We explore the transition from school to university through a commognitive (Sfard 2008) analysis of twenty-two students' examination scripts from the end of year examination of a first year, year-long module on Sets, Numbers, Proofs and Probability in a UK mathematics department. Our analysis of the scripts relies on a preliminary analysis of the…

Task-cuing experiments are usually intended to explore control of task set. But when small stimulus sets are used, they plausibly afford learning of the response associated with a combination of cue and stimulus, without reference to tasks. In 3 experiments we presented the typical trials of a task-cuing experiment: a cue (colored shape) followed,…

Two intervention studies are described. Both were designed to study the effects of teaching children about the inverse relation between addition and subtraction. The interventions were successful with 8-year-old children in Study 1 and to a limited extent with 5-year-old children in Study 2. In Study 1 teaching children about inversion increased…