Holistic Learning and Development
Mathematics, the practical meandering explorer
Arithmophobia means the fear of arithmetic or fear of numbers.
In the United States, many people believe that only a few "gifted" individuals have "what it takes" to learn math, and that hard work cannot compensate for this. Studies have shown "When asked to explain why some children do better in math than others, Asian children, their teachers, and their parents point to hard work, their American counterparts to ability."
Math is largely perceived as a difficult subject, and I have personally observed teachers and elders’ trying to scare students by saying that math is the most difficult subject in their curriculum. Math is looked upon as this monster subject that needs extra concentration and hard work.
“What makes a mathematician is not technical skill or encyclopedic knowledge but insatiable curiosity and a desire for simple beauty.” This means you just need to be an honest and diligent explorer to be good at maths. Anyone can be good at math, we first need to unlearn that it is difficult subject. Mathematician Paul Lockhart says, "People don’t do mathematics because it’s useful. They do it because it’s interesting … The point of a measurement problem is not what the measurement is; it’s how to figure out what it is."
He makes this interesting observation when he says that doing mathematics is like telling a story:
"A mathematical argument [is] otherwise known as a proof. A proof is simply a story. The characters are the elements of the problem, and the plot is up to you. The goal, as in any literary fiction, is to write a story that is compelling as a narrative. In the case of mathematics, this means that the plot not only has to make logical sense but also be simple and elegant. No one likes a meandering, complicated quagmire of a proof. We want to follow along rationally to be sure, but we also want to be charmed and swept off our feet aesthetically. A proof should be lovely as well as logical."
In his book Measurement, he offers several ways in which one should engage with mathematics:
-The best problems are your own. Mathematical reality is yours — it’s in your head for you to explore any time you feel like it… Don’t be afraid that you can’t answer your own questions — that’s the natural state of the mathematician.
-Collaborate. Work together and share the joys and frustrations. It’s a lot like playing music together.
-Improve your proofs. Just because you have an explanation doesn’t mean it’s the best explanation. Can you eliminate any unnecessary clutter or complexity? Can you find an entirely different approach that gives you deeper insight? Prove, prove, and prove again. Painters, sculptors, and poets do the same thing.
-Let a problem take you where it takes you. If you come across a river in the jungle, follow it!
-Critique your work. Subject your arguments to scathing criticism by yourself and others. That’s what all artists do, especially mathematicians… For a piece of mathematics to fully qualify as such, it has to stand up to two very different kids of criticism: it must be logically sound and convincing as a rational argument, and it must also be elegant, revelatory, and emotionally satisfying. [But don't] worry about trying to hold yourself to some impossibly high standard of aesthetic excellence.
The first step towards becoming good at math is to not be afraid. Start from scratch; create your own mathematical theories and proofs. Each honest approach to mathematics is like exploring an untouched and undiscovered land. Let that feeling of unlocking an eternal mystery keep you going.
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