# Cognitive strategies in simple addition and subtraction : Process models based on analyses of response latencies and retrospective verbal reports

Sammanfattning: The purpose of this thesis is to explore cognitive processes used by children and adults when solving simple arithmetic problems, and to develop process models for describing these processes. The studies in the thesis were based mainly on analyses of response latencies and retrospective verbal reports, separately and in combination. Process models are presented, describing problem solving processes in simple addition and subtraction in children and adults. For children, reconstructive solutions, i.e., solutions where a conscious cognitive procedure is used in the process, dominated. For adults, reproductive solutions, i.e., processes in which the answer to a problem is retrieved directly from long-term memory storage, were more frequent.The process models presented in the thesis are based on a simple counter model, which is gradually revised and elaborated throughout the thesis. In the original simple counter model for addition, a counter is initially set to a starting point, normally the larger of the addends, and then incremented in steps of one, until the answer is reached. For subtraction, the counter starts on the larger number in the problem and counts down, or on the smaller number and counts up, according to a certain rule. The starting point and the number of steps to count, and steps counted, are assumed to be stored in working memory.The reconstructive strategies for addition described by children in this thesis included counting up with units of one, counting up with steps greater than one, use of "ties" (problems where the addends are equal) as reference, and idiosyncratic strategies. Consistency in strategy choice resulted in good performances. Reconstructive strategies for children's subtraction included counting up from the smaller number or down from the larger number, in steps of one or in greater steps, use of "ties" as reference, and idiosyncratic strategies. As would be expected, the number 10 was an important point of reference, especially in counting down strategies. The process model for retrieved solutions in adults' subtraction suggested that traces of originally learnt strategies were present in retrieval. Finally, judged and observed error frequencies in adults' simple subtraction problem solving were compared. Error predictions were more accurate for errors in reconstructive solutions than for errors in retrieved solutions, i.e., in more complex rather than in simpler and more automated tasks.

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