We discuss teaching and learning situations that surfaced when computer programming and mathematics were brought together in a course where students write computer code to explore mathematics problems. Combining programming and mathematics creates a rich ecosystem which, on top of traditional mathematics activities (writing solutions, proofs,…

Practices such as making connections between topics, prioritizing content, and identifying broad themes are essential to learning mathematics. This paper describes a project designed to integrate these synthesizing activities into an abstract algebra class. Students used a classroom wall to record and organize their collective learning and…

Educators often argue that mathematics should be taught so that the students in the course are actually "doing mathematics." Is there a consensus among mathematicians and mathematics educators as to the meaning of "doing mathematics?" In an effort to answer this question, we administered a survey to hundreds of university-level…