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Dialogue and Learning in Mathematics Education is concerned with communication in mathematics class-rooms. In a series of empirical studies of project work, we follow students'' inquiry cooperation as well as students'' obstructions to inquiry cooperation. Both are considered important for a theory of learning mathematics. Special attention is paid to the notions of `dialogue'' and `critique''. A central idea is that `dialogue'' supports `critical learning of mathematics''. The link between dialogue and critique is developed further by including the notions of `intention'' and `reflection''. Thus a theory of learning mathematics is developed which is resonant with critical mathematics education.