Title: Investigating Subtleties of the Multiplication Principle

Date: 01/23/2018

Time: 1:15 PM - 2:45 PM

Place: 252 EH

Central to introductory probability, and a primary feature of most discrete mathematics courses, the Multiplication Principle is fundamental to combinatorics, underpinning many standard formulas and providing justification for counting strategies. Given its importance, the ways it is presented in textbooks are surprisingly varied. In this talk, I identify key elements of the principle and present a categorization of statement types that emerged from a textbook analysis. I also incorporate excerpts from a reinvention study that sheds light on how students reason through key elements of the principle. Findings from both the textbook analysis and the reinvention study reveal surprisingly subtle aspects of the multiplication principle that can be made concrete for students through carefully chosen examples. I conclude with a number of potential mathematical and pedagogical implications of the categorization.