Case 5: Teacher Candidates Engage in A Formative Assessment Practice Space

Effective mathematics instruction involves teachers eliciting and using the substance of students’ mathematical understandings to make instructional decisions during live instruction and the planning of future learning experiences. Formative assessment includes analyzing pieces of student written work to modify teaching and learning activities (Black et al., 2003). In this chapter, you will read about teacher candidates (TCs) eliciting and using evidence of student thinking (NCTM Teaching Practice #4) as they participate in a formative assessment space. The formative assessment space simulates a teacher analyzing pieces of student written work to identify student thinking and to use that thinking to plan subsequent instructional activities. Analyzing pieces of student written work is one way that a teacher can gather information about what a student knows and understands. Eliciting and using evidence of student thinking is connected to professional noticing of children’s thinking (Jacobs et al., 2010) and responsive teaching (Kavanagh et al., 2020). Professional noticing of children’s thinking involves three skills: (1) attending to student thinking, (2) interpreting students’ thinking, and (3) deciding how to respond based on interpretations of student thinking (Jacobs et al., 2010). Responsive teaching is both a teaching stance and a practice that emphasizes the importance of using the substance of student mathematical thinking to guide instructional decisions (Dyer & Sherin, 2016; Hammer et al., 2012; Richards & Robertson, 2016). Importantly, responsive teaching involves instructional moves that work to take-up and pursue student thinking rather than attempting to “fix” or “correct” student thinking (Dyer & Sherin, 2016; Richards & Robertson, 2016).