More recent studies, however, have shown that children's thinking is far more variable than such staircase models suggest.
Rather than adding by using the same strategy all of the time, children use a variety of strategies from early in learning, and continue to use both less and more advanced approaches for periods of many years.
Thus, even early in first grade, the same child, given the same problem, will sometimes count from one, sometimes, count from the larger addend, and sometimes retrieve the answer.
Even when children master strategies that are both faster and more accurate, they continue to use older strategies that are slower and less accurate as well.
This is true not just with young children, but with preadolescents, adolescents, and even adults (Kuhn, Garcia-Mila, Zohar, & Anderson, 1995; Schauble, 1996).