Teachers Have a High Regard for Their Students
Teachers’ demonstration of respect and regard for students as individuals and for their ideas serves to create a positive relationship between students and teacher (which has repeatedly been linked to students’ positive valuation of a discipline and their experiences of success; cf. D’Amato, 1992). In addition, a teacher’s demonstration of respect is integral to the creation of a safe classroom atmosphere wherein student thinking is the basis for instruction and mistakes are treated as a learning opportunity (Lampert, 2001). Thus, in terms of mathematical practices, holding high regard for one’s students might lead to the creation of opportunities for students to express their ideas, to justify the reasonableness of those ideas, and to revise their thinking in light of mistakes.
Teachers Believe That All Students Can Succeed
Teachers’ belief that all students can succeed has implications for the ways that they might organize their classrooms and make decisions about the curriculum. Specifically, a teacher who believes that all students can succeed is unlikely to partition his or her classroom into ability groups and is more likely to attempt to reduce status differences by employing pedagogical practices wherein students can learn from one another and can learn about and benefit from their differences (Cohen & Lotan, 1995). For example, such a teacher might organize whole-class discussions and ensure that all students have an opportunity to contribute to the discussions in a substantial way. Doing so effectively with a heterogeneous class requires being especially diligent about emphasizing students’ accountability to others for making sure that everyone understands so that all students have access to the content of conversations.