Using the 5 Practices in Mathematics Teaching

This article highlights three of the eight Mathematics Teaching Practices (MTP) published in the National Council of Teachers of Mathematics' (NCTM's) "Principles to Actions: Ensuring Mathematical Success for All" (2014): (1) facilitating meaningful mathematical discourse (MTP 4); (2) posing purposeful questions (MTP 5); and (3) eliciting and using evidence of student thinking (MTP 8). In this article, the authors discuss the meaning of the term "active learning" and discuss the five practices (Smith and Stein 2011) as a particularly illuminating model. The five practices offer a powerful framework that the authors have used to activate their mathematics classrooms. They share two vignettes of classroom learning from a first-year calculus class at a small university. Such teaching and learning experiences span all levels, K-16. The article's focus is on the implementation and management of active instructional practices, irrespective of mathematical content. The article includes examples of student feedback from having experienced active learning in their college mathematics class.