In this article, Daniel and Carl discuss how everyone has varying degrees of mathematical abilities. The author uses principles of logic and problem-solving to explain how mathematics is for everyone.
Mathematics is often seen as a subject set aside for those with some rare gift, those who see things in a different way. This, however, does not have to be the case. Mathematics is an activity that absolutely anyone and everyone can and should participate in. Whether it is believed or not, everyone has some mathematical ability, albeit to varying degrees. In my opinion, this makes the pursuit of mathematical knowledge even more exciting, as different areas of Mathematics require different levels of mathematical knowledge and skill. This means that you will always be able to find some interesting area of Mathematics that builds on the knowledge you already possess, starting at whatever level you are currently on — and this level can even be level zero. Using this kind of approach, everyone can enjoy at least some tiny part of the wonderful world we call Mathematics.
Mathematics is not only for the so-called gifted or genius. Mathematics can be of great use in everyone’s daily life; its ideas can be incorporated in a variety of ways. To explore this more deeply, we will have to answer the following question: What is Mathematics? Now, unfortunately, or even very fortunately, there is no one answer to this relatively simple-looking question. You will probably find as many answers to this question as the number of times you ask it. In a way, this is great. If a certain answer is not to your liking, you can search for another answer that makes it all sound more appealing, or better yet, make up your own.
To some, Mathematics is all about numbers, or at least it used to be right before they came to the conclusion that they are “not so good with numbers”. To others, it is all about solving arbitrary problems involving graphs, shapes, sequences, probabilities… or data? All of these are fields of study in Mathematics, but what is it that binds them all together — what makes out the glue? To me, the answer is quite simple: Mathematics is the science or study (just in case the term “science” is also a taboo in your mind) of logic, and it eventually leads to applying logical principles to problem-solving. Looking at Mathematics in this way might bring one to a realisation: Every field of study — every science — is, in some sense, a mathematical one, for if it were not, it would be illogical. And there is no point in pursuing something illogical (although it can, at times, be a lot of fun).
Logic is one of those fundamental building blocks that form part of the human experience, as opposed to the experience of the “lower” animals — just to be clear, an animal is in no way lower than a human; it is only an expression. The ability to think logically is very much a human thing, and this is why Mathematics can and does have so much meaning and use to so many people (people being humans, of course) around the world. To many, including myself, it is an escape (or at least it used to be before it got pretty damn hard). It takes one from the real world into an even more real one, where everything is precise, governed by the most fundamental of laws, nothing out of place, and everything in perfect peace and harmony. But before this becomes too philosophical, let’s move on with logic.
The ideas of logic can be used in so many parts of life, especially when it comes to decision-making. Now, I am not saying that after studying the logical structures found in Mathematics, you will magically be able to make the perfect decision regarding every single situation of your life. It just does not go that way. Life is too complex: there are too many variables. That, however, does not mean that you cannot employ logic as an aid in making better — though maybe not perfect — decisions.
The best piece of all this good news is that once you have developed for yourself a good foundation in Mathematical logic, it becomes a part of you, and you will not have to actively summon it: no, it will automatically weave its way into your way of thinking. Have you noticed the word “develop” there? That is right, the understanding of Mathematical logic is not a prerequisite for having some fun inside Mathematics; instead, having fun with Mathematics will lead to the eventual emergence of this understanding dormant within you. And with that, we head towards problem-solving.
The traditional belief is that Mathematics is only for those with exceptional problem-solving abilities. However, as with logic, skill in problem-solving can be gained by studying Mathematics. See how almost everything can be flipped on its head? Some see natural athletic ability as a reason to pursue sports, while others see sports as a means of improving their athletic ability. Let Mathematics be your sport, and you will find natural improvement in the skills you will eventually need to upgrade your level of Mathematics — that is, move on to a more challenging “sport”. Remember that Mathematics is a tool: let it work for you. Also, remember that to become proficient at using a tool, you need to spend some time with it, so do not expect it all to simply come to you. Struggle with Mathematics enough, and it will make you strong, at least in the case where strength refers to the understanding of mathematical logic and problem-solving skills.
“Now that I have my little toolbox of problem-solving skills, how do I actually use it; what do I apply it to? There really are not that many Mathematical problems out there in the real world, you know.” The common idea is that Mathematics is only for really specific, specialised problems. As with logic, however, problem-solving skills can be applied to a variety of real-life situations. It is all about the skill and how you choose to apply it, not where you got it from. Imagine a world where humans could only use skills as long as they are working within the subjects they picked that skill up — no carry-over, no real-world application. Then we humans would probably be called the “lower animals” by our rulers: The Elephants…
There might still be a certain group of people entertaining the notion that Mathematics, in spite of all the above, just is not for them, that they just are not “mathematical” enough. Well then, if you are one of these, you have read the above all wrong, and you will have to read it repeatedly until you are convinced. MATHEMATICS IS FOR YOU! You, like everyone else, absolutely have the ability to think mathematically!
Studies in Mathematics Education have shown that Mathematics contributes to forming competent citizens. So, go out, get your Maths on, and conquer the world!
Daniël Bester
Mathematical Science, Second-year student, Stellenbosch University
Carl-Heinrich Hancke
Physics (Laser), Student of Stellenbosch University
Bibliography:
- Marco Zarco Rotairo: “I believe that Mathematics should be for everyone because all of us have mathematical ability, but only with varying extent and degree. Also, we must let everyone enjoy the wonders of Mathematics. The notion that Mathematics is only for the gifted and the genius must change.”
- Blanca Margarita Parra Mosqueda: “Everyone needs mathematics in every aspect of their life. It is not only for specialised professional issues; it is not only for those who have a supposed gift. It is for everyone, every day.”
- Fin McLaughlin: “Many see themselves as not being mathematical or that maths is not for them, and yet it is for everyone, and everyone is capable of thinking mathematically.”
- Luis Miguel Paz Corrales: “In my opinion, access to mathematics should be democratised for everyone. Because traditionally, it has been believed that it is only for those who possess certain types of problem-solving skills. And research, mainly in Mathematics Education, has shown that Mathematics is compulsory all over the world because it contributes to the formation of competent citizens.
