Using Utensils With Your Feet
Imagine that you were raised in a secluded enclave by an eccentric but harmless cult. Imagine further that the cult leader was born without arms, so had to do everything with his feet, including eating with utensils, and all the cult members are required to do the same. So you are raised being taught to use utensils with your feet, that this is the only good and proper way to use utensils, and in fact it never even enters your mind that there might be any other way to use them. You do it so much, and from such an early age, that it even becomes easy and eventually feels “natural”.
Eventually you choose to leave the cult and discover to your amazement that people in the outside world use utensils with their hands. Once you get used to this heretical notion you decide to give it a try. Since it is new to you, and you have old habits to overcome, at first it feels awkward and uncomfortable, even a little embarrassing. You are plagued by the sense that you are cheating. But because you want to fit in you keep trying, and find that not only do you master this skill amazingly quickly, it actually feels even easier and more natural than using your feet did. It soon gets to the point where trying to use utensils with your feet
would feel like an almost unbearable restriction.
This is an allegory for the first reason why math seems hard: because it is taught in ways that make it seem hard. There are two reasons for this.
The first reason stems from the fact that while learning (the accumulation of knowledge and experience) can and does take place under any and all circumstances, teaching (directed, outcome-specific learning) functions best as a dialogue. The way we as a society structure education virtually eliminates the possibility of dialogue, due to two faulty assumptions:
1) teaching is necessary for learning
2) teaching and learning are separate activities
Since my purpose here is to explain why math is easier than you think, not to deconstruct modern educational theory*, rather than unpacking these assumptions I’ll just give you the simplified implication: one teacher can’t have a dialogue with twenty or more students. (I actually think the maximum number is around five.) Therefore, the constraints of the teaching environment itself inherently limit the effectiveness any teacher can have.
The second reason is a vicious cycle particularly endemic to math itself, which basically boils down to this: most teachers don’t teach it very effectively. That’s not their fault, though, because they tend to teach it the same way they were taught. But that’s not their fault either — it’s because they don’t have a very good understanding of it themselves, so it’s easier for them to teach what they learned than to teach what they know. But that’s not their fault — it’s because the way they were taught was not very effective. Which isn’t their teacher’s fault either, because… And so you can see how this cycle perpetuates itself. Couple this with the institutional and societal change resistance factor, and you get an educational process that is very slow to adapt and an educational industry with a very long lag time.
However, there are better ways…
*But stay tuned!