Indicator C.2.4. Analyze Teaching Practice
Well-prepared beginning teachers of mathematics are developing as reflective practitioners who elicit and use evidence of student learning and engagement to analyze their teaching.
To effectively reap the benefits of the process of reflection, teachers must base their instructional decisions on evidence of student thinking and reasoning (Wiliam & Leahy, 2015) (See Standard 3.3). Well-prepared beginners analyze the formative assessments used in a lesson to determine both student conceptions and future instruction. They recognize that their analyses must go beyond identifying an overall need and determine precise issues that an intervention could directly support (Hodges, Rose, & Hicks, 2012). For example, a diagnostic interview using a missing-addend problem (e.g., 12 + __ = 23) could reveal a gap in a student’s knowledge about the meaning of the equal sign. This information can lead to changes in instruction, such as ensuring that equations are written in a variety of ways in future lessons or the creation of an intervention for Tier 2 instruction incorporating a number balance.
Well-prepared beginning teachers of mathematics recognize that the processes of data collection, analysis, and reflection and the corresponding revision to classroom practices are systematic and continuous and grow in sophistication with teaching experience. Eventually this deliberate examination of practice helps well-prepared beginners become more reflective about their own teaching practices. Various tools enable teachers to design and analyze mathematics teaching. Using these tools, the teacher gathers evidence on students' multiple mathematical knowledge bases and culturally responsive teaching (Aguirre & Zavala, 2013; Roth McDuffie et al., 2014). Well-prepared beginners have the disposition to ask important questions like “How might I get better at this practice I am developing?” and “What other teaching practices might I prioritize?”
Reflecting on one’s teaching must not be solely at the individual level. The continuous monitoring of one’s practice leads well-prepared beginners to seek out collaborators or critical friends (Schuck & Russell, 2005) to observe one another's teaching, examine students’ work samples as a team, and, in concert, consider how particular teaching moves supported or inhibited student understanding and next instructional steps, more specifically. Abandoning carefully designed instructional plans is difficult, but if teaching practices are not working well for students’ long-term gains and evidence points to better ways of proceeding, change is necessary. Well-prepared beginners are committed to collaborative analyses of teaching, open to receiving and giving feedback, and capable of making conscious instructional choices on the basis of actual evidence of teaching practice. Changing professional norms encourage teacher-to-teacher collaboration through professional learning communities and formal mentoring and coaching programs. In addition, social media (e.g., blogs; Instagram; Mathematics twitter blogosphere (#MTBoS)) provide virtual spaces for teachers to connect and reflect on their instructional practices.