However limited our knowledge of astronomy, most of us have learned to pick out certain clusterings of stars from the infinity of those that crowd the northern skies and to name them as the familiar Plough, Orion, and the Great Bear Few of us would identify constellations in the southern hemisphere that are instantly recognizable by those in Australia.
Our predilection for reducing the complexity of elements that constitute our lives to a more simple order doesn’t stop at star gazing. In numerous ways, each and every one of us attempts to discern patterns or shapes in seemingly unconnected events in order to better grasp their significance for us in the conduct of our daily lives. The educational researcher is no exception.
As research into a particular aspect of human activity progresses, the variables being explored frequently turn out to be more complex than was first realized. Investigation into the relationship between teaching styles and pupil achievement is a case in point. Global distinctions between behaviour identified as progressive or traditional, informal or formal, are vague and woolly and have led inevitably to research findings that are at worse inconsistent, at best, inconclusive. In reality, epithets such as informal or formal in the context of teaching and learning relate to ‘multi-dimensional concepts’, that is, concepts made up of a number of variables. ‘Multi-dimensional scaling’, on the other hand, is a way of analysing judgements of similarity between such variables in order that the dimensionality of those judgements can be assessed (Bennett and Bowers, 1977). As regards research into teaching styles and pupil achievement, it has been suggested that multi-dimensional typologies of teacher behaviour should be developed. Such typologies, it is believed, would enable the researcher to group together similarities in teachers’ judgements about specific aspects of their classroom organization and management, and their ways of motivating, assessing and instructing pupils.
Techniques for grouping such judgements are many and various. What they all have in common is that they are methods for ‘determining the number and nature of the underlying variables among a large number of measures’, a definition which Kerlinger (1970) uses to describe one of the best-known grouping techniques, ‘factor analysis’. We begin the chapter by illustrating a number of methods of grouping or clustering variables ranging from elementary linkage analysis which can be undertaken by hand, to factor analysis, which is best left to the computer. We then outline one way of analysing data cast into multi-dimensional tables. Finally, we append a brief note on a recent, sophisticated technique for exploring multivariate data.
Seven constructs were elicited from an infant school teacher who was invited to discuss the ways in which she saw the children in her class (see Chapter 19). She identified favourable and unfavourable constructs as follows: ‘intelligent’ (+), ‘sociable’ (+), ‘verbally good’ (+), ‘well-behaved’ (+), ‘aggressive’ (−), ‘noisy’ (−) and ‘clumsy’ (−).