Creative thinking is critical to overcome many daily life situations. As such, there has been a growing interest on how creative thinking develops during childhood. However, little is known about the underlying mechanisms driving its development. Indeed, almost all research has focused on divergent thinking, leaving aside convergent thinking, and did not thoroughly investigate how internal and/or external factors influence their development. Here, 222 children aged from 4 to 12 years old attending either a Montessori or a traditional school performed drawing-based convergent and divergent standardized tasks. In addition, a subset of 41 children were tested using similar tasks for a second session 3 years apart. The results revealed dynamic developmental stages of convergent and divergent thinking. More specifically, a loss of divergent thinking was counterbalanced by a gain of convergent thinking, especially during the fourth-grade slump (8--10 years old). Although Montessori-schooled children showed overall higher creative abilities than traditionally schooled children, no differences were observed in the developmental trajectories of convergent and divergent thinking between the two pedagogies. This suggests that progress and decrease in creative thinking may be mostly due to internal factors such as brain maturation factors than external factors such as peer pressure.