…in all departments of knowledge, as experience proves, any one who has studied geometry is infinitely quicker of apprehension than one who has not.
– Plato, Republic (VII)
When students begin having trouble with their math, the question they ask most often is, “Why do I even need to know this? Am I ever going to use it?” Of course, we want to affirm the value of what a student is doing in a way that makes sense to them, and so we flip open to the “applications” section of their textbook. But a careful examination of those problems reveals something very startling: the math that most students learn does not apply to really real life. In order to apply high-school level algebra to real life, we need to construct problems so carefully that they no longer resemble real-life situations even in the slightest.
If George is twice Anne’s age plus 10, and if George’s age minus Anne’s age is 21, how old are they?
A student with some algebra under his/her belt will tell you that George is 32 and Anne is 11 (you can verify that these numbers fulfill both conditions stated in the problem). But here’s the thing – so what? This variety of problem is presented by many mathematics textbooks as an example of how math applies to real life, but no one has ever encountered a problem like this in real life. The student who says “but when will we use this?” deserves to be listened to. The fact is, the majority of the time one does not use sophisticated mathematics in everyday life.
Maybe we’re just not getting sophisticated enough. Say that we flip open a textbook to the quadratic equation section, where we might find a problem like this:
The path of a ball thrown at an angle from a 4-meter high platform is found to follow a path described by the equation
How far does the ball travel before hitting the ground?
The problem here is the same as before, namely that the information you are supposed to have access to is so much more obscure than the answer you’re supposed to provide. You’re really telling me that it’s possible to determine – down to the third decimal place – an equation describing the ball’s motion, but it’s not possible to just plain measure how far it travels? In real life, no one is ever presented with a question where they have access to this sort of information and are asked for this sort of answer. (The problem is more interesting when posed in a Physics course, in which case different information is given to the student and the requested response makes more sense.)
Well wait, math is everywhere. It’s used in banking, in making purchases, in measuring ingredients for cooking, in measurement of land for development, and in measurement of rhythm for music. Of course it’s used in real life!
Obviously, this is correct. Math really is “all around us,” as the same textbooks referred to above claim. But the sort of computational skills required to tackle truly “real-life” math are not what most students spend their time absorbing. Instead, they are taught a mixture of algebraic techniques developed over thousands of years – mostly to tackle imaginary problems. A problem from a mathematics textbook of the ancient world might read something like this:
Say that we know the sum and product of two numbers. Can we determine the two numbers themselves?
Or, in a textbook for the more advanced pupil, something like this:
Inside of a circle, draw a triangle with all three sides equal so that the corners of the triangle lie on the edge of the circle. Now outside of the circle, draw a triangle with all three sides equal so that the sides of the triangle only touch – but do not go inside – the circle. What is the relationship between the size of the triangle inside the circle and the triangle outside the circle?
Do you see the difference here? The two problems just stated do not name the numbers “George” and “Anne.” The triangles inside the circle and outside the circle are not two paths traveled by two different hikers. The problems are presented as exercises in thought, and never pretend to be anything other than that. In case it’s not obvious yet, the whole point here is that the connection between elementary abstract math like algebra and truly “everyday” life is a farce.
Well… then why study it? To the experts at Strength in Numbers, the plain answer is that even when mathematics is not “useful” in the ordinary sense, it is always beautiful. The ability to determine unknown numbers, unknown measurements, to look for patterns and make predictions, uses the human mind in a way that everyday life doesn’t allow us to. Most of the time, everyone needs to be concerned with getting food on our tables, gas in our cars, money in our bank accounts, smiles on our kids’ faces. Exercising our minds gives us a vacation from the humdrum pace of everyday life! Instead of pretending to validate mathematics by turning it into a tiresome list of “applications,” our expert tutors look beyond and teach the patterns that undergird math. Math hones the mind, develops our logical faculties so we can experience the world as something understandable. It is the language through which we can understand the workings of the universe. It is these things about mathematics which still cause it to be studied, and which motivate the tutors at Strength in Numbers to continue its pursuit.
In some ways, the current math curriculum serves more to confuse than to enlighten. We can’t wave a magic wand and make the traditional math curriculum go away, but we can give you the tools to understand the real nature of mathematics and how to practice it successfully. And ask any teacher – stoking our natural intellectual hunger will always lead to better educational outcomes. Get in touch with us today, so we can start working together!