Ellen Gillard

Dual Processes in the Psychology of Mathematics Education and Cognitive Psychology

Research in the psychology of mathematics education has been confronted with the fact that people blatantly fail to solve tasks they are supposed to be able to solve correctly given their available domain-specific knowledge and skills. Also researchers in cognitive psychology have encountered such phenomena. In this paper, theories that have been developed in both fields to account for these findings are discussed. After giving a summary of the state of the art in both fields, we argue that bringing together these largely separately developed (sets of) theories creates opportunities for both domains and we suggest a way in which this can be done.

Some effort for some: Further evidence that scalar implicatures are effortful

Under the assumption of the principle of cooperation (Grice, 1989), a statement such as “some eels are fish” is thought to be false since it contains less information than is considered sufficient. However, the statement is logically sound since the meaning of “some” is compatible with “all”. Currently, the primary interpretation of such underinformative statements remains subject to debate. According to Levinson (2000), the pragmatic “some but not all” interpretation is the default interpretation, while others (e.g., Sperber & Wilson, 1995) argue that this pragmatic interpretation only comes to the fore when relevant within the context and is thus considered secondary to the logical “some and perhaps all” interpretation. In this study, three factors that may influence the answer pattern are studied: task load, working memory capacity, and repetition of the statements. In Experiment 1, we used a secondary task paradigm to manipulate the cognitive load under which a number of underinformative statements had to be judged. We observed that for participants with a rather limited working memory span it is harder to reach a pragmatic interpretation under cognitive load. In Experiment 2, we manipulated the repetition of the statements. We observed that with a higher number of filler statements, participants produced fewer consistent answer patterns. This study provides further evidence against the automaticity of the pragmatic interpretation: It shows that the pragmatic interpretation requires more cognitive effort than the logical interpretation and that increasing the number of filler statements inhibits the development of a response strategy.