Wednesday, May 28, 2008

Are quadratics really that important

If I was a student who had just finished a course in Algebra I in most schools across America I think that I would think that the following were the most important things that we had done. I would think this because we had spent so much of our efforts on it.

  • linear equations
  • distributive law
  • quadratic equations
  • factoring
The problem with this list isn't so much what is on it, it is what isn't on it. It seems to me that we simply must include exponential functions and therefore also logarithms. I guess my question is, "Are quadratics really that important?"

The only way to add these topics in is to take other topics away. So what can go? Here is a partial list of topics that might be cut or reduced in the standard curriculum.

  • completing the square
  • conics
  • rational root theorem
  • long division of polynomials
Exponentials seem like such a natural topic, and one that could be made to support and build on linear equations so beautifully. I will give more of this idea when I write later about "schlope".

3 comments:

Pseudonym said...

You might as well ask if the numbers from 1 to 12 are so important that we only memorise multiplications involving those numbers.

Quadratics are important because a thorough understanding of them is critical to handling general polynomials, because they raise issues that don't turn up in linear systems.

Matt said...

I guess I was sort of lobbing a grenade here. You raise an excellent point. One thing that I feel though is that I am not sure that even polynomials are so important. I want to ask the question to make sure that we are doing things for the right reasons. Are polynomials more important than exponential functions?

Kate said...

Too bad you are not New York State. You would just throw the new things in without taking anything out! So easy! And then just give a final exam where only half the curriculum is tested. Except not tell people which half.

Yes, we "do" exponentials in Algebra 1. Half-assedly, of course.