Regardless of the fact that people are born with innate sense of number, mathematical thinking requires certain intellectual effort for which many children are not ready. While children investigate and discover new issues in everyday life, they meet the world of mathematics although they are not aware of it. As mathematics is becoming more and more important in today's age of technology, it is very important that children are introduced to the spells of mathematics before they start attending school, and to continue to learn mathematics with that knowledge throughout school education. As well as reading, mathematics is a subject necessary for adequate functioning in society. What is more, mathematics is a subject that develops logical thinking and perception, thus mathematical teaching of children ought to be on more accessible level than it is currently. Parents and educators have access to various games and activities that involve children into mathematical thinking and creative resolving, which develops their self-confidence.Through the research that has been conducted with both preschool and primary school children using various mathematical examples appropriate for their age, it has been found out that the children of younger age have early math skills, whereas, regarding primary school children, their later math achievement is fading over time or their conclusions are grounded upon the "expected". The traditional way of teaching mathematics and extensive material can cause poor mathematical achievement and cause a well-known fear of mathematics.Keywords preschool and school children, mathematics skills, sense of space, number and quantity, math anxiety

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