A New Notation Emerged from Student Thinking: Comparative and Conditional Inequalities Statements

Inequalities are an important topic in school mathematics. However, there is a limited body of research examining students’ understandings of inequalities or accounts of productive ways to support students’ understandings of inequalities. In this study, we draw a distinction between two uses of inequalities, comparative and conditional inequalities, that emerged from our interactions with students. We highlight that despite reasoning quantitatively to make accurate statements with both types of inequalities, the students struggled interpreting conventional notations for one type of inequality, instead inventing their own notation. We describe a third notation we introduced which the students were able to understand and use in later teaching episodes. We conclude by discussing important implications for the teaching and learning of inequalities, including the distinction between two uses of inequalities.