This thesis represents a study among elementary school children regarding different approaches to computing. In the theoretical part of the thesis we begin with children's early math knowledge, that is, how a child learns during his/her childhood and play until he comes to school. Since the main idea of this thesis are children's strategies for problem solving that they meet in math problems, in the next few chapters children's understanding of calculations and proccesses in which children learn to compute with whole numbers from preschool age and concrete objects which were established in the direct formation of the situation to methods that do not depend so much on the problem, they are mathematically more refined and rely on a standard computing algorithm, are thoroughly explained. In this work we showed in what way students learn and which diffuculties they meet during their learning. Acquiring new teaching material and its successful usage later, allows a good teacher. We are all aware which part a teacher has in class, upbringing and education of children. The goal was to gain insight into our schools and the work of teachers, so interviews and the surveys with teachers from different schools in Zadar are put forward. Besides this, the research among students has been also carried out. There were 214 participants, students of the 3rd, 4th and 5th grade. The students solved the tasks we have made specifically for this research. The research showed the development of children's strategies in the lower grades of elementary school. Students start resovlving computation tasks with disaggregation of tens and units strategies, and later they use written computation strategy. The next thing we explored was the difference between boys and girls in using strategy and evaluating results. It has been shown that boys use the strategy of computation operations more efficiently, and girls have a better estimation in some tasks in the 5th grade. Finally, we showed the opinions and attitudes of the teachers of the Zadar schools regarding the textbooks used in the teaching of mathematics. Through the conducted survey and interviews, we concluded that teachers mostly use textbook material and are generally satisfied with the chosen mathematical textbook.