#kenbain

The ability to understand the principles of calculus problem-solving and to apply those principles and concepts in thinking critically through a problem outranks any capacity to reach the correct answer on any particular question.

...the best teaching can be found not in particular practices or rules but in the attitudes of the teachers, in their faith in their students' abilities to achieve, in their willingness to take their students seriously and to let them assume control of their own education, and in their commitment to let all policies and practices flow from central learning objectives and from a mutual respect and agreement between students and teachers.

[Researchers found] that they could create a stereotype threat among people who have traditionally faced only positive social images about themselves in some domain. White males, for example, face no popular notion that 'their kind' can't do math. Yet the researchers could make European American male students with good grades in advanced math courses perform less well on a difficult test if they simply told them that Asian students generally did better on the exam than did 'white students.' Suddenly, they too faced the possibility that if they stumbled on the exam, others would see them as inferior to some other group.

...when victims of negative stereotypes face a task that popular prejudice says they are not very good at but that they nonetheless want to do and believe they can do, they cannot escape the shadow of beliefs around them. If the task is particularly difficult and stressful, that pressure will trigger at least a subconscious reminder of the stereotype.

...beyond the early grades most students receive little formal help with their reading, even though the sophistication expected increases substantially as they progress through school.

At the core of most professors' ideas about teaching is a focus on what the teacher does rather than on what the students are supposed to learn. In that standard conception, teaching is something that instructors do to students...