Academic journal article Psychological Test and Assessment Modeling

Integrating Mathematical Abilities and Creativity in the Assessment of Mathematical Giftedness

Academic journal article Psychological Test and Assessment Modeling

Integrating Mathematical Abilities and Creativity in the Assessment of Mathematical Giftedness

Article excerpt

Abstract

This study aims to examine the structure of the relationship between intelligence and mathematical giftedness and build a comprehensive model to describe this relationship and the nature of mathematical giftedness. This study also purports to clarify the structure of components of mathematical ability. The third objective is to examine whether students who were identified by two different instruments - (a) mathematical ability and creativity instrument and (b) intelligence instrument - have statistically significant differences across the components of mathematical ability. That is, we want to investigate if variance in identification may be explained by variance in mathematical abilities exhibited by these individuals. To achieve these goals, this study proposes a new domainspecific identification instrument for the assessment of mathematical giftedness, assessing mathematical abilities and creativity. The study was conducted among 359 4th, 5th and 6th grade elementary school students in Cyprus, using two instruments measuring mathematical ability and mathematical creativity and fluid intelligence. The results revealed that mathematical giftedness can be described in terms of mathematical ability and mathematical creativity. Moreover, the analysis illustrated that intelligence is a predictor of mathematical giftedness. Furthermore, the analysis revealed that different groups of students are identified by each type of testing; that is, through the mathematical instrument and the intelligence instrument. This variance may be explained by performance in specific categories of tasks.

Key words: giftedness, creativity, mathematical ability, intelligence

Introduction

In recent years, intelligence testing as the exclusive means of identification of giftedness has received extensive criticism by a number of researchers (Dai, 2010; Lohman & Rocklin, 1995). Contemporary conceptualizations of giftedness acknowledge the multidimensionality (Gagné, 2003; Renzulli, 1978, 2002) and the domain specificity of the concept (Csikszentmihalyi, 2000; Clark, 2002). Hence, former identification processes measuring giftedness solely using intelligence instruments, should be enriched with other domain specific instruments measuring all dimensions of giftedness.

In the field of mathematical giftedness, identification was in many cases conducted through intelligence testing with subtests designed to assess mathematical giftedness, such as the Naglieri Non-Verbal Ability Test (Naglieri, 1997), the Wechsler Intelligence Scale for Children Matrix reasoning Test (Wechsler, 1999) and the Raven Progressive Matrices (Raven, Raven, & Court, 2003). These subtests focus on visual perception, spatial ability and the ability to distinguish patterns and find missing elements. At the same time, instruments designed to capture mathematical giftedness, such as TOMAGS (Ryser & Johnsen, 1998) include tasks that are aligned with curriculum standards in mathematics, hence measuring mathematical knowledge more than mathematical reasoning processes. In contrast, we would argue that identification should attempt to capture students' mathematical reasoning abilities, rather than mathematical knowledge, because reasoning skills distinguish gifted from non-gifted students in mathematics.

Given these facts, the concept of giftedness should be expanded, in order to encompass contemporary conceptions, models and approaches. Thus, mathematical giftedness may be expressed as a multidimensional construct that is domain specific. To this end, it is the purpose of this study to integrate mathematical abilities and creativity into the assessment of mathematical giftedness through a theoretical model and to translate it into an empirically examined identification process of mathematical giftedness. At the same time, we will show that there is a discrepancy in identifying mathematically gifted students with conventional intelligence tests and specifically designed mathematical instruments, thus suggesting a new way of identifying giftedness in mathematics. …

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