Although constructivist discussions in the classroom are often treated as if they were all of the same kind, in this paper I argue that there are subtle but important distinctions that need to be made. An analysis of these distinctions shows that there is a continuum of different constructivist discussions. At one extreme are teacher-directed discussions where students are led to construct the ‘correct’ understanding of a pre-decided conclusion; at the other extreme are unstructured discussions where students are free to (...) construct any understanding. While there are many positions on the continuum, the middle ground is occupied by discussions that find a balance between teacher-control and student-independence, and between having set-answers and a free-for-all. I argue that the Community of Inquiry is a useful conception of constructivist discussions in this middle ground. (shrink)

The goal of this paper is to highlight the fact that the Philosophy for Children Approach can be used to stimulate pupil’s reflection within the framework of school subjects such as mathematics. First we situate P4C within the field of socio-constructivist epistemology. Then, P4C as adapted to mathematics is introduced. Finally, we describe an experiment linked to five types of exchanges, manifested between the beginning and the end of a school year while the pupils were learning to philosophize about mathematics. (...) In the discussion, emphasis is placed on the educational interventions of the teachers who facilitate the P4CM workshops. (shrink)

This article explains how teachers might navigate inquiry learning despite the experience of a constant tension between abandoning their students and controlling them. They do this by conceiving of themselves as guides who decide the path with students, not for them. I build on a conception of teaching as guiding from Burbules, and argue that inquiry teachers should take the particular stance of an expedition-educator (rather than the stance of either a tour-leader or an expedition-leader). They should guide students to (...) make progress during co-inquiry, rather than leading them to follow the teacher’s agenda. This stance gives a heuristic they can use to balance control and abandonment in their pedagogical practice—they judge which pedagogical actions to take, and when, according to which actions are likely to help their students to engage in autonomous inquiry and hence learn to guide themselves. Students thus can learn to inquire by participating in an inquiry which is guided, but not controlled, by their teacher. (shrink)

This article examines the possibility of philosophizing about mathematics with children. It aims at outlining the nature of the practice of philosophy of mathematics with children in a mainly theoretical and exploratory way. First, an attempt at a definition is proposed. Second, I suggest some reasons that might motivate such a practice. My thesis is that one can identify an intrinsic as well as two extrinsic goals of philosophizing about mathematics with children. The intrinsic goal is related to a presumed (...) inherent importance of presenting children with some philosophical questions about mathematics. The extrinsic goals consist of first the positive effects such a practice can have on mathematical learning and abilities and second the fostering of children's understanding of philosophical method of inquiry and thinking and therefore of their philosophical thinking competences. Third, some examples found in the literature of previously developed ways of practising philosophy of mathematics with children are presented. This article aims at giving a general outlining picture of the issues surrounding the practice of philosophy of mathematics with children and should therefore be read as an encouragement to further development and studies. (shrink)