MODELING AND PROOF IN HIGH SCHOOL

In this paper we propose a refinement of Chevallard's mathematical modeling process while still fully agreeing with his position that modeling is a key process in knowing mathematics. In doing this, based on our empirical study, we claim, 1) that there are at least two other stages in the mathematical modeling process; 2) that mathematical modeling is a non-linear process; and 3) there exists non-linearity at the interior of each modeling stage. We will illustrate each of these claims with episodes from our classroom intervention; one of the goals was to provide high school students the opportunity to use algebra as a modeling tool to prove.