In so many introductory science classes, the chemist [Dudley Herschbach] observed, students encounter what they see as "a frozen body of dogma" that must be memorized and regurgitated. Yet in the "real science you're not too worried about the right answer... Real science recognizes that you have an advantage over practically any other human enterprise because what you are after- call it truth or understanding- waits patiently for you while you screw up.
Ken BainDonald 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.
Ken BainSimply put, the best teachers believe that learning involves both personal and intellectual development and that neither the ability to think nor the qualities of being a mature human are immutable. People can change, and those changes--not just the accumulation of information--represent true learning.
Ken BainMots clés learning change best-teachers
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.
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