Jean Piaget underestimated the cognitive capabilities of infants, preschoolers, and elementary schoolchildren, and overestimated the capabilities of adolescents and even adults which are often biased by illogical intuitions and overlearned strategies (i.e., "fast thinking" in Daniel Kahneman's words). The crucial question is now to understand why, despite rich precocious knowledge about physical and mathematical principles observed over the last three decades in infants and young children, older children, adolescents and even adults are nevertheless so often bad reasoners. We propose that inhibition of less sophisticated solutions (or heuristics) by the prefrontal cortex is a domain-general executive ability that supports children's conceptual insights associated with more advanced Piagetian stages, such as number-conservation and class inclusion. Moreover, this executive ability remains critical throughout the whole life and even adults may sometimes need "prefrontal pedagogy" in order to learn inhibiting intuitive heuristics (or biases) in deductive reasoning tasks. Here we highlight some of the discoveries from our lab in the field of cognitive development relying on two methodologies used for measuring inhibitory control: brain imaging and mental chronometry (i.e., the negative priming paradigm). We also show that this new approach opens an avenue for re-examining persistent errors in standard classroom-learning tasks.