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)

In this paper, we explore Peirce's work for insights into a theory of learning and cognition for education. Our focus for this exploration is Peirce's paper The Fixation of Belief (FOB), originally published in 1877 in Popular Science Monthly. We begin by examining Peirce's assertion that the study of logic is essential for understanding thought and reasoning. We explicate Peirce's view of the nature of reasoning itself—the characteristic guiding principles or ‘habits of mind’ that underlie acts of inference, the dimensions (...) of and interaction between doubt and belief, and his four methods of resolving or ‘fixing’ belief (i.e., tenacity, authority, a priori, and experimentation). The four methods are then juxtaposed against current models of teaching and learning such as constructivism, schema theory, situated cognition, and inquiry learning. Finally, we discuss Peirce's modes of inference as they relate educationally to the resolution of doubt and beliefs and offer an example of belief resolution from an experienced teacher in a professional development environment. (shrink)