This article presents a critical review of complexity theory in relation to educational research. The "analytical reductionist" approach is one in which the educational researcher seeks to reduce complex wholes to particular factors and to identify correlations between them and desirable outcomes. Complexity theory shows how this approach in social research is both unreliable within its own terms of reference and misdirected. Complexity theory is characterised by a number of features. These include recognition that educational systems contain multiple variables. These connect in non-linear and dynamic ways, i.e. where factors are seen to interact in a causal relationship the effects do not necessarily relate proportionally to the cause, and few factors may interact with many and many may interact with few. The crucial point of focus is on (a) the nature of the connections that are products of previous interactions reaching into the particular history of the organisation, and (b) the constitutive nature of relationships between interacting factors. Three broad conclusions emerge. The first is that contrary to the promise of reductionist analytical methodologies, research cannot deliver the specific kinds of information that are expected to inform policy and practice. The primary role of educational research becomes one of providing descriptions and explanations that provide a broader perspective on development in which decisions are primarily situation-specific. The second is to recognise that school improvement (a) rests on problematic assumptions about desirable outcomes and (b) is dependent on multiple interacting variables and is thus likely to be local and temporary. The third conclusion is that, rather than seeking to understand schools in terms of factor analysis, research needs to look at the nature of information flow and its constitutive impact on clusters of possible causes and effects.