I began working when I was 16 years old. In-between then and my first teaching job, I worked at a fast food restaurant, a clothes store, a movie theatre, a snack shop, and a home decorating shop. When I remember these jobs, I think of two commonalities. First, they all went out of business when I left their employ (just saying, Mr. Macdonald!). Second, I had to take a math test to demonstrate that I had the necessary skills to work on the cash. And I will tell you, I still take secret joy at calculating my change before the cash register does.
In my own education, a calculator wasn’t put into my hands until my upper year mathematics when I had to calculate cosine and derivatives. I was never very good at proofs, but I knew my facts. I couldn’t always explain why, but I could calculate it. It wasn’t until I began teaching that I started to understand why. Why fractions must have a common denominator when you add or subtract. Why the answer is larger than the dividend when you divide by a number that is less than one, and why it is smaller when you divide by a number greater than one.
We hear a lot today about new math vs. old math, and has the pendulum swung too far. To me, it is really a question about math literacy. In our Intermediate Division, knowing the multiplication table up to factors of twelve and being able to mentally subtract sixty seven from one hundred are as important as knowing how to read and write. We want our students to be able to explain the why of math, and explore truths, but without the basic facts under their belts, their knowledge will never be complete. How can we expect them to “explore” the value of fractions when they don’t recognize that the numerator and denominator of 6/21 have a common factor of three!
That is why we don’t allow our students the use of calculators until the upper years, and that is why we have school wide mental math drills. We strongly believe that we need to create opportunity to practice, and yes, drill math facts, so that when they have mastered the how, they can understand the why.