Cognitive theories of human reasoning can benefit by distinguishing logics from implementations. An semantic analysis of the syllogism reveals what is common between apparently unrelated methods of reasoning and how such an analysis can guide experimental investigation. Existing accounts of syllogistic reasoning oppose rule-based linguistic to model-based methods. Stenning & Oberlander (1995) show that the latter are isomorphic to wellknown graphical methods correctly interpreted. We here extend these results by showing that equivalent sentential implementations exist, thus revealing that all these approaches are members of a family of abstract individual identification algorithms (IIAs) variously implemented in diagrams or sentences. We investigate whether subjects employ the IIA through an experiment using a novel reasoning task. Modelling of this data shows that behaviour is best explained at the abstract level of the IIA with consequences for the semantic and the empiri...

This paper describes an evaluation of an intelligent labelling explorer (ILEX),

Software visualization is nifty stuff; but is it the powerful cognitive tool it is often assumed to be? This chapter attempts to moderate the understandable enthusiasm for software visualization and to raise some of the questions for which the discipline doesn't yet have answers. The chapter is structured as a list of questions with discussion. The questions are not a comprehensive analysis of cognitive challenges in software visualization. Rather, the chapter attempts to provide a list sufficiently provocative to give designers pause, in order: (a) to establish that good software visualization isn't simply a matter of mimicking paper-based tasks or doing what is technically easy---and certainly isn't `solved' yet; but also (b) even simple tools can improve software comprehension, if they're the right ones.

The use of graphs to represent and reason about data is of growing importance in pre-high school mathematics curricula. This study examines middle school students' skills in reasoning about three graphical representations: histograms, scatterplots and stem-and-leaf plots. Students were asked to interpret graphs, select an appropriate graph type to represent a relationship and to generate graphs. Accuracy levels varied substantially across the three tasks and three graph types. The overall pattern of results is largely explained by the varying ease of transfer of student knowledge from a simpler graph type, based on surface similarity.

The concept map is becoming a ubiquitous tool in education. In recent years there has been a growing interest in "diagramming" or "mapping" ideas to be learned (e.g., Jonassen et al., 1998). The approach has been championed by study skills proponents such as Buzan (1993). Maps of concepts and relationships have been used by many researchers and practitioners to help diagnose misunderstanding, improve study methods and glimpse how learners come to know. In other areas, the representation of knowledge in formalisms such as the Net greatly assisted the development of intelligent tutoring systems (e.g., Sowa, 1983). In order to better understand the claims made for its efficacy, reference to how concept maps have been used and defined will lead to a plausible explanation of the process of "off-loading" of concepts during learning or study (McAleese, 1994, 1998). In order to demonstrate the widespread application of supporting learners with external "1earning spaces" (c.f. ISLEs/ and REALs-...

The design of any computer system with a multimedia interface involves the designer in fundamental theoretical questions concerning the manipulation of information expressed in a variety of forms. Furthermore, if the system is to be intelligent then it must reason with and about the information that it represents. We use the term heterogeneous reasoning to refer to this task of reasoning with information presented in multiple forms. We define a heterogeneous reasoning system (HRS) as a composite deductive system which includes multiple component subsystems, each with its own syntax, semantics, and proof theory, and which also includes deductive rules which operate between the different subsystems. In the first half of this paper we provide a formal model which is able to distinguish several important types of heterogeneous reasoning. Computer systems designers whose tasks involve the use of an HRS in an intelligent multimedia interface are typically faced with a choice of several impl...

Hyperproof is a multimodal tool designed for the teaching of first order logic. An experiment was conducted which gathered computerised logs of exam answers by a group of subjects undertaking this course. The current study utilises natural language corpus-based statistical tests to analyse the proof logs. A pre-course test was administered to the subjects on the Hyperproof class, and subjects were classified according to their performance on this test. Interesting differences in rule use and proof style were found between these groups. Considered with reference to theories of the fundamental reasoning mechanism, against the background of the individual difference literature, the current study has implications for several areas of cognitive science. First, the idea that there is just one observable reasoning mechanism underlying human inference is challenged. Second, support is provided for the position that graphical methods ought to be encouraged in reasoning. Third, with regard to hu...

Introduction 2 Cognitive styles heterogeneous visual multimodal We have been carrying out an evaluation of the effects of teaching logic with Barwise and Etchemendy's Hyperproof [1]. One of our major findings has been that individual differences between students have a significant effect on students' responses to Hyperproof: their prior cognitive style influences both the overall effectiveness of the teaching regime, and the actual proof structures that students produce under exam conditions [9, 7, 8]. Now, Barwise and Etchemendy designed Hyperproof to support reasoning, in which information from differing modalities---sentential and graphical---is combined, or transferred from one modality to another. It is obviously, therefore, a multimodal system containing a visual sub-system. But given that one group of students benefits particularly from being taught with Hyperproof, we can ask: do they do well because it is a logical system, or do they do well because it is

Computer-based logic proofs are a form of `unnatural' language discourse, but the structure and process of proof generation can be observed in considerable detail, and analysis is leading to a number of general insights. We have been studying how students respond to multimodal logic teaching. Performance measures have already indicated that students' pre-existing cognitive styles have a significant impact on teaching outcome. Furthermore, a large corpus of proofs has been gathered via automatic logging of proof development. This paper applies a series of techniques, including corpus statistical methods, to the proof logs. The results indicate that students' cognitive styles influence the structure of their logical discourse, via their differing methods of handling abstract information, and transferring information between modalities. As well as uncovering different thinking styles in this artificial domain, the observations raise the issue of the importance of individual differences in...

on the claim/reason relation) and argumentation (the deployment of informal reasoning in attempts to resolve disputes). Informal reasoning is a central component of critical thinking . How good are people are informal reasoning? U.S. studies indicate that although some are quite good at it, average levels are quite poor [13, 27]. For example, in the most thorough study of this topic, Kuhn found that a majority of the population cannot reliably produce genuine evidence for their opinions, entertain counterarguments, or rebut counterarguments. I have not found comparable studies in an Australian context, but it is plausible they would give broadly similar results. This is supported by experience in teaching. For example, I gave 95 University of Melbourne undergraduates a homework exercise in which they were asked to "analyse and evaluate the main argument" of a particular book chapter. Almost none performed the task adequately; indeed, very few even understood what the t