Thinking structures and mathematical achievements in children with mild intellectual disabilities

The development of thinking structures in children has a significant influence on their mastering of mathematical concepts. The appearance of concrete logical thinking and its indicators (conservation concepts) influence positive school achievement regarding mathematical contents. By shaping the formal operations which represent the final and supreme phase of cognitive development, the most complex forms of conservations become available. Combinatorics is a feature which belongs to the last phase of cognitive development; it represents the generalization of the operations acquired in the concrete operational stage. The purpose of this paper is to analyze the development of the operational thinking structures in relation to concrete logical operations (using the conservation of number, length, mass and volume) and formal operations (using combinatorics) as well as their influence on the mathematical achievement in students with mild intellectual disabilities at an later school age. For the purpose of this study we have collected a sample of 120 students of both sexes with mild intellectual disabilities. The subjects were 12 to 15-year-old, corresponding to the school age of fifth to eighth graders. Standard Piaget's conservation tasks (the assessment of number, length, mass and volume) and combinatorics have been used for the evaluation of the operational thinking. The mastery of mathematical contents was evaluated by means of a Criterium knowledge test constructed for the purposes of this study. The results have shown statistically significant differences in the mathematical Criterium knowledge test achievement among the students in our population sample, regarding the attained level of operational thinking on all tasks that have been used. Piaget's theory argues for the application of games that support reversibility, identity and conservation, which makes mathematical thinking more compliant, more active, broader, deeper, and more original