Learning abstract concepts with computers. The experience of users learning about correlation

This paper reports the results of a study of students' reactions to working with a prototype version of Correlation Explorer, a small program implemented using HyperCard on the Macintosh. This program is intended for use by students who already have had an introduction to correlation and scattergrams. It allows them to explore a number of aspects of correlation such as the relationships between the number of points and significance levels, the value of Pearson's r and the distribution of the points.

The philosophy guiding the development of Correlation Explorer was that computer-aided software should not lecture to you: that is best done by lecturers and by books. Rather it should use the strengths of the computer, which lie in interactivity and calculation, to help learners get a "feel" for or an understanding of concepts they are trying to grasp. Correlation Explorer is an attempt to strip away from a CAL package all text and instructional content. At the same time it attempts to help learners get to grips with what is essentially an abstract concept, viz. correlation, in a concrete way.

The main aims of this study were twofold. First, to identify problems with usability. Second, to investigate learning in a situation with minimal instructions where there is little to correct misconceptions or guide students. Six undergraduates, who had recently learned about correlation and scattergrams for the first time were allowed to `play' with the program with very limited prior instructions. Subjects were instructed to use the program with no specific task specified. They were briefly shown the features of the program and were provided with a short printed description of the major functional parts of the program. Their activity was recorded for 20 minutes using two video cameras arranged as a split screen, one showing the user and the other displaying the computer screen. They were asked to give a continuous set of think aloud verbal protocols (Ericsson & Simon, 1984) based on what they were doing with the scattergram on screen. Following this they reviewed the video with the researcher with a combination of open ended questions and post-event protocols (Preece, 1994).

Preliminary analysis of the data indicates that:

i) Using a sequential analysis of the subjects' activities there was a strong difference in approach which could be interpreted in terms of Marton's distinction of Holistic and Atomistic learning (Marton, 1988).

ii) Despite the absence of a specific task and the exploratory nature of the program there was clear evidence that subjects were learning by thinking as well as by doing (Carroll and Mack, 1984). Typically, a serendipitous "doing" was followed by significant examples of "learning by thinking" as evidenced by the verbal protocols.

iii) On the basis of their verbal protocols, even in 20 minutes subjects were learning significantly about the nature of correlation and scattergrams.

iv) There were several usability problems connected with the transfer of mental models derived from prior learning with other Macintosh programs, for example erroneously double-clicking.

A number of questions are raised by this study. It is clear that some learning can take place even in conditions of minimal didactic guidance and this in turn raises the issue of where the best balance between abstract and concrete and between exploratory and guided approaches to learning lies. Moreover, any answer to this is affected by the educational context of use, be it remedial, `compulsory for all' or merely available. Results suggest that verbal protocols and video recording are useful ways of capturing students' experience of learning with CAL software and are encouraging enough for the authors to be engaged on further developments of the program.