The development of kindergartners' mental-addition strategies

According to the distribution-of-associations model, the probability of stating an incorrect or correct answer to a problem is proportional to the associative strength between the answer and the problem. To estimate the associative strength between a problem and its answers. Siegler and Shrager (1984) and Siegler (1986) used an overt-strategies-prohibited task, which encouraged children to respond quickly without counting. A schema-based view suggests that children who have not yet memorized the single-digit addition combinations may respond to such a task by using estimation strategies. Indeed, on a pretest, 14 of 21 kindergartners appeared to use mechanical estimation strategies such as stating an addend, which produced one or two distinct answers per problem. After 8 weeks of computational practice with a different set of problems, some subjects adopted new estimation strategies on the posttest. The results indicated that errors and changes in error patterns on the overt-strategies-prohibited task cannot be explained entirely in terms of practice. They also suggest that Siegler's tables of associative strengths were confounded by compiling data over children using different estimation strategies.