I love my first exposure to calculus. I had read minor snippets from various sources prior to taking my first calculus class, but I never really understood it completely. My junior year was jam-packed with the wonderful world of calculus, and your years should seriously be just as fun as mine was. Sure, it was tough at times, and somethings aren’t in your control, like your teacher, textbook or course layout, but you can certainly do things to make your experience rock.
5 – Admit Openly What You Do Not Know
When you work alone, be honest with yourself: if you don’t know something, don’t pretend to know it. When you’re working with others, honestly tell them you don’t know something, you’re not very familiar with it, or that it’s a challenge for you. When you do that, you’re honest with yourself and with others. They can help you out. Encourage others to be the same, you can help them out with what they don’t know themselves.
I openly admit I have a hard time factoring polynomials. Seriously. I’m not ashamed either, I told everyone I worked with when it came up, and they helped me out. I was really good at other things though, like binomial expansions, so I helped out with that.
4 – Know when it is worth it to give up
A lot of people will say never give up! But that’s silly. Giving up is sometimes the best solution. If you’re facing the most impossible derviative you’ve ever seen, or you’re attempting to solve for x but just can’t seem to do it, give up. Come back later.
There were many times during the year. It was a late night when the snow and wind were howling, and I just couldn’t crack a problem. I was there for at least twenty minutes once, and I couldn’t. So I stopped, moved on, and went to bed after finishing what I could finish.
3 – Always try to understand what you did not understand
This goes in hand with #4. When you do give up, which is fine to do, you need to find out why it was so hard. How was that problem different? How was it harder than others? How can it be simplified and solved? Giving up for the time being is great, it’s fine, it’s honest. It’s productive. But then you need to figure out how to actually do it, when you have the resources: your friends and your teacher.
When you do find out how to do it, it still might be hard or confusing. Guess what, admit that you do not understand, like it, it’s hard for you, and you’ve arrived at #5.
2 – Practice, do not study
I always said to my friends that I never really studied. I insisted, though, that I practiced. I would come up with annoyingly complex problems that contained multiple elements of the topic at hand and previous topics and then solve them. I would ask my friends to solve them too, and help them out as they went along. It was a study group in a way, but I got my own practice by making my own problems that were much harder than anything that could be on any test.
In other words, you need to do this:
- Make up some really hard problems based on the current material you’re learning
- Write up solutions for those problems – if you find one is too hard for you, set it aside, you know you need to work on that one more later
- Get your friends to attempt to answer some of your problems
- Any problems you couldn’t solve yourself, focus on those with your friends
This is a team building experience too. Your friends can all make up difficult problems and practice them with you or alone. It’s easy to practice. It’s far harder to study, to read notes and read the textbook, and so on. Practice, don’t study.
1 – Pride yourself in knowing calculus
For the most part, you know calculus once in your life. You know it when you learn it, and then you forget. My parents forgot, most teachers either never took calculus when they were in high school or even in college or in fact, forget completely, and students might not ever make it into calculus. Your stamina and your dedication seriously matters if you want to make in calculus, or in any class for that matter.
Calculus for me open the doors to an unknown world of mathematics. I had an idea of what was behind that door, but I didn’t truly understand before knowing calculus. Enjoy that you know more than the average person, and use that joy to propel yourself even further in your mathematical endeavorers, to obtain knowledge that most people cannot even imagine.
My time with calculus was excellent: my friends and my teacher made a huge difference, but my own attitude and actions made a difference too. If I was not so open and honest, so willing to learn more and more and accept the joy from learning more and more, I would not have passed the IB Calculus 1 (Mathemaics 1) exam.
Have a good year in class!