Coordination of approximations in the understanding of the limit concept when prospective teachers anticipate students’ answers

Abstract

The aim of this study is to examine to what extent the identification of the coordination of approximations in the domain and in the range is considered a Key Developmental Understanding (KDU in Simon, 2006) by prospective teachers. 25 prospective secondary school mathematics teachers anticipated high school students’ answers to problems about the limit of a function showing different characteristics of understanding and proposed problems that would support students’ conceptual progress. Results show that identifying the coordination of the approximations in the domain and in the range as KDU allowed prospective teachers to consider progressions in students’ learning in order to support their teaching decisions.