I think I’m actually starting to do this…
I’m working through a Precalculus course on edX to help fill in my knowledge gaps in mathematics, and I’ve been enjoying working with their personal learning software.
I’ve started trying to solve problems on my own instead of looking at the sample solutions, and I’ve found that most of the time I’m able to reason through the problem and figure out an answer on my own. And it’s usually not the way the sample solution was solved, and I tend to understand my own solution better and am more able to answer similar types of questions in the future.
This has truly built up my confidence in feeling like I can do maths on my own. I still make silly mistakes, like forgetting a negative sign or adding the wrong two numbers. But that’s just the way my brain works: I tend to be forgetful, no matter what area of life I’m working in.
So I always have my calculator beside me to check myself. I’ve also noticed that I’ve gotten better at recognizing when my solution doesn’t make any logical sense. For example, I’m working with projects that require completing the square, but the solution I’ve come up with doesn’t factor cleanly. Then I know I’ve made a small mistake somewhere and can go back and figure it out without feeling stupid.
I never knew maths could be so exhilarating, and I’m so frustrated with the traditional American school system for not allowing me insight into this beautiful world much sooner.
But I also recognize that I could have done this years ago had I wanted to. If I’d had the desire and the want and need to learn this stuff back when I was in high school, or even college, I could have done so.
Still, it doesn’t do to look back and regret what one has or hasn’t done in the past. All that matters is that I’ve found it now, and from now on I can continue to fall in love with math.
And it is quite a beautiful love affair indeed.