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Education: How to Tackle the Complex World of Calculus

A Puzzling Solution?

Calculus—the name alone is enough to make high school students groan. So what can calculus teachers do to make this demanding subject a little less dull and confusing? We talked to some of the city’s differential buffs to see how they tackle the subject in the classroom.

Damion Walker, IB math teacher from Yew Chung International School of Beijing (YCIS Beijing), has experienced his fair share of baffled students. According to him, one of the biggest problems with calculus, as compared to algebra and trigonometry, is that the concepts are very abstract. Walker stresses the importance of learning the concept itself and understanding why you do these calculations. Solving questions in calculus involves a lot of smaller algebraic and trigonometric equations, so if students lose sight of the calculus concept behind the question, they can be overwhelmed by the amount of random steps that lead to seemingly unimportant answers.

Tying these big abstract calculus concepts back to real-life situations is the best way to make sure students don’t lose sight of the point of the equation. For example, Walker sometimes has his students discuss optimizing cost or profit for a company. Even the less confident students understand the need to minimize costs and maximize profits, and so the calculus involved in calculating these questions becomes more comprehensible.

At YCIS Beijing, teachers spark interest in calculus by giving students a problem where their main focus is reaching a solution, rather than completing the smaller algebraic steps. Walker explains that in a recent brainstorming session with his students over what to write in an IB math essay, the students became so invested in their particular problem, and in finding a solution to that problem, that they completely forgot about the bad PR surrounding calculus. “I believe the desire to solve problems of their own choosing is possibly the best motivation to learn calculus that students can ever get,” Walker says.

Math teachers over at the International School of Beijing (ISB) generally agree with Walker. The biggest problem with calculus, they believe, is that the concepts are abstract and students focus too much on algebraic equations. That’s why it’s important to teach students the big picture. If it’s a particularly complicated-looking solution, a teacher can help by pointing out where calculus is used, versus where algebra is used, so that students see that the calculus part is not all that much.

If teachers have done their job correctly, they’ll find that students have begun to make connections between previous concepts and new problems. ISB also discourages rote learning in calculus. Rote learning does have its place, but students who learn by rote only become experts on questions they have already studied. For similar reasons, they also discourage math tutors, as they often just teach students the “how” of solving problems, but not the “why.” ISB’s math department explains that knowing how to do specific problems is useless, because we live in an age where we can simply look up answers to those specific questions online. An in-depth understanding of calculus, however, can’t be found online. Thus, ISB encourages students to become what computers aren’t: original thinkers.

Simon Alles, a math teacher at The British School of Beijing (BSB), Shunyi, likes to get students interested in calculus concepts through hypothetical situations. One of his favorite classroom activities is to pretend Isaac Newton and Gottfried Leibniz are having an argument about a concept in calculus, then letting students decide whose method they favor. “[This] brings to light how some students’ learning style[s] differ,” Alles explains. Contrary to ISB, Alles thinks that rote learning can be useful. Calculus students have to be able to master basic problems in order for them to become experts and find parallels between simple and more complex problems, he says.

Once you break it down, calculus isn’t really so scary. You’ve just got to understand the larger concepts and be aware of why solutions look the way they do. Calculus can be fun too! As Jack Black sings in School of Rock: “Math is a wonderful thing/Math is a really cool thing/So get off your ath, lets do some math” ... and so on and so forth.

 

Cover photo by Yew Chung International School (YCIS) of Beijing


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