Final Activity Report Summary - LANGACAL04 (Language and Calculation)
In our western culture, multiplication tables are often learned through oral repetition. Does this fact influence the way in which we represent them in long-term memory? According to one of the most influential models on mathematical cognition, presented by Dehaene in 1992, it does, since multiplication facts remain stored in a verbal format. However, it has not been showed that this is the best code for learning them, and it also remains unclear whether the code used for learning arithmetical facts is the same in which they are subsequently stored. As a matter of fact, Campbell et al., in 1988 and 1992, proposed multiple representations and considered that what actually mattered was which format was used more frequently to solve multiplications. Since most of calculations were performed in Arabic digits, this format would have a privileged access to multiplication. Furthermore, a third model developed by McCloskey et al. in 1985 considered that multiplications were stored in an abstract semantic representation.
In order to check the predictions of these models a series of experiments using the number-matching task was conducted. During this task, participants saw two numbers followed by a third one and they had to decide whether the last number was one of the cues seen before. In relevant conditions, the third number, or target, was either the product of the two initial numbers or an unrelated number. Participants took longer to reject the product, indicating that the activation of the two initial numbers spread to other related numbers, such as the result of their multiplication.
In our case, we manipulated the format of numbers, including Arabic digits, written verbal numbers and auditory verbal numbers. Our rationale was that the amount of product interference found in each case would indicate the facility with which that format had access to the multiplication facts. Results indicated strong interference effects only when numbers appeared in Arabic digits, confirming the idea of Campbell that the relevant question was not that much the format in which information was learnt but the format in which it was mostly encountered and manipulated.
In order to check the predictions of these models a series of experiments using the number-matching task was conducted. During this task, participants saw two numbers followed by a third one and they had to decide whether the last number was one of the cues seen before. In relevant conditions, the third number, or target, was either the product of the two initial numbers or an unrelated number. Participants took longer to reject the product, indicating that the activation of the two initial numbers spread to other related numbers, such as the result of their multiplication.
In our case, we manipulated the format of numbers, including Arabic digits, written verbal numbers and auditory verbal numbers. Our rationale was that the amount of product interference found in each case would indicate the facility with which that format had access to the multiplication facts. Results indicated strong interference effects only when numbers appeared in Arabic digits, confirming the idea of Campbell that the relevant question was not that much the format in which information was learnt but the format in which it was mostly encountered and manipulated.