Before reaching this stage however, one of the primary points of debate has been whether this abstract knowledge of mathematics is an innate quality that infants are born with or whether babies start out with a conceptual blank slate and mathematical abilities are progressively developed in the their minds by observing, internalizing and abstracting regularities about the world. According to the “constructivism” theory of renowned researcher Jean Piaget, the latter seems to be true and he posited that children evolve gradually through characteristic stages of thinking, known familiarly as the sensorimotor, pre-operational, concrete operations, and formal stages of thinking (Piaget, 1952). He examined how cognitive growth takes place, a proposed a model that allows for a continual “folding in” of more complex understandings. Keeping this in mind, Piaget and his many collaborators seemed to believe that young children were unable to grasp or understand... [continues]
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