I articulate Charles S. Peirce’s philosophy of mathematical education as related to his conception of mathematics, the nature of its method of inquiry, and especially, the reasoning abilities required for mathematical inquiry. The main thesis is that Peirce’s philosophy of mathematical education primarily aims at fostering the development of the students’ semeiotic abilities of imagination, concentration, and generalization required for conducting mathematical inquiry by way of experimentation upon diagrams. This involves an emphasis on the relation between theory and practice and (...) between mathematics and other fields including the arts and sciences. For achieving its goals, the article is divided in three sections. First, I expound Peirce’s philosophical account of mathematical reasoning. Second, I illustrate this account by way of a geometrical example, placing special emphasis on its relation to mathematical education. Finally, I put forth some Peircean philosophical principles for mathematical education. (shrink)

Although John Dewey has had the most profound effect on education, less is known about the philosophy of education of the original founder of pragmatism, Charles Peirce Using Peirce’s theory of formal rhetoric, I try to show that Peirce’s philosophy of education, when fully understood, is aligned with Dewey’s pedagogy of experiential learning, and can provide a justification for the promotion of active learning in the classroom. Peirce’s rhetoric, as one part of his logical or semiotic theory, argues that reasoning (...) alone is not sufficient to gain knowledge, but that it must be embedded within a community of inquiry, of a certain sort. Applying this to the classroom, I argue that we, as teachers, should endeavor to create the features of a proper community of inquiry in the classroom, one that emphasizes engagement of the students in doing research rather than passively receiving information about its results. (shrink)

The later works of Charles Sanders Peirce (1839–1913) offer an extended metaphor of mind and a rich conception of the dynamics of knowledge and learning. After a ‘rhetorical turn’ Peirce develops his early ‘semiotics’ into a more general theory of sign and sign use, while integrating his pragmatism, phenomenology, and semiotics. Therefore, in this article I bring Peirce's notion of semiosis—the sign's action—to the forefront. In doing so, I hope to disclose how Peirce's rhetorical turn not only opens up towards (...) a richer conception of the dynamics of knowledge and learning, but also invites a shift of perspective from the psychological processes of learning to the semeiotic processes that characterizes the very dynamics of knowledge production. (shrink)

We propose a new relational direction in higher education that acknowledges external and internal images as integrated in thinking and learning. We expand educational theory and practice that commonly rely on discrete conceptual developments that exclude images. Our argument epistemologically relies on certain semiotic views that consider the role of iconic signs and iconicity (meaning making by the virtue of similarity) as significant in relation to knowledge and learning. The analogical and imaginative work required to discover similarity between external pictures (...) and any educational concept is a form of iconic mind work that opens a space for transformational thinking and creative solutions. The novelty of our argument lies in the schematic philosophy of mind by C.S. Peirce, and specifically, an adaptation of Peirce’s triadic sign diagram for learning, exemplified via an ‘inquiry graphic’ sign and reflective method. This outlook seeks connections in diversity, arguing for an education that acknowledges and teaches intrinsic human relatedness to other humans, beings and things in the environment, thus challenging any notions of anthropocentrism and superiority. It calls for a reaction in international higher education to acknowledge the iconicity of concepts and thinking and embrace integrated image-concept signs for deep and critical teaching-learning, towards a modest educational contribution to counteracting social and environmental crises. (shrink)

Currently, there is a focus in science education on preparing students for lives as innovative and resilient citizens of the twenty-first century. Key to this is providing students with opportunities, mainly through inquiry processes, for discovery making and developing their creative reasoning by bringing school science closer to authentic science. I propose, building on the work of Woods, Magnani and the authors of a 2005 special issue of Educational Philosophy and Theory on Peirce, that these efforts can be advanced through (...) the adoption of a Peircean logic of discovery in the science classroom. I further suggest that this can only take place if a classical logic that frames school science, which deems abduction—the creative element of reasoning that drives discovery—as fallacious and not valuable as an inference making process, is replaced with a naturalised logic. Such a logic positions students as practical, not ideal agents of reasoning who in their hypothesis making are inferential-experts... (shrink)