Deconstructing and Reconstructing the Multiplication Principle

The multiplication principle ("MP") is fundamental to combinatorics, underpinning many standard formulas and providing justification for counting strategies. Given its importance, the way it is presented in textbooks is surprisingly varied. In this talk, we identify key elements of the principle and present a categorization of statement types found in a textbook analysis. We incorporate excerpts from a reinvention study that shed light on how students reason through key elements of the principle. We conclude with a number of potential mathematical and pedagogical implications of the categorization.