5
" Donald Saari uses a combination of stories and questions to challenge students to think critically about calculus. “When I finish this process,” he explained, “I want the students to feel like they have invented calculus and that only some accident of birth kept them from beating Newton to the punch.” In essence, he provokes them into inventing ways to find the area under the curve, breaking the process into the smallest concepts (not steps) and raising the questions that will Socratically pull them through the most difficult moments. Unlike so many in his discipline, he does not simply perform calculus in front of the students; rather, he raises the questions that will help them reason through the process, to see the nature of the questions and to think about how to answer them. “I want my students to construct their own understanding,” he explains, “so they can tell a story about how to solve the problem. "
― , What the Best College Teachers Do
7
" When I interviewed one of the mathematicians in the study, he asked me if I knew how to define a function. I confessed that my knowledge was a little rusty, and that the definition I remembered memorizing in college didn’t spring immediately to mind, something about variables being related to the values of other variables. “But can you explain the basic concept in your own words?” he persisted. I stammered and began looking for the nearest exit. At that point, he tossed a pen in my direction, which I instinctively reached out to catch. “How did you catch that?” he asked. “I opened my hand and then closed it around the pen at the right moment.” “But how did you know when to open your hand and when to close it?” he pressed. After a little struggling, and some additional questioning from the mathematician, I stumbled to the conclusion that I predicted where the pen would be by observing its flight. “That’s a function,” he exploded. “You took information about where it was at this point, this point, and this point, and predicted when it would arrive in your hand.” He then turned to the board and wrote a formula. “I could have explained it this way, and that’s the way it’s ordinarily done. But when we do it that way, students just memorize formulas or definitions and really don’t grasp what’s involved in the concept. "
― , What the Best College Teachers Do
9
" Sure, they became frustrated with students at times and occasionally displayed impatience, but because they were willing to face the failures of teaching and believed in their capacity to solve problems, they tried not to become defensive with their students or build a wall around themselves. Instead, they tried to take their students seriously as human beings and treated them the way they might treat any colleague, with fairness, compassion, and concern. That approach found reflection in what they taught, how they taught it, and how they evaluated students, but it also appeared in attempts to understand their students’ lives, cultures, and aspirations. It even emerged in their willingness to see their students outside of class. "
― , What the Best College Teachers Do