Numerous studies show that adults solve simple arithmetic problems more or less exclusively by retrieval the response in a network of associations stored in long-term memory (Ashcraft, 1992, 1995 and Campbell, 1995). It is recognized that the arithmetic performance of young children are based on counting or other procedural strategies that are gradually replaced by direct memory retrieval (Barrouillet & Fayol, 1998). These first results were reported by Groen and Parkman (1972) by studying the resolution time. But average latency of trials involving different procedures can lead to erroneous conclusions about how problems are solved. Other authors have preferred the method of verbal reports. But Kirk and Ashcraft (2001) question this paradigm. We propose a new paradigm to shed light on how the addition problems, subtraction and multiplication are resolved by adults and children. This paradigm takes advantage of the fact that algorithmic computation degrades the memory traces of the operands involved in the calculation (Thevenot, Barrouillet, & Fayol, 2001). The time needed by the algorithm to reach the answer and its cognitive cost lead to a reduction in the level of activation of the operands. This decrease in activation would result both from a memory decay phenomenon, which damages memory traces (Towse & Hitch, 1995; Towse, Hitch & Hutton, 1998) and from the necessary concurrent activation of transitory results, which induces a sharing of the attentional resources between the operands, their components and the intermediate results necessary to be reached to solve the problem (Anderson, 1993). Therefore, when the algorithm leads to the response, traces of the operands are degraded and retrieval the operand in memory is more difficult. This phenomenon should be more pronounced for large numbers since arriving at the result requires more steps and more time. Thus, contrasting the relative difficulty that adults or children encounter in recognizing operands after either their involvement in an arithmetic problem or their simple comparison with a third number can allow us to determine if the arithmetic problem has been solved by an algorithmic procedure or by retrieval of the result from memory: If operands are more difficult to recognize after the operation than after their comparison, we can assume that an algorithmic procedure has been used. On the contrary, if the difficulty is the same in both conditions, then the operation has most probably been solved by retrieval, a fast activity that does not imply the decomposition of the operands
