Despite the name of this post, I have three claims.
(a) I am not Henry David Thoreau.
(b) I will not be spending a night in jail.
(c) GO ALONG! GO ALONG! GO ALONG! (though I am not full of contempt right now.)
In my calculus class this year, I started with a review of pre-calculus theory, but I think that it served mostly to intimidate the students. That was a wake-up call for me, and I will act on it next semester when planning the first few days.
Short memories are sometimes at hand, so I think it might be more effective to do just-in-time review of concepts from the pre-requisite courses. For example, review of simplifying rational functions might work best during the algebraic computation of limits.
And I feel that reviewing trig functions would be best to do after introducing limits of non-polynomials.
The textbook, frankly, has a limited review chapter, which made the first few days quite a drag and a challenge.
The Intro to Derivatives chapter in my calculus class’s textbook goes in the following order:
- Limit definition of derivatives
- Power rule and linearity rule
- Product and quotient rules
- Rates of change (“word problems”)
- Higher-order derivatives
- Derivatives of trig functions
- Chain (composite) function rule
- Implicit differentiation
- Logarithmic differentiation
- Related rates
I agree with sections 1 through 3. However, I feel that the beginning of the chapter should continue to develop the theory of derivatives through algebraic functions (i.e. after section 3, introduce the chain rule, implicit differentiation, and then higher-order derivatives).
After all of these general techniques have been learnt, and hopefully after the students are comfortable with taking derivatives of algebraic functions, introduce the derivatives of the exponential and trig functions. Follow that up with logarithmic differentiation, bringing back the implicit differentiation.
I feel that the Rates of Change and Related Rates should go toward the end of the chapter, or be thrown into the next chapter which is usually “Applications of Derivatives.”
Is this order done by anyone else? Or is this suggestion TRANSCENDENTAL BLASPHEMY?
Today is the nineteenth day of O.C.T.O.B.E.R. That makes two weeks and five days.
End of the Ad-Hominems: 20 days
Thanksgiving: 36 days
Lincoln: 62 days