The goal of the proposed paper is to show in what sense the approach of the community of philosophical inquiry (henceforth CPI) according to Lipman’s (1988, 2003) model can be promising for maths education.

I will take my cue from an opposition between the CPI and Rorty’s ideas on solidarity. In his obituary for Rorty, the Italian mathematician Giorgio Bagni (2007) pointed out that “[t]he connection between knowledge and social practice is really a crucial issue from the educational point of view […] Richard Rorty strongly underlined the crucial importance of the community as source of epistemic authority […]” (p. 2). While agreeing on the importance of the dimension of “social practice,” I will contest that “social practice” understood along Rortyan (1991) lines, and therefore as incompatible with any engagement with the issue of objectivity, is a valuable option for maths education.

In contrast with the Rortyan community, the CPI is committed to the “search for truth” (Gardner 1995/1996), without any capitulation, however, to a ‘Platonic’ objectivity (Rorty’s very bugaboo). This search for truth supplies the community with an inquiring horizon, which contributes to giving the dialogues a direction. While Rorty, emphasizing solidarity, stressed that “only dialogue counts and not also what the dialogue is directed to,” the sense of direction is essential in the very work of the CPI.

This discussion can be addressed from another angle and with a focus on dialogue more than on community. Paul Ernest (1994), discussing the dialogic nature of mathematics itself, showed how it “sits at the crossroads of two major currents of modern thought, the recent fallibilist tradition in the philosophy of mathematics, and the multidisciplinary use of the conversation as a basic underlying metaphor for human knowing and interaction” (p. 33). Even if we agree on taking leave of “the traditional absolutist views of mathematical knowledge” (p. 35) and on endorsing a dialogical turn in maths education, ‘dialogic philosophies’ are not equally suitable for renewing maths learning and teaching. And the idea of dialogue embodied in the CPI—this will be the first point of my paper—is more fruitful than the interpretation of dialogue in terms of conversation.

Against this backdrop, I will engage with a more specific question: if maths education has a dialogic nature, why and in what forms is a typically philosophical dialogue helpful? What distinguishes it from other inquiry-based pedagogies and, accordingly, what is the specific contribution it can afford to maths classes?

In reference to Lipman’s model of philosophical inquiry, Nadia Stoyanova Kennedy (2012a) has spoken of a sort of “interruption” that prevents students from falling into a ‘disciplinary’ slumber, that is, into the risk of taking for granted the concepts of a discipline. Simply promoting courses of (non-philosophical) inquiry may not be sufficient to ward off this danger of a disciplinary slumber. As a matter of fact, if not generated by “a genuine doubt,” in the Peircean (1877) sense, the inquiry which develops, brilliant and interesting as it may be, can be ineffective in terms of a real understanding. I will endeavour to illustrate in what sense, instead, via the deployment of philosophical inquiry according to a Lipmanian model, Pearceanly inflected,the teacher can support the development of the understanding of some concepts while enabling students to reconnect their learning of maths to the broader context of their own existence. 

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