Abstract
We bring two schools of research thought into a conversation. One engages with mathematics teaching, learning, and instructional design built on Freudenthal’s views of mathematics as a human activity, where learning emerges in participation. The other is Biesta’s philosophy-based perspective, where education is existential work in which students encounter the world and come to terms with it. We clarify when activities in classrooms are (or are not) mathematical, when they are (or are not) educational, and show that these pursuits align. This opens possibilities for clarifying what is involved in designing school mathematics that is both mathematical and educational.