Undergraduate students’ conceptions of inequalities

Inequalities are vital in the production of mathematics. They are employed as specialized tools in the study of functions, in proving equalities, and in approximation or optimization studies, to enumerate only a few areas of mathematics where inequalities are put at work. The concept of inequality, however, is problematic for high school and university students alike. Moreover, school curriculum seems disconnected from the role of inequalities in mathematics and mostly presents inequalities as a subsection of equations. The placement of inequalities in the school curriculum and the disconnect between school mathematics inequalities and mathematician’s approach to inequalities take the blame of research in mathematics education reporting on students’ misconceptions when dealing with this concept. This study moves from the theory of misconceptions to a framework of undergraduate students’ conceptions of inequalities. In an effort to learn more about what students ‘see’ when dealing with inequalities, three research questions are pursued: What are undergraduate students’ conceptions of inequalities? What influences the construction of the concept of inequalities? How can undergraduate students’ conceptions of inequalities expand our insight into students’ understanding of, and meaningful engagement with, inequalities? Data for this study was produced mostly through learner-generated examples of inequalities that satisfy certain conditions. The participants in the research were undergraduate students enrolled in two mathematics courses – a foundations of mathematics course and a precalculus course. The results of this research are five conceptions of inequalities. It is also found that the undergraduate students’ conceptions of inequalities occupy mostly the lower regions of Tall’s Three Mental Worlds of Mathematics. The speculation is that the met-befores as well as the missed-befores influence the construction of the concept of inequalities. Curriculum suggestions for preparing the ground for the work on and with inequalities are offered. This study contributes to the ongoing research on mathematics concepts formation.