Cognitive structure and/or development		221
Classification by:	Values:		Practical illustrations
• hypothesised	• women		for teachers:
developmental		‘gaining a voice’	• evidence from
progression	•	anti-authoritarian	interviews
	•	humanistic

Carroll’s three-stratum theory of cognitive abilities

Description and intended use

This theory is the outcome of factor analyses of some 460 data sets. Carroll (1993) found evidence for a ‘substantial number of different cognitive abilities’ (p. 712) that differ in generality. The purpose of the study was to order the field of cognitive abilities and guide psychological research and thinking in that domain. Carroll’s factor analyses allowed him to identify three strata of abilities: general (applying to all cognitive tasks); broad (relating to about 10, moderately specialised abilities); and narrow (numerous abilities, specialised in specific ways). This hierarchical model does not, however, imply a tree-structure in which higher factors branch individually into clusters of subordinates. A narrow ability may have loadings on more than one factor at a higher level.

Any relevance of the theory for thinking skill taxonomies rests on the extent to which a cognitive ability can be seen as a certain, purposive facility in thinking that is also open to instruction. Since Carroll defines cognitive ability as the conscious processing of mental information that enables a more or less successful performance on a defined task (paraphrasing the original on pp. 8–10), it admits a certain, purposive facility in thinking. Elsewhere, Carroll writes, ‘No simple answer can be given to the question of whether cognitive abilities are malleable or improvable through specific types of experiences and interventions. Undoubtedly, some abilities are more malleable than others’ (p. 686). He sees general and broad abilities as relatively long-lasting and persistent attributes but allows that narrow abilities may be open to instruction. This stratum of abilities, then, could have relevance for thinking skills taxonomies. Carroll does, however, say that the general ability (g) stratum is the best predictor of ‘school success’ (p. 687) but this could reflect an absence of attempts

222 Frameworks for Thinking

to improve narrow abilities rather than a difficulty in doing so. Insofar as his data sets allowed, Carroll also looked for differences in factor structures across cultural, ethnic and racial groups and across gender and found little evidence of systematic variation.

The following list indicates what is in each level (but is highly selective at Stratum 3, where our selective focus is productive reasoning):

Stratum 1: General intelligence (likely to be correlated with speed of information processing and capacity of working memory)

Stratum 2: Broad abilities

fluid intelligence (concerned with the basic processes of reasoning that have a minimal dependency on learning)

crystallised intelligence (mental processes which depend heavily on developed abilities, especially those involving language)

indeterminate combinations of fluid and crystallised intelligence broad visual perception (involved in tasks requiring the perception

and visualisation of shapes and spatial relationships)

broad auditory perception (involved in tasks requiring the perception of sounds, including speech sounds and music)

broad cognitive speediness (involved in tasks that require rapid transmission and processing of information)

general memory ability (involved in tasks where new content or responses are held in short-term memory)

broad retrieval ability (involved in retrieval from long-term memory)

Stratum 3: Narrow abilities (approx. 170 of these) e.g.

sequential reasoning (starting from stated premises, rules or conditions and engaging in one or more steps of reasoning to reach a conclusion that follows from the premises)

induction (discovering the rules that govern the materials or the similarities or contrasts on which rules can be based)

quantitative reasoning (reasoning with concepts involving mathematical relations in order to arrive at a correct conclusion: the reasoning can be either inductive or deductive or both)

Piagetian reasoning (at different levels of complexity and abstraction)

Cognitive structure and/or development	223

visualisation (ability to manipulate visual patterns) originality/creativity (success in thinking of original verbal/

ideational responses to specified tasks)

The examples above of narrow abilities which are relevant to productive thinking are drawn from what Carroll calls ‘level factors’. These factors can exist at various levels of ability. There are also speed factors but these have not been illustrated here. In education, the prime concern is generally to establish a certain level of functioning before speed of functioning is addressed, if addressed at all. The stratum is an indication of the degree of generality but there may be intermediate strata.

Evaluation

This is not a taxonomy of thinking skills, or even of human mental abilities. However it does reflect the range of abilities and skills which have been of interest to the constructors of psychological tests and is a comprehensive attempt to order the field. The three-stratum theory makes the prediction that success in learning will very often depend to a certain extent on general intelligence and to a lesser extent on broad abilities. It also predicts that where narrow abilities are concerned, transfer is unlikely to happen spontaneously between skilled activities which make demands on unrelated abilities. These ideas have pedagogical implications and have been supported by empirical findings, for example the meta-analysis of learning skills interventions by Hattie, Biggs and Purdie (1996) which confirmed that near transfer is more readily achieved than far transfer.

The view that abilities range from general to narrow will feel intuitively sound to teachers. Carroll’s ‘ambitious attempt to create order among the primary abilities’ (Gustafsson and Undheim, 1996, p. 193) points to a hierarchy of three levels of generality and identifies abilities in each. For a teacher, the crucial matter is the extent to which these abilities are malleable. Carroll is of the view that the narrow abilities are more likely to be susceptible to instruction than abilities at higher levels. Again, this has intuitive appeal but it has yet to be substantiated. Assuming it to be correct, teachers and researchers interested in thinking should attend to areas such as sequential

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reasoning, induction, Piagetian reasoning and creative thinking. Of course, these may not be equally susceptible to instruction or equally susceptible to the same instructional strategy. However, there has to be a caveat, as the practical value of the list of narrow abilities has been questioned on the grounds that they do not seem to predict particular kinds of achievement (Ree and Earles, 1991).

We offer some further comments about the relevance of Carroll’s theory for teachers who are interested in thinking skills:

•the ‘three-stratum theory’ may be useful in thinking about thinking skills (e.g. What are the aims of a thinking skills programme? What thinking skills might be relevant? How fundamental/elemental are these skills? Are there other skills that have been overlooked? Do some skills underpin others?)

•some abilities (such as visualisation) are specific to a particular mode of representation and may not therefore be most effectively taught or assessed through different modes or even through the use of language

•the narrow abilities are founded on empirical study, but they do not map easily onto popular lists of thinking skills

•many of the narrow abilities have been studied only in laboratory settings and teachers are likely to see only about one third of them as having direct curricular or pedagogical relevance.

Summary: Carroll

				Relevance for
Purpose and structure		Some key features		teachers and learning
Main purpose(s):		Terminology:		Intended audience:
•	to provide a	•	generally uses	• researchers
	structure to guide		specialised
	research and thinking		vocabulary
Domains addressed:		Presentation:		Contexts:
•	cognitive	•	academic weighty	• academic and
•	psychomotor		tome with detailed	applied psychology
			statistical analyses