Is mathematics about product or process?

Several years ago, a group of mathematics educators at GVSU decided to address an issue prevalent in our course, Mathematics for Elementary Teachers I. Many preservice elementary teachers in this course viewed mathematics from a product perspective. They considered only the answer as important. In response, we attempted to be more explicit regarding the mathematical processes by revising the course using the NCTM Process Standards as a framework. Below is one of the units that we developed around the theme of polygons.

In an effort to model promising teaching practices while maintaining the focus on the Process Standards, we introduced learning centers addressing Communication, Connections, Problem Solving, Representations, and Reasoning & Proof. The following centers came from a unit with Pentominoes as the theme. The preservice teachers rotated between these centers over the course of a two-hour class at the end of the unit.

Most of the ideas for the centers came from articles in Teaching Children Mathematics - NCTM's journal supporting improvement of pre-K-6 mathematics education. The content foci for the Pentominoes Unit were Measurement and Data Analysis and Probability. Some of the centers were closely related to the activities done during the unit, such as the Connection Center. Others, like the Reasoning & Proof Center, were new contexts that applied ideas found in previous lessons.

The preservice teachers looked forward to these centers at the end of each unit and were grateful for the instructional modeling of mathematics learning centers. Many had never experienced anything but traditional mathematics instruction in their K-12 experience. Still, I am not sure that one or two courses focusing on the Process Standards is enough to provide a more balanced perspective on what it means to do mathematics. After all, the process is as important as the product.