Constructing Plausible, but Uncommon Stories: Gaining Subversive Insight into the School Mathematics Tradition

This chapter seeks to understand the resistance of the school mathematics tradition (Gregg, J. J Res Math Educ 26(5): 442–466, 1995) to calls for reform, specifically to calls that would have mathematics classrooms outside of geometry instruction more closely follow disciplinary norms regarding justification and proof. It argues that writing scripts of plausible potential classroom interactions with uncommon characteristics is one way of doing thought experiments that will help mathematic educators understand the above resistance. The argument proceeds by analysis of one example, a story complex called “The Great Divide.” The Great Divide assumes a class where students were taught a method to solve linear equations by writing down a standard order of equivalent equations with the result of isolating the variable and producing a value for that variable. It then examines what happens when students solve correctly, but in a non-standard way. The chapter suggests that: making such story artifacts is an important way to understand and communicate about proposed changes in teaching; stories that illustrate breaches of existing norms can be important illustrations for inservice and preservice teachers of the potential benefits for leaving the comfortable confines of the familiar on occasion; and story artifacts like The Great Divide may also be useful in classroom teaching itself to share new mathematical ideas for consideration.