Indicator C.3.3. Anticipate and Attend to Students’ Mathematical Dispositions
Well-prepared beginning teachers of mathematics know key facets of students’ mathematical dispositions and are sensitized to the ways in which dispositions may affect students’ engagement in mathematics.
The ability to engage in mathematics must be coupled with an inclination to see such engagement as worthwhile. Teachers need to know if a student has the disposition “to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics” (NRC, 2001a, p. 131). Well-prepared beginners know about these facets of disposition and how to gather information about them from their students. This knowledge reaches beyond determining whether students like mathematics and beyond being able to answer students’ “When are we going to use this?” questions. Well-prepared beginning teachers recognize that students may attribute mathematical proficiency to innate ability or to the application of effort. They know that these dispositions, although strong at times, are not fixed. They also know the ways in which teachers and schools can inadvertently perpetuate unproductive dispositions. With this knowledge, beginners are prepared to teach in ways that move the student more toward attributing mathematical learning to effort and to extending the meaning and usefulness of mathematics in their students’ lives. Finally, well-prepared beginners recognize that disposition is a key area for involving families—in challenging the notion that mathematics is inherited and providing strategies to help their own children develop positive mathematical dispositions.
Well-prepared beginners have ways of learning about, and fostering, the mathematical dispositions of students to include confidence, flexibility, perseverance, curiosity, self-monitoring, and appreciation of mathematics. They recognize the effects of their own language, tone, and expectations in influencing dispositions and mathematical self-images of their students. More than just focusing on the kinds of mindsets that students develop in the mathematics classroom, well-prepared beginners realize that perseverance can be supported when students think that a problem is meaningful. Even though they are well prepared, beginning teachers will not initially know the kinds of variations that exist in students’ dispositions. They will not initially have many ways to integrate attention to mathematical dispositions into what often appears to be a school curriculum filled to capacity. With experience, they will develop abilities to refine their approaches to learning about dispositions of the students they teach—such as tailoring their practices to learn about very young students, students with special needs, and students with cultural backgrounds that differ from their own. Well-prepared beginners recognize that such pressures like high-stakes assessment can decrease students’ appreciation and confidence and try to minimize such pressures on students.