
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