Mathematics education is a branch of applied mathematics that is mainly concerned with K-16 mathematics teaching and learning for understanding. Mathematics education researchers develop and implement instructional programs, professional development for teachers and teacher leaders or design and implement instructional materials for students and, more generally, support teachers’ daily work in classrooms, to name a few.
One of the important areas of research includes studying effective ways students develop understandings about mathematical concepts that are addressed in K-16 education. To study these ideas, researchers often build models to describe what students understand and how these ideas become increasingly complex as their educational experiences develop along a mathematical learning trajectory.
These research programs have informed and expanded the field of mathematics education. Some important findings include:
- New developments in social learning theory
- Understanding students’ complex thinking about number, rational number and more advanced topics in mathematics
- The critical role that mathematics teacher leaders play in supporting teacher and student learning
- The role that technology and, more generally, representations play in modeling mathematical concepts
Mathematics education is not mathematics. It is a domain of professional work that makes fundamental use of highly specialized kinds of mathematical knowledge, and in that sense it can, I suggest, be usefully viewed as a kind of applied mathematics.