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In this paper we attempt to map out some relationships between pedagogy and student behaviour in a mathematical microworld. We illustrate our analysis by a series of episodes which occurred in a Logo-based microworld constructed around the notions of ratio and proportion. We explore the patterns of pedagogy associated with on and off-computer activities and suggest how the teacher has significant roles in both settings; particularly in helping pupils to bridge the discursive disjuncture between the practices of Logo- and schoolmathematics.