The fundamental counting principle (fcp) is a “big idea” in mathematics. It says that if an event E can occur in a ways and event F can occur in b ways, then event E followed by event F can occur in a × b ways. It is easy to understand and easy to apply. For instance, if Ng has 3 sweatshirts and 2 pairs of jeans, he has the possibility of 3 × 2, or 6, different outfits. Yet many learners whose view of mathematics is strictly procedural have little conceptual understanding of the fcp. This deficiency becomes evident when they try to remember formulas or procedures, such as those for counting various types of arrangements or subcollections. The activity described in this article offers a meaningful introduction to the principle.
Elliott Bird visits several elementary school or middle school classes every week to model constructivisit teaching and learning principles.