The development of addition problem solving skills in grade one children : a microgenetic approach.

Thesis (M.A.)-University of Natal, Pietermaritzburg, 2000.This thesis replicates and explores some of the recent findings by Robert Siegler regarding the development ofaddition skills in grade one children. Siegler states that children employ a number ofdifferent strategies to solve single digit addition problems, these strategies coexist and compete, and cognitive variability is an essential aspect of cognitive development. He also advocates the use ofthe microgenetic approach in order to explore cognitive development. Many of Siegler' s observations were replicated while the microgenetic approach produced valuable information. Consideration of Siegler's work resulted in two research questions being formulated, both concerning the actual selection of strategies. First, a prediction analysis was employed to test the hypothesis that children attempt to match the most appropriate strategy to the problem presented according to a principle ofleast effort (defined as the attempt to maximise benefit and minimise cost). The predictions were stipulated prior to the analysis and were based on the arithmetic development literature. It was predicted that children would tend to retrieve the answers to small problems and tie-problems or calculate the answer by counting on from the larger addend by the amount indicated by the small addend (which involves reversing the order of the addends when the first addend is the smaller of the two). The strategy selections (n=229) made by a sample of 12 grade one learners on 21 single digit addition problems were categorised and compared to the predictions. The prediction analysis reduced the expected error by 63%, supporting the least effort model of strategy choice. The result is statistically significant (2=10.231,