The Calculus Experience

In the spirit of a challenge lies the soul of resistance. Learners tend to not appreciate a challenge if it threatens their conception of self. A challenge must not throw a student’s self esteem out of gear. In the interest of fresh minds encouragement fuels their enthusiasm like no other impetus. By getting learners to participate in the classroom experience learning happens without inhibition. The tutor must remind the learner that making mistakes is by no means a taboo and numbers that were seen in the air by renowned Mathematicians were seen by human beings who were just as human as any other learner. Einstein said that he was not exceptionally smart but was just somebody who cultivated sparkling curiosity.

If we can shift the preoccupation from being smart to being inquisitive we would be alarmed by not only our intensity of participation but also our unique creative play. This is how Calculus was discovered. Unfortunately formal classrooms do not nourish learning experiences enough to stimulate unique perspectives. Isaac Newton had a different perspective when he had to find the area of a shaded region under the curve and above the axis. He felt that we should not be led to ask a specific question but a general one. The rationale behind this approach was that by answering a general question we would be able to determine the answer to the specific question.

Newton’s insight came from a shift in paradigm from the linear approach. It is not rare to find students answering difficult problems with ease but struggling to answer simple ones. This could be because a difficult problem evokes free cognitive play whereby the existing schema is rattled thus bringing about a state of cognitive anarchy. Then there is room for creating a new order. This is how shifts in perspectives are achieved. The same can be said about various physicists and Mathematicians from time to time.
Just think how delightful an experience it would be if our purpose in learning is to discover truths rather than merely get outstanding grades. Grades are just margins. Although they are important they ought not to displace the imperatives of learning which are to comprehend fundamental concepts and discover insights while solving different problems. As teaching Mathematics is enhanced by available technology such shifts in perspectives can be more easily stimulated. Classes conducted through the online medium or online tutoring have the benefits of new age approaches that encourage students to learn by asking questions even if it involves making mistakes. Why do we fall? – So that we can learn to pick ourselves up.