Students’ Productive Struggles in Mathematics Learning

Using a predetermined framework on students' productive struggles, the purpose of this study is to explore high school students' productive struggles during the simplification of rational algebraic expressions in a high school mathematics classroom. This study is foregrounded in the anthropological theory of the didactic, and its central notion of a "praxeology" - a praxeology refers to the study of human action, based on the notion that humans engage in purposeful behavior of which the simplification of rational algebraic expressions is an example. The research methodology comprised a lesson study involving a sample of 28 students, and the productive struggle framework was used for data analysis. Findings show that the productive struggle framework is a useful tool that can be used to analyze students' thinking processes during the simplification of rational algebraic expressions. Further research is required on the roles that noticing and questioning can play for mathematics teachers to respond to and effectively support the students' struggles during teaching and learning.