Philosophical In(ter)ventions in the Mathematics Classroom

• In Event: The Role of Philosophy in Elementary and Secondary Education

Abstract

Abstract: This presentation argues that philosophical inquiry has a place in the study of the elementary and secondary content areas in helping to open a “wider horizon of interpretations” that includes a critical dimension. I specifically address the case of teaching and learning of mathematics, and claim that philosophical inquiry may facilitate interrogation of the epistemological assumptions of the discipline, and thereby development of understandings that serve to complement the inferences acquired in and with mathematics per se.
1. Purpose: to offer an example of the transition from standard classroom mathematics inquiry into a form of philosophical inquiry, and the new understandings that such a multilayered inquiry can invite.
2. Theoretical framework: I use Bateson’s (2002) notion of “ extra depth” as exemplified by the metaphor of binocular vision to advocate for bringing different perspectives together. In G. Bateson’s view, an ‘extra depth’ results when two perspectives are combined, as long as the second perspective provides information on the context in which the first perspective was obtained. Philosophical inquiry promises to supply such a second perspective by way of furnishing a more global perspective regarding mathematics, its nature, and its instrumentarium. I also use O. Skovsmose’s (1994) notion of “critical mathematics education,” which emphasizes the importance of bringing a critical lens to the mathematics classroom and the general blueprint of mathematics as a method that includes not only the mode of access to the products of mathematization, but also the mode of using, interpreting, and evaluating them.
3. Methods, techniques, or modes of inquiry: I use anecdotal data from philosophical inquiries conducted with middle school students to show how the mathematical explorations based on a given mathematical task might be extended and philosophical inquiry provoked.
4. Data sources, evidence, objects, or materials: I use examples of mathematical exploration focused on developing mathematical descriptions of things in the world (built space, sporting events, songs, social events, etc.) that was then widened to include philosophical inquiry, based on questions like: Why do people use math descriptions? Are mathematical descriptions always helpful? What can we gain by using them? What might be lost in using them? Can a math description be harmful?
6. Conclusions and scholarly significance of the study or work: I conclude that the inclusion of philosophical inquiry in the mathematics classroom can provide a wider and more accessible entry point for engaging with mathematics. In addition, opening a space for philosophical inquiry in the context of communal, dialogical deliberation with peers may function not only a) to bridge students’ school mathematical experience and their experiences outside of school; b) feed and regenerate students’ curiosity towards mathematics; c) enhance their understanding of the presence of mathematics across the disciplines; and d) provide them with a metacognitive space that acts to enhance and even improve their classroom practice through enlarging their understanding of the field of mathematics as a particular discourse.

Author

• Nadia Stoyanova Kennedy, New York City College of Technology - CUNY