A 4-year-old child, who is very interested and precocious in mathematics, was interviewed doing mathematical tasks in order to find out how advanced can a 4-year-old child be? His mathematical knowledge and ability are very high. Danny was able to count objects and add them, memorizing many of the addition facts. He was able to check if numbers are even or odd. He solved a variety of challenging addition, subtraction and multiplication problems. He could read and write large numbers in hundreds and thousands and could add large numbers. Analysis was done on the kind of problems the child was able to solve, their level of difficulty and the solution strategies the child used in light of what children usually do to solve these problems in ages 5-8 (Carpenter et al., 1999). Danny also showed creativity, including inventing problems for himself to solve and finding mathematical situations in his environment to attend to. An analysis was done on the creative components of his solutions and problem posing using the literature on creativity and creativity in mathematics learning (Leikin & Pitta-Pantazi, 2013). Interview with his mother showed that she supports Danny’s mathematical development by being responsive to his initiations and allowing him to explore his ideas autonomously. Her support was discussed in light of different support patterns of parents and what kind of support is especially beneficial to the child and encourages creativity (Leder, 1992). I discuss implications for education with an emphasis on what kindergarten and school can do to promote problem solving and creativity in mathematics.
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