for the learning of mathematics

an international journal of mathematics education

Jason Cooper ,  Alon Pinto - Vol. 37 Num. 2 (2017)
 Mathematical and pedagogical perspectives on warranting: approximating the root of 18


"The root of 18 is closer to 4 than it is to 5 because 18 is closer to 16 than it is to 25". Is this statement, voiced in an 8th grade class, valid? We suggest hypothetical arguments upon which this statement might be based, and analyze them from two complementary perspectives – epistemic and pedagogical – drawing on Toulmin’s notion of field-dependence in argumentation and on Freeman’s classification of warrants based on the type of underlying intuition, belief or prior understanding. We propose that our investigation of this statement may serve as a model for inquiry in teacher preparation.