Indicator C.4.2. Cultivate Positive Mathematical Identities

All mathematics teachers are identity workers in that they contribute to the kinds of identities students develop both inside and outside the classroom (Gutiérrez, 2013b). Students harbor perceptions about what someone who is good at mathematics “looks like” more so than for most subjects; even very young students can identify who in their classrooms are “good” at mathematics, often choosing those who are quick to recall facts or perform algorithms. Well-prepared beginners know that research and standards provide a different description of what being "good at mathematics" entails. For example, Adding it Up (NRC, 2001a) described a productive disposition as “the inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy” (p. 116). Well-prepared beginners seek to actively position all learners as mathematical doers. They understand that developing positive mathematical identities begins with focusing on robust goals for what is important to know and be able to do in mathematics and includes doing mathematics for one’s own sake, not just to score well on mathematics tests.

Well-prepared beginners analyze their task selections and implementation, reflecting on the ways they may shape students' mathematical identities. In addition to considering the extent to which the mathematics of the task positions learners as doers, well-prepared beginners consider the contexts of tasks. Contexts such as baseball, rocket launching, or farming may privilege a particular group of students who are familiar and interested in that context. Some classroom practices, such as board races and timed tests, have long-standing history in U.S. classrooms, despite the fact that they exclude those who need more processing time while also communicating that those who are fast are good at mathematics.

Additionally, well-prepared beginners understand that how students' peers and teachers listen to and respect their ideas affects students’ emerging mathematical identities (Aguirre et al., 2013). For example, posing higher level questions to students perceived by the teacher as more capable, though perhaps unintentional, can negatively affect the development of positive mathematical identities for those students who are not asked such questions. Similarly, students' failure to attend to one from whom they do not expect a good strategy or to take up the ideas of some group members shapes students’ mathematical identities. Issues of power and privilege arise when students judge the validity of mathematical work more on the bases of racial and gender stereotypes of good mathematics students than on the ideas presented (Esmonde & Langer-Osuna, 2013). Well-prepared beginners view their planning, teaching, and assessment as “identity-in-the-making” (Gutiérrez, 2013a, p. 53), resisting explanations that position a student as inferior or on the margins of the classroom culture when they do not participate in the ways expected; these teachers focus instead on how to adapt classroom practices to better support each student’s development of a positive mathematical identity.