What is Algebra?
A couple of years ago this question was asked at a conference, by Dr. Kahn from Wayne State University. We knew what Biology, Psychology, and Geography we but could not define Algebra.
How could 35 math teachers not define something we are so familiar with?
The answer is so simple, yet I think it underlines a serious problem with math education in that we make things too difficult.
Dr. Kahn gave us an example of how hard English is to learn. The word "laugh" should be "laf" and how can "air" be spelt as in "bear", "care", "their", "they're", and "fair". The reason for this is that English is a mix of languages and there was no one person "in charge" of how it should be put together.
Math didn't have anyone in charge when things were invented and it has the same complexity as English but it is acceptable to not learn math. You'd never hear someone saying "I wasn't good in English, its ok not to learn it". Math gets beaten down, even by our own teachers.
How do we fix this? We need to make math simpler, not easier, but simpler. I believe that Dr. Kahn has the first piece (and many others) to the puzzle. Algebra is the "study of operations". Think about it, "the study of operations". Biology is the "study of living organisms", now Algebra is the "study of operations".
How cool is this? This blew me away. How can all of the 500+ standards and benchmarks in high school math boil down to adding, subtracting, multiplying, and dividing; and if you really put some thought into it, Algebra is about adding and multiplying.
It's amazing to see students brains light up after I give them the answer to the question "What is Algebra". It makes sense and it gives my class a clear focus throughout the year.
The "Study of Operations" is the first step in the quest for getting all of our students through Calculus in high school.
Homework: Ask you colleagues this question at your next meeting, see how many of them can define Algebra.
*By the way, I've asked this question to about 500 students and still haven't had one come close to being correct.