Afterword: Bootleg Mathematics

Søren Kierkegaard once wrote of sitting in the Frederiksberg Garden on a Sunday afternoon, asking himself what he was going to do with his life. Wherever he looked, practical men were preoccupied with making life easier for people. Those considered the “benefactors of the age” knew how to make things better “by making life easier and easier, some by railways, others by omnibuses and steamboats, others by telegraph, others by easily apprehended compendiums and short recitals of everything worth knowing, and finally the true benefactors of the age … (making) spiritual existence systematically easier and easier…”. Kierkegaard decided, “with the same humanitarian enthusiasm as the others,” to make things harder, “to create difficulties everywhere.” (Kierkegaard, 1947, p. 194) I was reminded of this story re-reading Maxine Greene's (1978) essay “Toward Wide-Awakeness,” in her compilation entitled Landscapes of Learning. Like Kierkegaard, and like the authors in this current volume, Greene is concerned with ‘civilizational malaise’, reflecting the inability of a civilization directed toward material triumphs and improvements — higher incomes, better diets, miracles of medicine, … - to satisfy the human spirit. In education, as in social life in general, we seek out simple slogans, ‘best practices’, ‘test score increases’, and other forms of simplicity that make everything ‘easier’. Kierkegaard noted that, with so many people trying to make things easier, the only thing left would be to make things harder; he imagined people would soon be seeking out the difficulties of life, and he would be there ready. The authors in this volume, too, worry that, at least within the field of mathematics education, we find ourselves embracing the “easier” without addressing the difficulties, and, like Kierkegaard, these thinkers are here, ready for us, now that we have had enough with “the easier” and its dissatisfactions. Maxine Greene writes that making things harder for people means “awakening them to their freedom”; it means “communicating to them in such a way that they … become aware of their ‘personal mode of existence,’ their responsibility as individuals in a changing and problematic world.” (Greene, 1978, p. 162) Reading the contributions to this volume communicates our collective and individual responsibilities as mathematics educators in a changing and problematic world.