SUMMARY.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, learnercentred exploratory strategy and a deductive teachercentred 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.INTRODUCTION IF a line of regression relating learner-aptitude to learning outcome is drawn for each treatment under consideration, then non-parallelism w i l l indicate the presence of an aptitude-treatment interaction (ATI). An ordinal interaction is defined as one in which the order of treatments A and B is the same over the entire aptitude range, i.e., one treatment is superior overall (Figure 1). Where the regression line for treatment A crosses the regression line for treatment B within the aptitude range, however, the interaction is said to be disordinal and decision rules for differential instruction may be formulated. Pupils at one end of the aptitude range may be assigned with advantage to one treatment, while those at the other end of the range are assigned to the alternative treatment.Where analysis of variance is employed then mean outcome scores will be examined at blocked high and low levels of aptitude. A significant F-ratio for interaction, with crossing graphs of cell means, was formerly considered suffcient for disordinality (Lindquist, 1953 ; Lubin, 1961), but Bracht (Bracht andGlass, 1968) proposed more stringent criteria, conservative in relation to the risk of false rejection of the ordinality hypothesis. Differences between outcome means at both high and low levels of the aptitude variable were required to be separately significant, as well as opposite in sign. Reaction against the severity of this suggestion (Leith, 1972 ;Cronbach and Snow, 1973) has been based upon the extremely low probability of joint occurrence of two separately significant events. A recent distinction has been made between research set up Dr. Trown is now in the Depa...