Thinking About Thinking - 2018

Formulas are Draculas!

By Balaji Prasad

“Teach principles not formulas."
~Richard P. Feynman

One way to think about formulas is as not-too-distant relatives of Dracula: As vampires that suck the blood out of living things, leaving behind the carcass of what once used to be something more vibrant.

On the other hand, if you have some faith in mathematicians, physicists and such, you would see formulas as innovative concentrates that reduce complexity, paring them down to something that would otherwise not fit into a very small, but very important space: your brain. Formulas are like freeze-dried substances that can be resurrected to their pristine state by simply rehydrating them when desired. They can be stored away for a long time, and brought out for use, as and when needed.

There is a problem with freeze-dried formulas though. When you show them to people who are not familiar with them, all they see is dust. Young students, especially feel this way, because they see things with a clearer eye. They find it hard to understand that you would subject them to memorizing and applying this dry-as-dust stuff that only produces more dust when it is applied. So, we beat our students into submission, and get them to comply. The result is that we subject our young ones to cruel and unusual punishment! Disenchantment sets in, and education is viewed with resigned hopelessness.

We don't need no education

“We don't need no education
We don't need no thought control
No dark sarcasm in the classroom
Teachers leave them kids alone
Hey! Teachers! Leave them kids alone!
All in all it's just another brick in the wall.
All in all you're just another brick in the wall."
~Pink Floyd – Another Brick in the Wall (Part 2)

Do children view their school work as drudgery? Some of the students I have spoken with say they do. Also, I used to know a child once upon a time (at very close quarters) who used to wonder why teachers and schools did this to the students. He got through all that and more just fine, but kept wondering if there weren't a better way: something that was a bit more interesting and engaging?

Teachers: Please stand on your heads!

There are at least a couple of things that can make learning a more real thing than it sometimes is. First, while formulas, patterns and rigorous structures can be valuable, maybe we should not get intoxicated with those as things unto themselves, but view them as a means to an end. This means that we would spend more time on the richness of meaning that underlies these formulas, and focus a bit less on mind-numbing, repetitious application of these shells of reality.

Another thing we could do is to turn the education system on its head, and make it about learning, rather than about teaching. After all, the learner's mind is the object of focus, not the teacher's prowess. We are in a very different world today than when the whole business of teaching was invented and designed. There are all kinds of experts we can summon up on YouTube and from different websites, on demand. There are many bite-sized as well as meal-sized tutorials, documentaries and other resources at our fingertips. Literally.

It is not that there would not be a need for teachers in this new world. We would just look at them as facilitators of learning. Maybe we would call them coaches, or perhaps, even trainers. These are people, who would, of course, be skilled in what they help learners learn, but rather than pushing things at their students, they would enable, facilitate, push, prod, poke, challenge and direct students' thinking in directions intended to stretch and enhance their abilities.

Top-down or bottom-up learning?

When you stand on your head, everything looks different. Teaching becomes learning. Formulas become formlessness. What is on top goes to the bottom, and what is on the bottom goes to the top.

Formulas are the poster child for top-down. The reality doesn't matter; reality is just this annoying thing that needs to be dealt with because it is there. Just figure out the aspects of the real thing that you want to stuff into the formula. Then stuff those into it, shake it a bit, and out comes the result – the magic answer. A-squared plus B-squared is equal to C-squared. So said Mr. Pythagoras, a long while back, and he was a really bright man, though he apparently ran naked, screaming “Eureka!" when he discovered buoyancy, while floating in his tub. So that formula must be correct! Who are we to challenge such a man? Therefore, when we see a right triangle, we heed the famous man's formula, and apply it. Blindly.

Then there is bottom-up. We play with triangles. We draw various kinds. We ask questions about them. We notice things about them that are different. Some are right and some are left. Some are obtuse, and some are bright. This is the way children play when they are young, before they are indoctrinated by the top-down world of formulas. These are the days when they are fascinated by blood-sucking Draculas that are mythical creatures. Before they are homogenized, and indoctrinated into the world of formulas. Those then become the real Draculas that we live with, for a long, long time!

Formulas are not just with regard to math. Formulas are everywhere – in writing, reading, geography, history. In everything. We are told to do this, this way, and that, that way. Can we find a different way? Can we make learning fun and make it real learning, as opposed to the thing that is its faint shadow? Can we overcome the vampires that we have created? I am hopeful. Are you?


Balaji Prasad is an IIT/IIM graduate, a published author, SAT/ACT Online and Offline Coach, interview, resume, and career coach at NewCranium. Contact: 704.746.9779 or