What if we looked at learning math like we look at learning how to read? How differently could we 'read' the world if we knew math as a language? What type of stories would it tell?
When learning to read the English language we start with the simplest part, the letters. Twenty-six symbols that each stand for a specific concept, each one meaning a different thing.
We teach someone learning to read what each letter is, what its name is, how to pronounce it and what order it comes in the alphabet.
Then, once they have that mastered, we start putting the letters together into simple combinations that we call words. Some of these words are just the sounds of the letters put together:
c + a + t = cat
Some of the words contain sequences of letters that when put together make a different sound from their individual letters:
t + h = th
c + r = cr
s + h = sh
Then there are the ever elusive vowels and the rules surrounding what they sound like when they are on their own, versus when two are put together, or when an 'e' sits at the end of a word. For example the 'a' sound:
fat ≠ fate
But eventually we get that down and then we start putting the words together into sentences, where we give them context with nouns and verbs and adjectives and adverbs.
Finally these sentences come together to form paragraphs and then novels and papers and website blogs like this one.
Once we know the letters and how they go together to form words and sentences and paragraphs we can then read and this opens up a whole new world of possibilities. Suddenly we can learn just about anything our mind can imagine, even more so with today's access to the internet and its whole online world.
Not only can we learn from reading but we can dream, fantasize, escape, visit worlds that don't exist in the 'real world'.
Not only that but we can use those words to communicate our own thoughts and ideas, dreams and fantasies.
It's amazing to think that all that came from just those twenty-six little symbols!
Now, what does this have to do with math you might ask. Well what if instead of letters we now had numbers. Let's put those numbers together with some other symbols (called operators) to give us equations. You know like 1 + 1 = 2 or Euler's identity
eiπ + 1 = 0
(which is called the most beautiful equation in the world)
Well, what's now stopping us from putting those equations together into theorems with axioms (a true statement) and then creating proofs.
Those proofs can then be used to describe, and validate, the world around us.
All of a sudden we've created an entirely new language that describes the world around us in a whole new way.
What type of a world can we now 'read'? What new adventures could we go on with this whole new language at our disposal? How different would the world now look?
It's amazing how similar learning math and language could be. Yet most math is taught very differently from language in a number of ways. Often it is taught isolated from other parts of the subject. You learn numbers first but then you learn equations separately. Then you memorize those equations to apply them to areas called trigonometry or calculus.
It's typically not taught on what's called a connected scaffold, and that means that a lot of the connections are missed along the way. These missed connections lead to missed understanding, which leads to frustration, anxiety, fear and even hatred of math as a subject.
Maybe it's time to take a different perspective with how we approach this rich and beautiful subject so we can start to 'read' the world in a different, more mathematical, and more fascinating, way.