S ummary . A mathematical task was used among 432 junior school pupils in a search for personality‐teaching strategy interactions. Factors of sex, ability, anxiety, extraversion, model and teaching strategy were incorporated into a replicated design. An inductive, learner‐centred exploratory strategy and a deductive teacher‐centred supportive strategy each employed the same mathematical models. There was no evidence of strategy‐ability or strategy‐extraversion interactions but the strategy‐anxiety interaction was significant. Linear functions, relating the retained learning outcome to anxiety score, were used as the basis of decision rules for differential instruction. Pupils at the lower end of the anxiety range may be assigned to the exploratory strategy and those at the upper end of the range to the supportive strategy if advantage is taken of the disordinal nature of the observed interaction. The consistency of a negative linear relationship between outcome and anxiety for the exploratory strategy contrasted with the complex pattern associated with the supportive strategy. In the latter case, linear functions of differing sign afforded predictability for subgroups of introverts and extraverts and for subgroups of low ability and high ability children. When all data were combined for the supportive strategy, however, a non‐linear relationship was revealed.