Abstract:
Previous studies have indicated that children use mental procedures when calculating, which do not reflect the school taught algorithms, and that presentation of real world contextual problems tends to elicit these mental strategies, whereas algorithmic presentation of exercises tends to elicit school taught algorithms. This paper reports on a longitudinal study in which 104 years 2 and 3 children were presented with 2 and 3 digit addition and subtraction word problems and algorithmic exercises. Clinical interviews were undertaken over 6 interviews. The strategies students used for both word problems and algorithmic exercises were identified and compared within each interview and across the 6 interviews. Analysis of the strategies indicated a greater variety being employed for word problems than for algorithmic exercises. The highest percentage attempted were word problems and these resulted in the highest success rate. The exception to this was 3 digit regrouping problems, where the most attempted were exercises presented in algorithmic form and resulted in a higher success rate. Non traditional procedures were dominant for the first 3 interviews, however, a right-to-left strategy became the most popular strategy by interview 5. This was particularly so for algorithmic presentations. The paper also discusses how an understanding of children's spontaneous strategies may be useful for developing more effective mathematics curricula.