Two experiments examined reliance on schematic knowledge in source monitoring. Based on a probability-matching account of source guessing, a schema bias will only emerge if participants do not have a representation of the source-item contingency in the study list, or if the perceived contingency is consistent with schematic expectations. Thus, the account predicts that encoding conditions that affect contingency detection also affect schema bias. In Experiment 1, the schema bias commonly found when schematic information about the sources is not provided before encoding was diminished by an intentional source-memory instruction. In Experiment 2, the depth of processing of schema-consistent and schema-inconsistent source-item pairings was manipulated. Participants consequently overestimated the occurrence of the pairing type they processed in a deep manner, and their source guessing reflected this biased contingency perception. Results support the probability-matching account of source guessing.

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Based on research on expertise a person can be said to possess integrated conceptual knowledge when she/he is able to spontaneously identify task relevant information in order to solve a problem efficiently. Despite the lack of instruction or explicit cueing, the person should be able to recognize which shortcut strategy can be applied – even when the task context differs from the one in which procedural knowledge about the shortcut was originally acquired. For mental arithmetic, first signs of such adaptive flexibility should develop already in primary school. The current study introduces a paper-and-pencil-based as well as an eyetracking-based approach to unobtrusively measure how students spot and apply (known) shortcut options in mental arithmetic. We investigated the development and the relation of the spontaneous use of two strategies derived from the mathematical concept of commutativity. Children from grade 2 to grade 7 and university students solved three-addends addition problems, which are rarely used in class. Some problems allowed the use of either of two commutativity-based shortcut strategies. Results suggest that from grade three onwards both of the shortcuts were used spontaneously and application of one shortcut correlated positively with application of the other. Rate of spontaneous usage was substantial but smaller than in an instructed variant. Eyetracking data suggested similar fixation patterns for spontaneous an instructed shortcut application. The data are consistent with the development of an integrated concept of the mathematical principle so that it can be spontaneously applied in different contexts and strategies.

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One crucial issue in mathematics development is how children come to spontaneously apply arithmetical principles (e.g. commutativity). According to expertise research, well-integrated conceptual and procedural knowledge is required. Here, we report a method composed of two independent tasks that assessed in an unobtrusive manner the spontaneous use of procedural and conceptual knowledge about commutativity. This allowed us to ask (1)