Why is it hard to engage students? Investigating epistemological theories underlying teaching and learning mathematics

There is a considerable emphasis today on bridging the gap between theory and practice. On the other hand there is a divergence of thinking through a traditional perspective that mathematics exists independently of its applications and should be taught in its pure form. The purpose of this paper is to examine the key epistemological theories underlying teaching and learning mathematics from above (i.e. traditional approaches) and mathematics from below (contemporary approaches) and how they relate to adult numeracy education. This begs the question: Why is it hard to engage students and why can’t we connect with both the real‐world and mathematical abstractions?