Resumen

Using the Peircean semiotic perspective, the paper introduces the notion of mathematical wealth. The first section argues the intrinsic relationship between mathematics, learners of mathematics, and signs. The second argues that interpretation, objectification, and generalization are concomitant semiotic processes and that they constitute a semiotic triad. The third argues that communicating mathematically is a powerful means of semiotic objectification. The fourth section presents the notion of mathematical wealth, the learners’ investment of that wealth, and the synchronic-diachronic growth of its value through classroom discourse. The last section discusses how teachers, with different theoretical perspectives, influence the direction of classroom discourse and the growth of the learner’s initial mathematical wealth.