Chapter 10: On Field(ing) Knowledge

The authors have worked together, now, for nearly twenty years. In many settings we’ve found our individual and collective way around classrooms from Kindergarten to Grade Twelve, through undergraduate classes in teacher preparation programs, up through Masters and Ph.D. level work. Sharon has been deeply involved with school assessments, provincial and cross-provincial curriculum development and implementation. Our work has been persistently (re)composed around an evolving question: How can mathematics be experienced in the classroom as a living field of knowledge? We think, for example, of some of the work that was coincident with our first connections with Professor Ernest—early, now-ancient-seeming mediations on the analogical and generative kinship fields of mathematical language (Jardine, 1990; for an expanded version, see Jardine, 1994) and early thoughts on the nature of time and its passing and how to enact a classroom practice of such matters out from under the spell of simply “managing” (Clifford & Friesen, 1993). In that 1990 paper entitled “On the Humility of Mathematical Language,” the eco-analogical character of mathematical language showed itself to be a wide, complex field of kinships and interrelationships that are not reducible to a univocal, singular sense. It was Professor Ernest’s generous response to this paper after its publication (a long, handwritten, red-ink missive sent in the post) that provided such encouragement for both of us to continue exploring this territory.