It seems to me that you are suffering from a mid-year slump – maybe having to do with some disappointment about the recent midterm exam, or maybe something more. Recently I have heard: “You never taught us that.” “Nobody cares about understanding. Only the grade matters.” “I haven’t learned anything in here.” “You don’t like me.” And a few more. Ouch.
You may fault me for not being a teacher who leads you through every step of the way. It’s true. I ask you to practice problems on the homework that are harder than what we did in class. I ask you to be ready for a graded assessment at any time, and without warning. I ask you to be assertive and self-aware - requesting clarification when you need it, both inside and outside of class. I also put problems on tests that I have not previously solved for you in class. I know this makes it more challenging, but to me it’s the best way. I see the world of mathematics as a vast universe of possibility. I get to be your guide for only this tiny little region, but ultimately, I want you to trust your own instincts and skills and venture out without me.
You have a choice to make. One option is to be bold; take a leap out into the vastness and use the tools you already have to find your way through this wonderful world. I promise: you are not alone; you will not perish; and when you find that you need new tools, they will be there, ready for you to learn how to use them. Or, you can sit still and wait for a personal guide. It’s ok; sometimes this is the better way. I know that fear or insecurity or any number of things can freeze any of us in our tracks. Nevertheless, I cannot stop encouraging you to be bold and venture out independently, because I know that a richer and more beneficial world is there for those who do. There will always be problems on ‘tests’ that have not been previously modeled for you. This much, I can guarantee. I wish we lived in a world where all the problems were previously solved, but I assure you, you will be confronted with problems that I cannot even imagine yet. The question is, what will you do with those?
In the end, it’s not important to me whether you attribute your growth to me or not. I just hope you notice what I do: that you HAVE grown. Don’t let the vastness of the universe lead you to a narrow view of your own successes. You have come a long way. I have evidence to prove it. And while we both know that there’s an even wider view in front of you, that doesn't diminish the excellent work you have done to get this far. It is one of life's great ironies that success and failure travel so well together:
“Failure is simply the opportunity to begin again, this time more intelligently.” Henry Ford
“I know that I am intelligent, because I know that I know nothing.” Socrates
“It’s not that I’m so smart, it’s just that I stay with problems longer.” Albert Einstein
“I've missed more than 9000 shots in my career. I've lost almost 300 games. 26 times, I've been trusted to take the game winning shot and missed. I've failed over and over and over again in my life. And that is why I succeed.” Michael Jordan