Thinking about interactions between variables is a necessary condition for accurate scientific thinking. The purpose of this study was to investigate difficulties in thinking about interactions between variables and to suggest remedial educational means. A conceptual analysis distinguishes between valid interaction inferences, invalid interaction inferences, and limited inferences which can be seen as a partial or a primitive interaction inference. Empirical findings show that expert thinkers demonstrate thinking about interactions at both an operational and a metastrategic level. Some lay-adults however, although able to draw many limited inferences, encounter substantial difficulties in drawing valid interaction inferences while engaged in an investigation of a scientific sort. Four types of difficulties were identified in this study: lack of a “double set of controlled comparisons” strategy that is necessary for valid inferences about interacting variables; lack of the conceptual framework for interacting factors; diversion of attention to other features; and difficulty in maintaining the necessary control of other variables. The implications of the findings to science curriculum are discussed.

In this Monograph, knowledge acquisition is examined as a process involving the coordination of existing theories with new evidence. Although researchers studying conceptual change have described children's evolving theories within numerous domains, relatively little attention has been given to the mechanisms by means of which theories are formed and revised and knowledge is thereby acquired. Central to the present work is the claim that strategies of knowledge acquisition may vary significantly across (as well as within) individuals and can be conceptualized within a developmental framework. To study these strategies and their development, we use a microgenetic method. Our application of the method allows extended observation of the acquisition of knowledge within a domain, of the strategies used to acquire this knowledge, and of the change in these strategies over time. The method also allows qualitative analysis of individuals and quantitative analysis of groups to be used in complementary ways. Knowledge acquisition processes were examined at two age levels. Community college adults and preadolescents participated in two 30-45-min individual sessions each week over a 10-week period. Subjects worked on problems involving a broad range of content from both physical and social domains. A transfer design was situated within this microgenetic framework, for the purpose of assessing generality of strategies with the introduction of new content. Subjects of both ages showed progress across the 10 weeks in the level of strategies used as well as similarity in the form that this progress took. Despite initial performance levels that did not vary greatly, children showed less strategic improvement than adults and inferior knowledge acquisition. Strategic progress was maintained by both groups when new problem content was introduced midway through the sessions. The results thus indicate significant generality of strategies and strategy change across content, as well as populations. A further indication of generality was the emergence of new strategies at about the same time in the social and physical domains, even though performance in the social domain overall lagged behind that in the physical domain. At the individual level, mixed usage of valid and invalid strategies was the norm. This finding in an adult population suggests that this variability is a more general characteristic of human performance, rather than one unique to states of developmental transition. Another broad implication of this variability is that single-occasion assessment may provide an at best incomplete, and often misleading, characterization of an individual's approach. Still another implication is that at least part of variability in performance across content resides in the subject, rather than exclusively in the task. That superior strategies present in an individual's repertory are not always applied highlights the fact that more is involved in competent performance than the ability to execute effective strategies. Metastrategic competence-the ability to reflect on and manage strategic knowledge-and metacognitive competence-the ability to reflect on the content of one's knowledge-are emphasized as critical components of cognitive development. These competencies determine the strategies that are actually used, among those potentially available, and therefore the effectiveness of an individual's performance. Finally, the presence of multiple strategies and multiple forms of competence greatly complicates the portrayal of developmental change. Rather than a unidimensional transition from a to b, the change process must be conceptualized in terms of multiple components following individual (although not independent) paths.