Abstract
Learning concepts can be very difficult, especially in science and mathematics. For instance, children continue to struggle with fractions even after several years of formal instruction on the topic; and adults display persistent difficulties with algebra, biology or physics. Why these failures—and what happens during the long periods of time during which learners are struggling? While most theories of conceptual learning contend that learning proceeds gradually, little step by little step, I will present evidence showing that people experience sudden Eureka moments while learning mathematics. During these episodes, an insight suddenly breaks into consciousness, leading to a leap in understanding. These findings invite us to reconsider learning mechanisms in light of theories of conscious and unconscious processing.
