Using the Five Practices to Promote Active and Equitable Learning Environments

Introduction

Research on active learning in STEM fields has found that student-centered instruction can result in deeper learning and higher achievement (Freeman et al., 2014), as well as greater persistence and self-accountability on the part of students (Braun et al., 2017; Bressoud, 2015; Laursen, 2013). Active learning (AL) may take on many different forms, appear under different labels, embrace a variety of philosophies, and/or be grounded in different design theories. Some examples include:

• 1.

  Process Oriented Guided Inquiry Learning (POGIL) and Inquiry-Based Learning (IBL). POGIL and IBL are well-known in the mathematics community as evidenced by readily available curricular materials (e.g., Rockhurst University, 2018; Straumanis et al., 2013). For a discussion on what makes inquiry particularly unique, see Laursen and Rasmussen (2019).

• 2.

  Thinking Classrooms. Thinking Classrooms (Liljedahl, 2021) enhance mathematics learning by physically transforming the classroom space. They also reformulate the ways students work and communicate, and place students at the center of the learning process.

• 3.

  Realistic Mathematics Education (RME). RME’s foundational roots (Freudenthal, 1991; Gravemeijer, 1994) have inspired a multitude of materials in post-secondary education, ranging from topic-specific lessons (Larsen & Lockwood, 2013; Wawro et al., 2012) to curricular units designed for guided reinvention across entire subject areas (e.g., for differential equations, see Rasmussen & King (2000) or Rasmussen et al. (2018)).

• 4.

  3-Act Tasks. Three-Act Tasks have earned a dedicated following of educators at all levels, PK-12 (Fletcher, n.d.; Meyer, n.d.). Three-Act Tasks harness the power of video to perplex students, engage them in deep thinking, and eventually allow students to see for themselves (by video) if they produced a reasonable solution.

• 5.

  The Five Practices for Orchestrating Productive Mathematics Discussions. The Five Practices (Smith & Stein, 2011, 2018) offer a framework for how to activate K-12 classrooms using carefully selected student work. Teacher decision-making and student explanations together help achieve the intended goals of the lesson.

The above list¹ provides evidence of the mathematics community’s movement toward and commitment to student-centered learning. Regardless of the form of AL a teacher may choose to adopt, all share the following two characteristics: (1) students are the producers of the mathematics, and (2) teachers trust that the work of students will be the centerpiece of meaningful classroom discussions. Even while every major mathematics and mathematics education professional organization has endorsed this change (CBMS, 2016), one cannot overlook the fact that embracing a shift to AL is enormously challenging for teachers.