How Diagrams Can Improve Reasoning

Abstract

We report an experimental study on the effects of diagrams on deductive reasoning with double disjunctions, for example: Raphael is in Tacoma or Julia is in Atlanta, or both. Julia is in Atlanta or Paul is in Philadelphia, or both. What follows? We confirmed that subjects find it difficult to deduce a valid conclusion, such as Julia is in Atlanta, or both Raphael is in Tacoma and Paul is in Philadelphia. In a preliminary study, the format of the premises was either verbal or diagrammatic, and the diagrams used icons to distinguish between inclusive and exclusive disjunctions. The diagrams had no effect on performance. In the main experiment, the diagrams made the alternative possibilities more explicit. The subjects responded faster (about 35 s) and drew many more valid conclusions (nearly 30%) from the diagrams than from the verbal premises. These results corroborate the theory of mental models and have implications for the role of diagrams in reasoning.

Teachers’ and Students’ Preliminary Stages in Physics Problem Solving

“…The respondents of the first category performed stages that could help them lead to successful solution. This data also support finding of Bauer and Johnson-Laird (1993) that diagrams helped learners solve a problem more effectively and efficiently.…”

Against Logical Form

“…The model theory makes the opposite prediction, because an exclusive disjunction has two models whereas an inclusive disjunction has three models. The results corroborate the model theory (see, e.g., Bauer & Johnson-Laird, 1993). A new formal rule theory, however, could accommodate these results by changing the rules to make exclusive disjunction basic.…”

Mental models of Boolean concepts

“…The evidence corroborating this account of deductive reasoning has been described elsewhere, and it falls into three main categories. First, inferences that call for multiple models are more difficult than inferences that call for only a single model: they take more time and are more likely to elicit errors, e.g., inferences from exclusive disjunctions are easier than inferences from inclusive disjunctions (e.g., Bauer & Johnson-Laird, 1993). Second, the meanings of clauses and the situations to which they refer modulate the interpretation of Boolean connectives and influence the conclusions that individuals draw from them -as a consequence the meaning of, say, conditionals transcends a purely Table 2 The truth table for the exclusive disjunction: The switch isn't on or else the battery is dead.…”