An effective mathematics teacher preparation program ensures that practice-based experiences, including mathematics methods courses and equivalent learning experiences, provide candidates with experiences using tools and frameworks grounded in research to develop core pedagogical practices and pedagogical content knowledge for teaching mathematics. |

In effective mathematics teacher programs, mathematics methods experiences utilize a practice-based approach (Ball & Cohen, 1999). The decomposition-of-practice movement (Grossman et al., 2009) engages candidates in detailed activities set in the everyday work of teaching. For example, rehearsals (Horn, 2010; Lampert, et al., 2013), launches (Jackson et al., 2013), and student-based experiences ought to play a central role in the mathematics methods class. This practice-based notion of teacher education is different from the traditional view in that teachers experience the emergence of theories from analyses of practice rather than separating the learning theories from the later application of these theories to practice (Smith, 2001).

In mathematics methods experiences, research-based frameworks, tools, and strategies serve as important vehicles for connecting theory and practice and guiding candidates in their work with authentic artifacts of teaching. For example, when focusing attention on key elements of planning a lesson, the methods instructor strategically uses planning tools that emphasize building on students’ thinking and orchestrating a productive discussion (Smith et al., 2008), teacher questioning, differentiating instruction, and culturally responsive instruction (Bay-Williams, McGatha, Kobett, & Wray, 2014).

Collaborating with clinical-experience coordinators is an effective way for methods instructors to connect their methods experiences with Pre-K–12 classrooms and children. Professional development schools are an excellent environment for collaboration. Having experiences in clinical settings prior to the student-teaching experience helps teacher candidates situate their learning in practice.

These classroom-based experiences can be enhanced through the careful selection of artifacts of practice, including the use of video and classroom-based cases. Carefully selected videos, paired with focused reflective questions, can change candidates' views of what constitutes effective mathematics instruction (Chval, Lannin, Arbaugh, & Bowzer, 2009). Videos or cases are selected to offer illustrations of practice and learning that capture real teachers teaching real children in real classrooms, including students from various backgrounds, abilities, and understandings engaging in powerful mathematics and utilizing productive strategies, thereby challenging negative racial and gender stereotypes as well as fixed mindsets about who is capable of engaging in rich and rigorous mathematics. When the selection of examples is broadened to classroom-based examples that show students learning mathematics in multiple languages (Celedon-Pattichis & Ramirez, 2012; Moschkovich, 1999, 2002; Vomvoridi-Invanovic & Chval, 2014) and cultural and community experiences (Aguirre & Bunch, 2012), programs make clear statements about not only how mathematics teaching can be effective but also for whom.