Encoding numbers: Behavioral evidence for processing-specific representations

Abstract

The aim of this study was to test the hypothesis of a complex encoding of numbers according to which each numerical processing requires a specific representational format for input. In three experiments, adult participants were given two numbers presented successively on screen through a self-presentation procedure after being asked to add, to subtract, or to compare them. We considered the self-presentation time of the first number as reflecting the complexity of the encoding for a given planned processing. In line with Dehaene's triple-code model, self-presentation times were longer for additions and subtractions than for comparisons with two-digit numbers but longer for subtractions than for additions and comparisons with one-digit numbers. The implications of these results for different theories of number processing are discussed.

Children's number processing is context dependent

“…Once the different circuits are integrated, there would be no reason for the resulting complex system to be different in children and adults. Accordingly, beyond differences in response times reflecting an increase in processing efficiency, the pattern of encoding times observed in children perfectly fitted adults' encoding times reported by Thevenot and Barrouillet (2006). Though the results were in line with our expectations, it could be argued that the differences in the self-presentation times of numbers were not due to differences in the encoding process per se, but to processes such as additional mental preparation or cognitive efforts put into the more difficult tasks, namely complex addition and subtraction.…”

“…Exactly as we observed in adults (Thevenot & Barrouillet, 2006), self-presentation times were shorter in the comparison (1720 ms Table 2). Out of the 27 children of this study, 16 of them exhibited the expected pattern (i.e., longer self-presentation times of the first number both in the addition and subtraction conditions than in the comparison condition), pB.002 (binomial test).…”

“…234Á235). However, in this experiment, as well as in Thevenot and Barrouillet (2006) and contrary to Campbell and Metcalfe's studies, the trials were presented to participants in a completely random order. Therefore, there was no more probability for a given trial to be preceded by a specific condition (i.e., addition, subtraction, or comparison) than another condition.…”

“…The participant was instructed to replace the letter by the first number by pressing the spacebar on the keyboard when she was ready. This procedure was introduced by Thevenot and Barrouillet (2006) to ensure that the self-presentation time of the first operand was not contaminated by any mental preparation to the forthcoming task and reflected only encoding time. In this previous study, the pattern of presentation times of the first operand was exactly the same when the signal for the task to be performed was either self-presented or displayed on screen for a fixed time of 1 s, strongly suggesting that mental preparation is terminated when participants press the key for presenting the first number.…”

“…It is exactly what we have shown (Thevenot & Barrouillet, 2006) by measuring the time that adults took to read and store two-digit numbers after being informed whether they will be subsequently involved in an addition, a subtraction, or a comparison task. Participants were presented with series of three numbers that successively appeared on a computer screen.…”