Children's thinking has often been described as something like a staircase, in which children first use one approach to solve problems, then adopt a more advanced approach, and later adopt a yet more advanced approach.
For example, students of children's basic arithmetic (e.g., Ashcraft, 1987) have proposed that when children start school, they add by counting from one; sometime during first grade, they switch to adding by counting from the larger addend; and by third or fourth grade, they add by retrieving the answers to problems.