Computational thinking and activity are a fundamental aspect of what it means to conduct scientific and mathematical work. In light of this, some propose that studentsâ€™ mathematical education should include an integration of computational activity into their mathematical experiences, giving students opportunities to engage with computational tools as they reason about mathematical concepts. In this talk, I make a case for this focus on and integration of computing in mathematics education. I present some broad rationales for this integration, as outlined in education literature and policy documents, and I propose ideas for how this might practically be implemented. As a motivating example, I present results from a study in which undergraduate novice programmers engaged with basic Python programming as they solved combinatorial problems. I demonstrate how this focus on computing is a natural extension of prior work on combinatorics education, and I highlight noteworthy aspects of studentsâ€™ experiences with using computation in a mathematical context. I conclude by framing this work within ongoing efforts to better understand the nature of computational thinking and activity for undergraduate students.