Abstract
A study of two logic courses employing different modalities of information presentation (Stenning, Cox, & Oberlander, 1995) demonstrated improvements of general reasoning ability as measured by Graduate Record Exam (GRE) type analytical ability reasoning pre- and post-course tests, as well as interactions between students' pre-course aptitudes and modality of teaching. This paper investigates the reasoning processes involved in the students' solutions of one sub-scale of the GRE problems from that study by analysing their ‘work-scratchings’ on analytical reasoning (AR) items. These data are used to examine changes in what representations students select; their association with correct and incorrect solutions; the changes in selection brought about by teaching different kinds of students in different kinds of courses; the association between these changes and improvements in solution performance; and the relation between intuitive teaching recommendations and a theoretically motivated taxonomy of representations.
Stenning & Oberlander (1995) present a theory of the cognitive differences between graphical and sentential representations which ascribes major cognitive properties of graphics to weakness of expressiveness. We apply this theory to the GRE AR problems and derive principled predictions of some constraints on the appropriateness of representations for problems. Analysis of the students' spontaneous representation selections shows that representational strategies do change differentially as a result of different teaching methods; the kinds of representation proposed by intuitive teaching recommendations as embodied in ‘crammers’ are globally correlated with success at solution; the theoretically based predictions of appropriate representations based on weakness of expression make rather better predictions that can be related to individual differences between students known to be important predictors of performance. These results are argued to have important practical pedagogical implications.
