I am a teaching assistant at a school. My job is mostly to help them solve problems given by their teachers. Students are at high school level. I assume the curriculum In Brazil is similar to the one in US, except that we don't have the possibility of taking AP Calculus/Physics type of courses. You don't get to pick your courses, everyone is subject to everything at the same level.
I hope the answers are applicable despite of what specific things they are dealing with, but as a small breakdown we have
- Last year high school students are dealing with polynomials in algebra;
- Second year high school students are learning matrices;
- First year high school students are learning functions.
They all have geometry in a separate class, creating two math classes, but I don't know at what stage each of them are.
I see that they study hard and do many exercises, yet they lack basic understanding and their knowledge is almost completely procedural. As a remedy for this I've recommended them some of the strategies proposed by Polya, with a strong emphasis in understanding what are the terms involved and what is asked. Consequently, I'm constantly hammering the point that they know the definitions and how to apply them.
Is this sound? I know this is learned behavior and that it's uncommon to proceed from definitions, but I think this approach will result in better outcomes than they have now.