In deciding if a student is indeed ready to take calculus, I look at the topics covered in the class(es) they've taken in the past year. If they match the list below, then I consider the student more or less ready to go and needing minimal remediation. It's worked out pretty well so far.
As far as I can see "Pre-Calculus" is the algebra and geometry of three main kinds of functions:
- polynomials
- exponential & logarithmic
- trigonometric
Students should be able to:
- recognize domain and range over bounded or unbounded intervals
- find x & y intercepts
- understand scaling and translation f(x) vs a*f(b*(x - h)) + k
- find end behavior as x goes to +/- infinity
- find horizontal & vertical asymptotes
- understand function combination & composition
- understand the concept of an inverse and how it relates to domain & range, graphically & algebraically
- hand-sketch a given function and clearly highlight its important features
- evaluate functions at specific points
- algebraically manipulate & simplify trig identities, log rules, and factoring, cancelling, and collecting like terms
- know the entire unit circle and the trig sum & difference formulas
- use graphing software to dynamically visualize all of the above
- understand how each kind of function can be used to model real-world situations
- unambiguously communicate their thought process in their written solutions (or statements) of problems
I feel that students who enter my AP Calc class with these skills are well-prepared and tend to enjoy the course more because they are better able to see the calculus concepts through the "pre-calculus" algebraic manipulations, graphing, etc.
What are your thoughts? Am I missing something? Am I asking for too much?
This may be somewhat tangential, but it is applicable to the list above. The Core Curriculum standards
ReplyDeletehttp://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
don't say what is Pre-Calc, but do say what practices, processes, knowledge, and skills should possess by the end of certain grade levels. It might be another way of organizing the list above.