One frequent question that I get from students is some form of “when will this ever be useful to me?” or “what is the real-life application of this?” These questions are typically asked with relation to mathematics problems. As an educator, the correct answer that I am supposed to give (according to the rules of the international teachers code) is some version of “engineers/scientists/coders use these types of skills to build ________ (insert name of the latest hi-tech gadget or cool-sounding technology in an attempt – although it will not satisfy the student’s original question – to dissuade him from continuing to push the issue).”
Well, since today is Labor Day in East Africa. I’ve decided to take a break from the teacher code and tell you all the truth:
Beyond foundational topics, you’ll likely never use most of what you learn in your mathematics classes. The same can be said for many other classes as well.
I once had a student who was interested in pursuing a career in medicine. We were studying calculus and he often lamented about how he would not need to use calculus as a doctor. Being a guardian of the sacred teacher code I knew that I couldn’t let that sentiment stand in my classroom. I approached a doctor friend of mine and asked her to give me examples of how she used mathematics in her day-to-day work. If I could get the backing of a whole doctor, then I’d be sure to eliminate the attack on my classroom’s integrity.
Sɛ ɔbaa no ka anyansasɛm bi ara a, fa w’aso kɔ fam. Ɛnyɛ Ntikuma na ɔkyerɛɛ ne se Ananse kwan a ɛsɛ sɛ ɔde nyansa kukuo no foro dua no? Sɛ mmɔfra no mpo de nyansadwen ba a, fa.If a woman speaks some wise words, take your ears to the ground (listen humbly). Was it not Ntikuma that showed his father Ananse the Spider what he needed to do to be able to climb the tree with the pot of wisdom? If children even come with wise thoughts, then we should indeed take those wise thoughts.
To my surprise the doctor actually validated what the student said! She told me that, with the exception of simple arithmetic used in calculating patient dosages that they truly did not use much (if any) advanced mathematics in their day-to-day work. When I began to think about it further I realized that, even as an engineer, I did not use many of the advanced mathematics topics that I learned in school. The reality is that if you approach an engineer with 10 or 20+ years of experience and ask him about a calculus or differential equations problem, he will likely have no idea how to solve the problem without first researching it online or in a textbook.
So then what is the point? If we, as professionals in science, technology, or engineering, will likely never be asked to use partial integration to find the volume of cones or be tasked with writing a proof that shows that two angles are congruent according to the side-angle-side theorem, then why do we learn this stuff?
The answer is that in science, technology, or engineering you may actually need these skills in the context of solving more complex problems. And although professionals typically use softwares to perform complex calculations for us, knowledge of the underlying mathematics is still useful in troubleshooting or debugging.
But what if we’re not pursuing a career in STEM?
One thing that most do not understand about education is that the content knowledge – the math formulas and algorithms, the literature passages, the dates in history class, the grammar rules, and all of the chemical formulas – is not the only purpose of our education. The content knowledge is only half of the picture. Learning the content is obviously necessary, but we must also simultaneously learn how to learn.
New college and university students soon realize the difference between their teachers in secondary (middle and high) school and their college professors. One of the main differences is that in secondary school students are taught by their teachers while in post-secondary colleges and universities students must begin to teach themselves. This applies to STEM and non-STEM subjects alike. Secondary school has teachers, post-secondary colleges and universities have professors. A teacher’s job is to teach, while a professor’s job is to profess.
If we think back to who we consider to be our best teacher, it will likely be a teacher from secondary school. College professors tend to have greater content knowledge and more credentials related to their field. However, greater content knowledge and greater credentials do not translate into better teaching. Teaching is a separate skill from knowing. Having advanced knowledge in one’s head does not at all ensure that one will be able to effectively transfer that knowledge into someone else’s head.
The Most Important Skill
So then, the most important skill is not the content that we learn – the math, the science, the coding; the most important skill is knowing how to teach oneself – how to figure things out without instruction. This is one reason why homeschooled students tend to perform better in post-secondary institutions than students from private or public schools. Homeschool students, often due to their parents’ schedules, learn early on to become independent learners. In that way, they get a jump start in learning skills that other graduates will only begin to learn during their years in college or university.
Technology is constantly changing. New programs, new computer models, and new tools are always developing and replacing technologies that were once considered cutting-edge. Having a well-honed ability to teach oneself new things then becomes one of the most valuable skills for an engineer/scientist/technologist/mathematician. The same may be said of entrepreneurs.
Because of this, learning how to learn mathematics and science becomes just as valuable for the medical student or the liberal arts student as it does for the engineering student. Focusing on learning the process of how you learn is the best way to maximize the benefits of studying any subject.
So, when will you use this stuff? You’ll use the same thought processes that you used to learn the foreign concepts of arcsine, arccosine, and arctangent to figure out how to build your own website for your new business venture. You’ll use the same step-by-step method that you used to learn how to solve quadratic equations to figure out the rules for how to market your company’s products in that new country. You’ll use the same logic that you followed in creating that geometric proof to learn how to model using that new software platform.
Every person has two educations: the one which he is given, and the one that he gives to himself.