Children's use of addition strategies : a closer look at procedural and conceptual knowledge.
Three issues from studies of primary children's addition are
identif ied and investigated with children between 6 and 8
years old. The first is why descriptions of strategy use
der i ved from chronometr ic studies vary so much from those
based on observation and interview. The second and third
concern the factors influencing strategy choice and are the
relation between procedural and conceptual knowledge and
characteristics of the sum. Whereas reaction time studies have been interpreted as showing that primary schoolchildren predominantly use one strategy, counting on from the larger addend (COL), interview and observation studies suggest each child uses a variety of strategies. In Experiment (1) children were given a large set of single digit additions and both their reaction times (RT) and their overt behaviour recorded. The best predictor of RT was a model based on COL. The tactic of recording both RTs and observations was continued in Experiments (2) and (3) and in Experiment (4) children were interviewed as well as timed. The major concern, however, was to investigate why children so rarely use decomposition (ie analysing a given sum into a known number fact and counting on the difference). To this end children were presented with number facts and asked to read them out prior to doing the sum. The relation between the given number fact and the sum was varied and the effect on RT determined. Presenting a number fact that was the same or a commuted version of the sum had major effects on observed and reported strategy and overall response latency. When the number facts differed by 1 or 2 from the sum children typically ignored them. Overall the utility of chronometric studies for identifying strategy use was questioned as there was much variation between studies in the best fitting RT model. Also, apart from COL, no RT model of a specific strategy made adequate predictions. Experiments (5) and (6) explored whether children do not use decomposition because they do not understand it. Awareness of the potential use of decomposition was assessed by presenting number facts and asking how these would help do particular sums. In Experiment (5), which was conducted with the participants in Experiment (4), the children were also asked to select which number facts would be useful. The same children who so rarely used decomposition demonstrated that they understood how to use it. How children's use of COL was related to understanding of
commutativity was tested in Experiment (7). While children who used COL often typicallY passed commutativity tests there
were some who did not.The influence of problem characteristics on strategy use was tested in Experiment (8) by using sums with very large second addends (eg 2 + 95). Every child who attempted these sums used the COL strategy on them whereas many never used COL on the more traditionally used single digit additions, but counted on from the first digit instead. This implies that the common practice of classifying children's strategy use on the basis of how they solve single digit sums may be misleading. In reviewing these and other findings it is concluded that what children know about number and addition strategies may bear little relation to how they solve simple addition sums. The explanation of why children choose a particular strategy may lie instead in the amount of 'cognitive effort' that is involved.