Cognitive processes in solving variants of computer-based problems used in logic teaching

The effect of two instructional variables, visualisation and manipulation of objects, in learning to use the logical connective, conditional, was investigated. Instructions for 66 first-year social science students were varied in the computer-based learning environment Tarski's World, designed for teaching first-order logic (Barwise & Etchemendy, 1992. The language of first-order logic: including the Microsoft Windows program Tarski's World 4.0 for use with IBM-compatible computers. Stanford, CA: CSLI). For all instructional conditions, the scores on the transfer tests showed a significant increase in understanding the conditional. Visualisation, operationalised as presenting only formal expressions or a geometrical reality in addition to these, showed no differences on the transfer test. If only presented formal expressions, about half of the participants needed to make drawings of the objects, especially when the problems increased in complexity. The manipulation condition, in which the participants could either construct a geometrical world or were presented a fixed world, significantly influenced the participants' cognitive processes in solving the logic problems. The students worked affirmatively and were tempted to stay in familiar situations. The results support the authors' view that visualisation facilitates cognitive processing. Moreover, the results are congruent with Piaget's theory of the development of knowledge of formal science concepts from the action with objects.