# A Geometric Understanding of Integration By Parts

## Pushing past the formula to build a visual understanding of the concept of integration by parts

Recently I asked myself: if I was a mathematics high school teacher, how would I push my brightest students and prepare them to be great mathematicians?

I thought back to my time studying math in high school, and I realised that much of the math curriculum is fed to students in a very rote and formulaic way. They are given a standard approach and formula for a given type of problem, and they practice the approach again and again so that they can use it effectively when it comes up in an examination paper.

But learning how to approach a formulaic problem does not necessarily help you fully understand and appreciate the meaning of the concepts you are being taught. And if you don’t fully understand the meaning of the concepts you are being taught, you won’t know how to apply those concepts in unfamiliar territory.

To be a great mathematician, you have to kick into a higher level when the terrain becomes unfamiliar. In these situations, the formula won’t help you when you don’t properly understand what it actually represents. So I challenged myself to think of how I might teach a common high school mathematics topic in a way that…