At the school I am now at, the students do not have a strong mathematics background. When I say that, I do not speak of their basic computation or their ability to manipulated algebraically, I refer to the ability to think conceptually.
This is something that can be fixed; however, this causes a big problem when it comes to Calculus and Precalculus. Precalculus has a ton of conceptual mathematics early on in the course, including parent graphs, transformation, limits, and end behavior. AP Calculus starts off with a huge amount of limits, which is a very strange concept for students who are weak in conceptually.
Luckily, organization can be a miracle worker! Currently, my precalculus students are organizing information and working with laboratory activities. With Calculus, I decided to go back to the source. The year began, instead of with numerical and graphical approximations of limits, with infinitesimal and algebraic methods of taking the derivative. I know that infinitesimal are not part of the AP curriculum, but for my students, it seems to have worked well. They can take the derivative of anything I through at them, and they do not even know what a limit is (as their precalculus teacher last year told me, before she retired at the end of last year, that she did not cover anything about limits). I think this is an exciting find for my students, they understand how to take a derivative and that the derivative stands for the slope of a line and have gained a lot of confidence in their abilities. After their first test tomorrow, I will enter into basic integration.
The point is this, I have organized my courses to be easy for students to gain confidence while still being rigorous in the amount of material covered and pacing of the subject. I am also being strict on my students organization, which I will talk about in my next post.
