The Best Context for Understanding Mathematics is Mathematics

Recently we've spent some time with teachers discussing the practice – so ingrained in elementary and middle school math classrooms – that it is important to connect mathematics activities and exercises to the “real world.”  Though this is prevalent thinking, we take issue with the idea.

Surely mathematics has validity of itself; the ideas and reasoning that are inherent within mathematics can truly be understood only within the discipline itself. When we provide students real-life situations, they have to extrapolate or "de-contextualize" the mathematics. They, then, reason the mathematics using their knowledge of mathematical ideas. Thus, the discipline, in all its abstractness, is that which students have to understand. The real-life context does not offer the clarity of the mathematics that we suppose. As a matter of fact, it often gets in the way of the math. At best, the incorporation of real-life situations in the study of mathematics helps us to see the usefulness of mathematics in offering clarity and possible solutions for those situations. But in the end, the mathematics and the reasoning exist independent of those “real life” situations; it is part of the world of mathematics.  Perhaps if we – simply within the context of “mathematics” – grant children more time to truly investigate numbers, while helping them gain understanding of ideas that numbers and number expression convey, they could have greater success adapting this knowledge in other situations. We need to work to overestimate our belief in our students’ abilities to find the mathematics fascinating, the discipline-specific reasoning useful, and the “real mathematics” engaging.