Math Wars and the Epistemic Divide in Mathematics

Abstract

(a) Why do school (K-12) students find mathematics especially difficult? (b) What is a good way to ameliorate these difficulties? (c) Would the new technology of computation fundamentally change the content of mathematics? Learning difficulties peculiar to mathematics are here traced to an epistemic schism in mathematics. Using “phylogeny is ontogeny” these difficulties are seen as reflections of actual historical difficulties. Much mathematics taught at the K-12 level is of Indo-Arabic origin: (1) arithmetic, (2) algebra, (3) trigonometry, (4) calculus. This mathematics arose in a different epistemic context, and Europe experienced difficulties in assimilating it because it recognized only a single “universal” European mathematics. This led to the real math wars, lasting for a thousand years, first over algorismus and zero and then over calculus and infinitesimals. Computers have precipitated a third math war by again greatly enhancing the ability to calculate in a way regarded as epistemically insecure. The suggested correction is to recognize the distinct epistemic setting of mathematics-as-calculation and teach it accordingly.