مدل سازی هدیه ریاضیاتی کودکان با استفاده از شبکه های عصبی و رگرسیون لجستیک

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.

Previous research (Johnson, 2007) emphasized the need for accurate detection and further development of mathematical gift. Mathematical giftedness of children in elementary schools was detected by using mathematical tests such as SAT-Math, as well as scientifically approved standard Raven progressive matrices in the process of psychological evaluation of a child (O’Boyle et al., 2005 and Pind et al., 2003). In schools where psychologists are not available, teachers usually use mathematical competencies as the only criterion for determining a child’s gift. Pavlekovic, Zekic-Susac, and Djurdjevic (2009) created an expert system that uses five components of mathematical gift, identified upon theoretical background (Sterberg, 2001, Tannenbaum, 1983, Terman and Oden, 1959 and Vlahovic-Stetic, 2006) and heuristics, such as (1) mathematical competencies, (2) cognitive components of gift, (3) personal components that contribute gift development, (4) environmental factors, as well as (5) efficiency of active learning and exercising methods. Their research shows that MathGift ES detected more children as gifted than teachers did in their estimates, and that the expert system estimations are more similar to psychologists’ estimations. The model did not include grades of the pupils which are often used by teachers in gift detection. This paper aims to extend the previous research (Pavlekovic et al., 2009) by including pupils’ grades into the model, as well as to test quantitative methods based on learning theory in order to avoid the dependence on heuristics and human expert. To identify important selectors that teachers usually use to identify gifted children, it was challenging to test an intelligent method that has abilities of dealing with nonlinear functions in the purpose of prediction, classification, and association. Therefore, three neural network (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 be used as a part of a decision support system in schools where psychologist’s estimations are not available. A survey was conducted at 10 Croatian elementary schools where the psychologists’ and teachers’ estimates were obtained for each child in the sample. The results of the neural network model and logistic regression model were compared in terms of important predictors. The advantages and limitations of both approaches are also discussed. The output of the model was binary defined representing two categories: (1) mathematically gifted children and (2) mathematically non-gifted children. An empirical research was conducted in 2006, including pupils of age 10 (fourth grade) in 10 elementary schools in Osijek. The estimations were compared using statistical tests. The structure of the paper is the following: Section 2 contains a review of previous research in the area, followed by the description of neural network and logistic regression methodology used in the paper. The data about examinees are described in a separate section. After the results, the conclusion and guidelines for future research are given.

The paper deals with modeling children’s mathematical gift by using neural networks and logistic regression. The initial model included 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 tested by the logistic regression. The results of the best neural network model and the logistic regression model were compared on the basis of model accuracy and the selection of important variables. Although the logistic regression shows better accuracy in term of the average hit rate of giftedness category, the neural network model is more successful in recognizing gifted pupils. Both models extract a similar set of input variables as relevant. Therefore, a set of features relevant for recognizing mathematical gift can be extracted and emphasized for taking into consideration while deciding on a child’s mathematical gift. Besides mathematical competencies and grades, important features include environmental factors showing that the environment (school, family, and community) with its measures can also affect realization of a child’s mathematical gift. Future research could focus on improving the accuracy of the best model, as well on testing some other methods such as support vector machines, decision trees and other intelligent methods in addition to statistics. The suggested model could be used as a decision support tool for teachers in schools as well as a basis for further research in this area.