Comparison of intelligent systems in detecting a child’s mathematical gift Margita Pavlekovic a , Marijana Zekic-Susac b, * , Ivana Djurdjevic a a Faculty of Teacher Education, University of Josip Juraj Strossmayer in Osijek, L. Jagera 9, 31000 Osijek, Croatia b Faculty of Economics, University of Josip Juraj Strossmayer in Osijek, Gajev trg 7, 31000 Osijek, Croatia article info Article history: Received 24 February 2008 Received in revised form 7 January 2009 Accepted 12 January 2009 Keywords: Elementary education Evaluation methodologies Mathematical gift Expert system Neural networks abstract This paper compares the efficiency of two intelligent methods: expert systems and neural networks, in detecting children’s mathematical gift at the fourth grade of elementary school. The input space for the expert system and the neural network model consisted of 60 variables describing five basic compo- nents of a child’s mathematical gift identified in previous research. The expert system estimated a child’s gift based on heuristically defined logic rules, while the scientifically confirmed psychological evaluation of gift based on Raven’s standard progressive matrices was used at the output of neural network models. Three neural network algorithms were tested on a Croatian dataset. The results show that both the expert system and the neural network recognize more pupils as mathematically gifted than teachers do. The expert system produces the highest average hit rate, although the highest accuracy in classifying gifted children is obtained by the radial basis neural network algorithm, which also yields lower type II error. Due to the ability of expert systems to explain the result, it can be suggested that both the expert system and the neural network model have potential to serve as effective intelligent decision support tools in detecting mathematical gift in early stage, therefore enabling its further development. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Precocious mathematical ability of children in elementary schools is usually detected using scientifically approved standard Raven pro- gressive matrices in the process of pychological evaluation of a child. When investigating the brain activity of high-level mathematical thinking and reasoning, O’Boyle et al. (2005) used psychometrical identification of math-gifted male adolescents by SAT-Math and SAT- Verbal tests, as well as Raven standard progressive matrices. In schools where psychologists are not available, teachers usually use math- ematical competencies as the only criterion for determining a child’s gift. However, it is also important to include other components while deciding about giftedness in mathematics, as emphasized by Johnson (2000), whose research also highlights the need for accurate detec- tion and further development of mathematical gift. The paper compares the efficiency of the expert system (ES) called MathGift suggested by Pavlekovic, Zekic-Susac, and Djurdjevic (2007) and the neural network (NN) model for detecting a child’s mathematical gift in the fourth grade of elementary school. Besides mathemat- ical competencies, both systems include cognitive components of gift, personal components that contribute the gift development, strate- gies of learning and exercising, as well as some environmental factors. The initial survey (Pavlekovic et al., 2007) showed that MathGift ES detected more children as gifted than teachers did in their estimates. The ES and teachers’ estimations were compared to psychological findings (obtained by Raven’s standard matrices). Since the statistical tests showed the expert system estimations are more similar to psy- chologists’ estimations, it was challenging to test another intelligent method that has abilities of prediction, classification, and association of robust data. Therefore, three NN algorithms were tested in order to classify children in one of the two gift categories. The model is aimed to learn psychological findings, and to use the incorporated knowledge with children in schools where psychologist’s estimations are not available. A survey was conducted at ten Croatian elementary schools where the psychologists’, teachers’, and the expert system estimates were obtained for each child in the sample. The results of the expert system and the best NN model were compared. Besides finding the most accurate model, this paper discusses some differences among the estimations of children’s mathematical gift obtained by teachers, psy- chologists, the expert system and the NN model. The advantages and limitations of both approaches are also discussed. 0360-1315/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compedu.2009.01.007 * Corresponding author. Tel.: +385 31224400; fax: +385 31211604. E-mail addresses: pavlekovic@ufos.hr (M. Pavlekovic), marijana@efos.hr (M. Zekic-Susac), idjurdjevic@ufos.hr (I. Djurdjevic). Computers & Education 53 (2009) 142–154 Contents lists available at ScienceDirect Computers & Education journal homepage: www.elsevier.com/locate/compedu