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Individual differences in proof structures following multimodal logic teaching

We have been studying how students respond to multimodal logic teaching with Hyperproof. Performance measures have already indicated that students’ pre-existing cognitive styles have a significant impact on teaching outcome. Furthermore, a substantial corpus of proofs has been gathered via automatic logging of proof development. We report results from analyses of final proof structure, exploiting (i) ‘proofograms’, a novel method of proof visualisation, and (ii) corpus-linguistic bigram analysis of rule use. Results suggest that students’ cognitive styles do indeed influence the structure of their logical discourse, and that the effect may be attributable to the relative skill with which students manipulate graphical abstractions. Introduction: multimodal logical discourse Computer-based multimodal tools are giving people the freedom to express themselves in brand new ways. But what do people actually do when given these tools? Does everyone end up generating the same forms of multimodal discourse? Do multimodal systems lead to better performance than monomodal systems? These questions arise in many areas related to humancomputer interaction, but they are particularly important in educational applications, since multimodality is believed to be especially helpful to novices (di Sessa 1979, Schwarz and Dreyfus 1993). Hyperproof is a program created by Barwise and Etchemendy (1994) for teaching first-order logic (see Figure 1). Inspired by a situation-theoretic approach to heterogeneous reasoning, it uses multimodal (graphical and sentential) methods, allowing users to transfer information to and fro, between modalities (see Figure 2). We have been carrying out a series of experiments on Hyperproof, to help evaluate its effects on students learning logic. The study has established that there are important individual differences in the way students respond to logic taught multimodally (Cox, Stenning and Oberlander 1994; Stenning, Cox and Oberlander 1995). In the course of this larger study, we have built up a substantial corpus of proofs. These ‘hyperproofs’ are an unusual form of discourse, for two main reasons. Firstly, they are primarily used for self -communication: a student arranges proof steps and rules in an external representation as an aid to their individual problem-solving activities. Secondly, hyperproofs are, of course, multimodal discourse: they involve both language and graphics, and are therefore in some ways more complex than text or speech. We believe that the corpus of hyperproofs can provide a detailed insight into the paths which students follow in their Figure 1: The Hyperproof Interface. The main window (top left) is divided into an upper graphical pane, and a lower calculus pane. The tool palette is floating next to the main window, and other windows can pop up to reveal a set of goals which have been posed. Apply Extracts information from a set of sentential premises; expresses it graphically Assume Introduces a new assumption into a proof, either graphically or sententially Observe Extracts information from the situation; expresses it sententially Inspect Extracts common information from a set of cases; expresses it sententially Merge Extracts common information from a set of cases; expresses