According to previous findings, math anxiety already occurs at early school age and is negatively correlated with math achievement. So far, however, little is known about the nature of math anxiety in young children. To fill this gap, we present the results of a longitudinal study on the math anxiety of children that were followed in the first year of elementary school. We tested the level of math anxiety and its prevalence. We also investigated the reasons for math anxiety that were reported by the children at the beginning of elementary education. For this purpose, we adopted both individual-difference and developmental perspectives. The results show that first-grade students experienced mild math anxiety that peaked at the beginning of the school year. Most children experienced a low level of math anxiety; some of them were not anxious at all or experienced moderate anxiety, while only a few children were highly math anxious. The reasons for math anxiety that were most frequently reported by the students were associated with risk of failure, task difficulty, time pressure, and fear of receiving a bad grade. We discuss the obtained results in the context of actions aimed at improving the mathematical achievement of students.