Understanding teacher affect, knowledge, and instruction over time: an agenda for research on productive disposition for teaching mathematics

Teacher affect heavily influences instruction and learning (Cross 2009; Pajares 1992; Philipp 2007; Robertson-Kraft and Duckworth 2014). Teacher affect, which includes partially cognitive traits such as attitudes and beliefs as well as noncognitive traits such as emotion, motivation, and grit, is often defined in opposition to purely cognitive traits such as IQ or mathematical knowledge. As a consequence, teacher affect has often been studied in isolation from teacher cognition (Philipp 2007; Thompson 1992).By contrast, some researchers collapse cognitive and partially cognitive categories, grouping mathematics teacher knowledge and beliefs together as beliefs (e.g., Leatham 2006) or as knowledge (e.g., Beswick et al. 2012). Mathematical knowledge for teaching (MKT), one of the most widely used frameworks for teacher knowledge, is defined to comprise ‘‘skills, habits, sensibilities as well as knowledge’’ (Ball et al. 2008; p. 403). Although this definition of MKT seems to include components of teacher affect, measures of MKT do not include affect-specific items (e.g., Hill et al. 2004). As these examples suggest, teacher affect is recognized as a critical area for research, but researchers have wrestled with how to conceptualize and measure constructs that are sensitive to the content and context of instruction (e.g., Herbel-Eisenmann et al. 2006; Newton 2009) and that can even seem inconsistent with teachers’ own instructional practice (cf., Francis 2015). Moreover, researchers have struggled to clarify how teacher affect changes during teacher education or in the context of established instructional practice (Philipp 2007). Managing these complex interactions has led to definitions of teacher affect constructs that are distant from teaching itself.