When was the last time you opened up a textbook? What about testing your understanding of fundamental concepts used everyday? How do you keep your understanding fresh?
The problem is that we rushed to complete high school and college so we can say goodbye to our textbooks and homework. But true professionals know that the true state of learning has only begun. Doctors and professionals attend conferences and read the latest research papers in an effort to stay on top of their game. Software developers are scouring for new services & libraries to use, heavy in research and new functionality. Regardless of what your profession is, have you maintained your understanding of core concepts like mathematics?
I’ve recently acquired over 20 different Schaum’s workbooks, covering a variety of subjects. My daily routine has been to crack these open and begin working through problems in the morning. Not too many problems, but enough to give my brain a good morning stretch before it runs through the day. This is the fastest way I’ve come to realize I don’t really know what I think I know. The same applies to everyone else, including you.
You think you do. I recently asked someone who has been out of school for twenty years and working in physical therapy, how they think they would do in the SATs. They said they’d ace it even better than when they were in high school. But even I, myself working in a field that requires constant use of mathematics, have come to the sobering realization that working through these problems, I have a lot I need to brush up on.
You may remember taking calculus and remember the core concepts behind it — but look at a problem on derivatives and you’re stuck. Much of these problems require learning what operation to apply to the function, or a nifty trick you used when you took a final exam. While I grasp the overall meaning behind calculus, knowing the formulas and why certain algorithms behind them behave in the manner they do, is arguably a better proxy for understanding a concept you have likely spent year(s) learning.
These exercises are humbling. Try them.