The aim of this study is to assess the factors that are related to preschool children and their mothers on children's intuitional mathematics abilities. Results of the study showed that there were significant differences in children's intuitional mathematics abilities when children are given the opportunity to think intuitionally and to make estimations, and when their mothers believe in the importance of providing such opportunities in the home setting. Children who tended to think fast and to examine details of objects had significantly higher scores. Also, the working mothers aimed to give opportunities to their children more often than non-working mothers. The mothers whose children received preschool education tended to give more opportunities to their children to think intuitionally and to make estimations. When incorrect intuitional answers or estimations were made by children, lower-educated mothers tended to scold their children much more than higher educated mothers. Mothers having at least a university degree explained more often to the children why they were in error than did the less-educated mothers.