Be skeptical. Never blindly trust. Don’t believe that everything I say is true in math is true. Don’t believe everything you read on the AoPS wiki. Don’t blindly believe everything any other math teacher, in school or extracurricular, says. Don’t believe every bit of math you read on the internet, no matter how reputable the source. Everyone is human. Everyone makes mistakes. Always try to find counterexamples to new theorems you learn, even if they are well known theorems. If a certain theorem seems to be true for n=1,2,3…10, try to figure out if you can understand if it is always true, and if so, why. If you slowly digest and don’t believe anything in math until you can fully convince yourself of every “fact” you learn, you will gain a much deeper understanding of things.
Advice for Current Students:
Please ask me lots of questions!
That’s the main point of taking lessons from me.
If you are in class and don’t understand something I said, please do ask!
I don’t bite. Really!
It is very helpful feedback to hear that someone in class doesn’t understand something. Chances are, if you don’t understand, several other people don’t understand either. Also, I won’t get angry or think you are stupid or anything like that. Instead, I will take this into account and try to explain it a different way (or just again).
Oftentimes, if someone doesn’t understand something, it is good feedback for me, indicating I didn’t explain it that well.
I try to place everyone in classes as best as a I can, so I try to avoid scenarios where you don’t have the background to understanding something I’m explaining.
2. Please do the suggested homework! You won’t improve if you only do math during my classes. Most of math improvement comes from doing problems on your own. So when I suggest homework, please do it! Really! Even 1-2 hours a week reinforcing what we learned the last less will help in spades.
I don’t really force anyone to do any homework, as my classes themselves are optional to begin with, but if you really want to improve, you should do the homework, or choose better homework you think is more suited to yourself at the current time.
My Philosophy: you doing the problem on your own in 15 minutes is 10 times more valuable than me guiding you through it it 5 minutes. I want everyone to come to their own understanding of math, even if it’s different from my own. (as long as it’s correct) It’s not easy to come to this level of mathematical maturity and depth of understanding, but if you can get there, you don’t need to hear me explain anything- you can guide and travel your own math journey. Thus, I always think the least important parts of class are when I explain, and the most important parts of class are for you to play around and come to your own understanding of the problem (often in silence).
You may also be interested in some of my previous posts I have made on AoPS giving advice: https://artofproblemsolving.com/community/my-aops