School mathematics can share this attraction if
students are able to engage in authentic mathematical
activity. Unfortunately, “most people do not know
what mathematics is” (Devlin, 2000, p. xvii), perhaps
because they have not experienced authentic
mathematical activity and are thus dissuaded from
further mathematics study. School mathematics is
characterized by the memorization and regurgitation of
rote procedures in isolation from peers (Burton, 2004;
Stigler & Hiebert, 1999). Therefore, it comes as no
surprise that, devoid of its intellectual and social
appeal, mathematics is not motivating for many
students and that many do not continue formal
mathematics study past high school. A corrective
possibility is to harness the intellectual and social
potential of mathematics activity; allowing students to
engage in mathematical activity in their own
classrooms affords simple, straightforward options to
improving mathematics instruction by returning to root
motivational aspects of the subject.