Slow maths - a metaphor of connectedness for school mathematics

Abstract

This dissertation proposes a metaphor of connectedness for school mathematics that honours the discipline of mathematics and engages students in authentic mathematical activity. It is located at the intersection of mathematics, education and philosophy, providing a fresh reading and synthesis of established ideas. It is thus an argument about what really counts in school mathematics, rather than a presentation of new empirical research. Part 1 of the thesis establishes the personal and political imperative for the thesis. It highlights the mismatch between dominant pedagogies of mathematics education and an alternative view that foregrounds students as mathematicians. I argue that the political debates that have punctuated and permeated school mathematics education over several decades are less about achievement levels or effective teaching than they are about epistemology. I examine dominant metaphors of education, arguing that they are locked into what Heidegger terms the technological enframing, casting students as products of, rather than participants in, the educational process. I describe the origins of slow food as a protest against a one-size-fits-all philosophy, and introduce the metaphor of Slow Maths as an alternative to these metaphors of education. I then re-examine the philosophical and epistemological underpinnings of mathematics education, arguing that absolutist and relativist philosophies of mathematics, rather than being binary opposites, arise from viewing mathematics from the outside and the inside, or far away and close-at-hand, respectively. Part 2 of the thesis presents extensive evidence to support three dimensions of connectedness that underpin Slow Maths: mathematical connectedness, cultural connectedness and contextual connectedness. I show that mathematics is legitimated through a knowledge mode, providing evidence that mathematics "speaks for itself". I show that it is continuously developing as a field, and describe the cultural context that promotes this development. I describe the reflexive relationship between mathematics and the world, providing evidence that mathematics both models the world and develops in response to the world. For each of these dimensions I use evidence from the discipline of mathematics itself, from the work of mathematicians and their personal narratives and from influential and contemporary mathematics education research. This thesis is unique in synthesising evidence from these three different sources in support of a philosophical position. Part 3 of the thesis moves from theory to practice. I give a practical example of a unit of work in secondary mathematics that moves beyond mechanistic solutions methods with contrived pseudo real world applications to one that has strong and rich mathematical, cultural and contextual connections. I argue for a new dimension of mathematical knowledge for teaching that I term cultural and contextual knowledge of mathematics, and provide reflections from a preservice teacher education course that affirm its value. The thesis does not purport to provide ready-made solutions. Rather it asserts the centrality of connectedness as a critical aspect of school mathematics and promotes an attitude of slowness as a way of engaging with both the discipline of mathematics and the activity of doing mathematics. Show more