Rebranding Mathematics

I have been absolutely infatuated with mathematics since my junior year of highschool. I took that love of the subject and decided to pursue it in my college career. My ability and general enjoyment of the subject led me to tutor other students as they struggled with the maths that I had completed. This supporting educational role brought a few things to light: math is scary/hard, how will this be useful, and math is boring. These views broke my heart. Then the thought of "Why is math viewed this way?" crept its way into my number laden mind. The conclusion I have come to after teaching in a one on one enviroment for the past four years is that the issue is a branding or rather a presentational issue.

• How math is typically taught and presented

Math is a factual and truth diven field. I do not hold that in contention. The beauty of the field is that in our world of opinion, almosts, and constant change mathematical truths are constant(once thoroughly proven and peer reviewed). The essence of this field is then put forth to students as they learn beyond basic arithmetic. Students are cast from a world of multiplication and order of operations into an incresingly complex world of variables and functions. We drive home rules and process, students are given formulas, proofs, and example problems. The students are taught the words to this language and the general sentence structure, then we have them translate sentence after sentence with the exacting and percise tongue. The practice and rules are essential, but all to often it seems that is the end of the exposition before the next set of vocabulary and rules are presented. This process is repeated until students are up to date with what they are required to learn. Keep in mind mathematics has the added stress that previous rules are essential to the next steps. Here we run into the two core probelms; math is scary and math is boring.

The stucture of your common mathemtical presentation compounded with teachers who are burdened with hundreded of students, changing standards, and their own personal problems: is a recipe for disaster. As a result we have students who get caught up in the new mathematical topics they are learning and forget the basic logic and rules. I am not suggesting we forgoe the exposition of rules and logic. I am also not disparagining the teachers who are tasked with teaching mathematics. It is not an easy subject to learn let alone teach.

• Somethings to highlight in mathematical education

One realization that I have come to across on my numerical journey is that mathemtics is a game of optics via the rules for a given subfield of mathematics. This may feel absolutely antithetical to core of math but allow me to explain.

Take the photo at the begining of this article. Direct your attention to the fifth and fourth lines from the bottom of the final column. Here we have two terrifying integrals. Not only is integration required but we also have some crazy rational functions nestled within. Almost by magic the next line we have a the antiderivative as a function: the monstorous integrals nowhere to be found. The trick here is a crative reassigning of the variable we derived with repect to such that we can use the concept of u subsititution which rids us of the fractions in the square root. Then the problem looks like the antiderivative of some natural log function; like any calculus student that was paying attention would tell you. In all of these complicated process we did not change the core of what was being spoken about. Rather we simply changed how the equation looked so that we might pick out information to make the problem easier to solve. Much like the indidual pages of a novel while the words and setting from page to page are different, but the core story and goal of the tale has not changed. The difference is what information is moved to the forefront to allow us to recieve the most pertinet information for the question.

This takes skill with the language (the reason why the rules and such are important) but it also takes effective translation on top of some creativity. We should seek highlight the creativity needed to do math. Perhaps more so than pure calculation speed and memorization. We should seek to show our students that learning math is hard but if we are sly with how we treat variables and the like we can make many problems much easier. If we treat it more as game to win and possibly speedrun the subject becomes more engaging.

• Some extra considerations

Another common compliant and misconception from students is that they don't see how the math they learned would be useful in real life. This is problem can be a little hard to circumnavigate due to time constraints and the pacing of school years. However if we want students to appreciate the majesty and sheer pwer of mathematics we should address it. My love for science and mathematics blends in all the right places as such I am constantly recognizing the different mathematical techniques that are used and developed as necessity for scientific endeavors. Here are a few of my favorites.

Harmonic osscilations: The scientific topic that is paramount in electronics and quantum systems relies heavly on complex numbers and trigonometric functions. So you don't get cell phones without "imaginary" numbers.

Space travel: Without calculus and how it pertains to the motion of planets as approximated by newtons laws and even more so Einstein theories (although that is more so tensor calculus) amazing things such as going to the moon, gps, and space travel as a whole is not possible.

Making Bank: Investments and savings that are put into banks, stocks, and even NFTs (I'm rolling my eyes too) rely on complex formulas built around exponential functions and their behavior with respect to time and other conditions.

These are just a few of the incredible real life cases of how mathematics is used to create a world that provides us with great comforts and how it allows us to push further into the future.

Believe me, I know mathematics is hard, it is a field built around truth and accuracy. It does not seem to let any human emotion or creativity to seep through, however mathematics is a field that has toiled endlessly to be correct so that human emotion can be present elsewhere. Perhaps if we approach mathematics as what it is a tool to flex logic, and creativity in conjunction with showing students a passion for mathematics. We can highlight its prowess and make the academic bogeyman into, at worst, an aquiantance who helps us out from time to time.