Top Reasons for Everyone Should Learn Calculus
Top Reasons for Everyone Should Learn Calculus
Top Reasons for Everyone Should Learn Calculus: In my opinion, very. It is the pinnacle of mathematics. It goes beyond everything being so perfect (linear) and it is the true study of changing quantities. When you travel 60 miles an hour on average, do you really travel a full 60 miles in one hour? Calculus shows you the math behind what really happens when you travel at that speed.
Go back 500 years and literacy rates appear in the single digits. Even in the "developed" nations of the time, literacy was largely limited to the elite.
Why? Because it was common knowledge that not everyone needed to know how to read and write and thus it didn't make sense to invest the (limited) energy and resources necessary to train them to do so. Moreover, it was largely suspected that the commoner couldn't be made literate.
Top Reasons for Everyone Should Learn Calculus
The Protestant Reformation, with its emphasis on personal reading and study of scripture, helped to spark a literacy revolution in Europe. Nonetheless, only 50 years ago the global illiteracy rate was double what it is today at nearly 40%.
Now we're in the midst of a similar debate about Calculus (or more generally, advanced mathematical training). Does it make sense to invest our (limited) energy and resources in training the general population to understand Calculus? Is it even possible?
Is It Worth It?
As the printing press transformed civilization half a millennium ago, we're now facing a (much more) rapid transformation of society. Computer and Information Science, Engineering, Economics, and the Natural Sciences all make (increasingly) heavy use of the Calculus. But, perhaps more importantly, automation is replacing many menial jobs and there is an increasing demand for complex problem solving and analytic skills. Calculus (and higher mathematics in general) is a training ground to teach these skills that can then transfer to other areas of one's life. This helps explain why General Electric's CEO Jeff Immelt recently stated, "I use my math major every day — I don't use the MBA quite as much."
But careers aside, Calculus is by all measures one of humanity's most impressive intellectual accomplishments. Just as everyone should have an opportunity to see great art, hear great music, and have some comprehension of our modern understanding of the universe (note well, Calculus will be useful here), so everyone should have the opportunity to reflect on the central ideas of Calculus. Not just for utilitarian reasons, but also because there is something deeply beautiful about it. We can accomplish this without demanding full proficiency in every technique of differentiation or integration, just as one can walk through an art gallery and appreciate the great paintings without fully understanding the techniques behind every brush stroke--granted, there is an added bonus from an appreciation for the details.
Is It Possible?
I teach Calculus. In doing so, I often come up against the sentiment that some people are "math people" and some people are not. Many have come to believe that they are not, and in particular, that they are incapable of learning Calculus.
What I find so bizarre about this belief is how widespread it is and how casually it is tolerated, if not promoted, while at the same time we shudder at the thought of a society where people are taught that the majority of them were just not born to be literate.
Every semester of teaching Calculus, I'm intentional to dispel this myth. In fact, I have it listed as one of the learning goals for my course.
Carol Dweck, a psychologist at Stanford, has done some fascinating research showing that individuals are not born with a fixed intelligence level, rather intelligence can be developed. She's also shown that when students are exposed to this research, it helps them reassess how they interpret failure. If you think you are either a "math person" or not, then failing a math exam will signal to you that you must not be a math person, and so you give up. However, if you believe that intelligence is something that is developed, then failing a math exam will signal to you that you need to persevere (and perhaps do things a little differently) before you can master the material.
Very recently another team of researchers studied the brains of mathematicians and how they solve complex mathematical problems. They discovered that mathematical thinking activates different regions of the brain than other complex thinking tasks. However, we also know that advanced mathematics activates the same regions of the brain used in basic arithmetic. That is, in some deep sense, we're all wired to learn and think about complex mathematics.
It may sound trite, but again and again I've seen this work in my Calculus students. In one instance, I had a student taking my multivariable calculus class who did poorly on both of the midterms. I saw that it discouraged her--she began to check out during lectures. So I talked with her. I told her about the research and helped her reinterpret what she had seen as failure as opportunities for further growth. It reinvigorated her. In the final weeks of the course, she fully invested. She was engaged in class and was the first to appear at all of my office hours. Then the final exam came. It wasn't an easy test. She scored 100%.
At the end of the semester she shared, "This class changed my life." I don't think it is just because she then understood Stokes' Theorem. Rather, it changed her view of herself--she knew she was capable of something she had previously given up on. I suspect one of the chief reasons everyone should learn Calculus is precisely because so many people believe they can't.
Let's prove them wrong. Let's show them that they're capable of far more than they believe. Who knows what may result.
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