Mathematics viewed through the lens of information theory
(2019) Advances in Numerical Cognition Research — Location: Blankenberge (9.May.2019)
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- Abstract
- In this presentation, we will propose a new theoretical approach to the study of arithmetic problem solving. It is commonly accepted that mental arithmetic is cognitively demanding, costly and thus aversive, but little is known about the factors influencing this cognitive cost. Borrowing concepts from the field of information theory, we propose that individuals constantly construct online probability models of the environment and cognitive cost results from the need to upgrade these prior internal models. In this view, arithmetic problem solving consists in refining prior knowledge about the response range as the system progressively integrates the numerical information conveyed by the operands. We assume that the cognitive cost depends on the way each information contained in the problem will affect the predictability of the answer. To test this model, we designed an experiment where participants were asked to add two numbers presented one after each other through headphones. Prior to the experiment, participants were informed of the response range (11 to 78), so they knew the prior probability distribution of the responses. The arithmetic problems (21+7 or 6+41) combined double-digit operands, which convey much information about response predictability because they contribute to narrow down the response range, and single-digit operands, which conveys less information with regard to the response. Throughout each trial, we measured the pupil size dilation as an index of the arousal associated with the cognitive workload. As predicted by the model, results showed a stepwise increase in pupil size as participants were listening to the terms of the problem and this increase was higher after hearing a double-digit operand than after hearing a single-digit operand. This finding validates the idea that arithmetic problem solving involves adaptive strategies to refine the probability distribution of the responses and opens up perspectives to study difficulties in mathematics.
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Salvaggio, S. (2019). Mathematics viewed through the lens of information theory. Advances in Numerical Cognition Research, Blankenberge. https://hdl.handle.net/2078.5/64311