Using Prior Knowledge to Advance Students’ Mathematical Understanding: Geometric Translation as a Function

Abstract

Mathematics education researchers and curriculum developers agree that instruction should be designed by considering students’ prior knowledge. The purpose of this research was to present an approach to how prior knowledge can be used in instructional design to advance students’ mathematical understanding of any mathematical subject. Translation was chosen as one of the crucial subjects for school mathematics and the education of pre-service mathematics teachers. An action research was designed drawing on the folding backs and interventions in the Pirie-Kieren theory. The participants were 28 pre-service secondary mathematics teachers studying in the fourth year of the Mathematics Teaching program at a state university. The data consists of the written answers given by the participants to the pre-test applied before the translation lessons, the recordings of the mathematical discussions that took place during the lessons, the lesson observation notes, and the notes taken during the pre-or post-lesson interviews of the instructors. Interventions that encouraged pre-service teachers to work on their prior knowings through folding backs helped them understand translation as a function. The research has the potential to provide an approach to mathematics educators who want to design instruction based on prior knowledge to support students’ mathematical understanding.