One of the mantras in my Calculus (non-AP) classroom is that the hardest part of Calculus is Algebra. Seriously. I find it really depressing because often when I am correcting tests and quizzes, they will have the Calculus PERFECTLY correct and then just royally mess up the algebra. This year, the students in this class have incredibly weak backgrounds and I’m not sure why (well, I do have an idea that I will keep to myself…), but I do know is that many are really smart kids who just have serious holes in their math education. I’m really struggling to find a balance between teaching Calculus and remediation of basic math, which forcing me to go really slow and snip out wonderful projecty-type applications that really make the class what it is. It’s a balance between “Teach them where they are” and “Teach what I am supposed to be teaching”

I’m posting about this as a call for help to try to fix the crazy problems that I am having. I think the biggest problem is that the notation is so abstracted that they don’t have a basic feel for what you can and can’t do when manipulating expressions. I’d say the problems fall into two main categories…

NOT RESPECTING THE TRIG FUNCTIONS AS OPERATIONS:

GENERAL ALGEBRA CRAZINESS, MOSTLY HAVING TO DO WITH PARENTHESES:

In all six of the examples I picked above, the Calculus is EXACTLY correct, but it just gets completely and unfortunately ruined. I think that I will show them this when we go back to school on Sunday:

My AP class literally laughed out loud when I put that up on the board and I hope they have the same reaction and maybe help them realize that I have the same reaction when I see them manipulate some of the algebraic expressions the way that they do.

Any ideas on how I can do an Algebra boot camp of sorts to remediate some of these misconceptions? Are these normal Algebra mistakes for a senior in high school? Do other people have similar problems?