A tension has been identified between the acquisition and participation metaphors for learning, and it is generally agreed that this tension has still not been adequately resolved. In this paper, we offer an alternative to the acquisition and participation metaphors for learning: the metaphor of mastering. Our claim is that the mastering metaphor, as grounded in inferentialism, allows one to treat both the acquisition and participation dimensions of learning as complementary and mutually constitutive. Inferentialism is a semantic theory which explains (...) concept formation in terms of the inferences individuals make in the context of an intersubjective practice of acknowledging, attributing, and challenging one another's commitments. We first introduce the key concepts of inferentialism and consider the perspective on learning that inferentialism inspires. Then, we condense the lessons of the inferentialist concepts into a single mastering metaphor for learning and argue that learning consists in the process by which learners come to master concepts and practices. We conclude by discussing how the mastering metaphor could be put to work in a theoretical reconciliation of the cognitive and sociocultural dimensions of learning. (shrink)

In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations of mathematical problems. As a paradigmatic example, we apply a Peircean semiotic framework to answer the question of how students learned the concept of "distribution" in a statistics course by "diagrammatic reasoning" and by developing "hypostatic abstractions," that is by (...) forming new mathematical objects which can be used as means for communication and further reasoning. Peirce's semiotic terminology is used as an alternative for notions such as modeling, symbolizing, and reification. We will show that it is a precise instrument of analysis with regard to the complexity of learning and of communication in mathematics classroom. (shrink)