Am I learning math wrong?

Question

This may be not really related to math. I'm currently learning differentiation, and no matter how many math problems I do, it seems that I always get it wrong in the exam, either having calculated something wrong or just misunderstanding it completely.Then I do more, but things are still the same. Same goes for other math areas that I am learning.Is it just I'm learning math the wrong way?What would be the right way? Also would like to have some recommendations on useful differentiation textbooks.

Answer 1

I'm not a teacher and I don't know the best way for you to learn. But here are a couple of thoughts.

Your question is clearly written. So if you are smart enough to write this, then I'd say you are perfectly capable of understanding and mastering high school differentiation. I'd guess that the issue is that the way you have been taught hasn't been quite right for you. You will get there in the end.

There are lots of YouTube videos out there which teach you differentiation in various ways. Have you tried some of these?

I can see two ways to 'learn' differentiation.

Path A is starting from the fundamentals. You learn things like:

• What's the slope of a straight line (rise over run)?
• What's the slope of a chord to a graph?
• What is a tangent to a curve?
• The slope of a graph at a point is the slope of a tangent
• The derivative at a point is the slope of the graph

Then you might learn about speed as the derivative of distance traveled. And you might learn about limits and indeterminate forms and l'Hopital's rule.

This is all good stuff, but it might be a bit overwhelming.

Another approach is to just learn the rules. Things like

• the derivative of $x^4$ is $4x^3$.
• the derivative of $7f(x) + 2g(x)$ is $7 f'(x) + 2 g'(x)$
• product rule
• chain rule etc

In this path, you don't worry too much about the "why", you just accept the rules (which aren't that hard) and learn to answer the questions. Eventually, you fill in the gaps and start to understand why it all makes sense.

I don't know which (if either) of these approaches you may have followed. But perhaps think about trying the other one. If you've skipped over the theory then go back to the beginning ans try to understand that. If you feel you've done too much theory - then just learn the rules and try to get through the tests.

Good luck!