Tuesday, June 26, 2007

On becoming a math fact "expert"

"An expert musician can remember the sequence of notes in a new melody much better than a novice. An expert chess player can remember the position from a game at a single glance. An expert waiter can remember the orders from a table of twenty people without writing them down. All these exceed the normal capacity of our "working memory.” How is this achieved? It's simple. You become an expert. --Brian Butterworth, Neuroscientist

I believe that basic math fact mastery is crucial. I do not doubt the importance of my children being able to quickly access these facts with ease. We work on training their memory much like a serious athlete would-- consistently and incrementally. Why such a focus on something so "basic"?

As someone who works in a "non-math" field, even I find it strange that I've placed such a priority on mathematics. This prompted me to reflect on my own math education and upon doing so it became more clear to me why I feel the way I do.

My elementary education was certainly traditional. After a couple of years in a public school, my mom (who was a teacher’s aide) decided that the public school I attended was not the ideal learning environment for me and instead chose to enroll me in the neighborhood Catholic school. For the most part, grades 2-6 were exactly what you would expect from a parochial education. Very traditional.

Nevertheless, the nuns were more forward thinking back in those days than many schools are today. They allowed me to move a couple of grades up for reading and one grade up for math. I would then return to my classroom for all other subjects. I was already the youngest in my class, and the nuns thought this was the best plan to keep me challenged. I think it worked well.

Early in seventh grade, we moved to another city known for excellent schools and I attended a public middle school. Looking back, it was also very progressive in that students were given a math assessment that determined his or her starting point by ability, almost like “independent study”. They were already about 3 months into the school year when I got there and students had been working at their own pace for some time. I must not have done very well on that original assessment because I had to work my way up to the higher levels of the math program. Boy was that sobering!

However, by the end of the school year I had moved past almost every other student in my class. I am convinced that it was because I had a strong foundation in mathematics (the basics) and the necessary work ethic to allow me to move through each unit rapidly. I’m still not sure how my math teacher managed a classroom full of students each learning a different unit according to his or her ability, but somehow it worked. It certainly gave me the tools I needed to take advanced math in high school and later on in college.

I am proud to say I am a survivor of rote memorization (I attended a parochial school, after all). It wasn't just lots of prayers and math facts either. I memorized the periodic table of elements, all the bones in the body, the parts of the heart, the Gettysburg Address and lots of speeches and scripts--and that was by the end of seventh grade. There were lots of things to memorize, basic math facts among them. I am not traumatized and I don’t hate math. I use it every day and then some.

There are so many new ways to learn basic math facts in today’s world that it’s doesn’t always have to be flashcards and tables ad nausea. Still, it takes work, lots of practice, repetition, and perseverance. You have to practice to mastery, until those math facts are second nature and are automatic. You have to become by all intents and purposes a math facts “expert.”

Despite the fact that my grown-up work has little to do with mathematics, it’s clear that without mastery of those fundamentals, I would never have had the opportunity to excel in advanced mathematics. Because of the hard work expended in mastering the fundamentals, I had a choice of what to be when I grew up.

While I didn’t choose to enter one of the STEM disciplines, I had the tools to do so if I so wished. How could I not want the same choices for my own children? I want them to choose their field of study because they have a love of it, not because they couldn’t do something else that required a better preparation in mathematics.

After all these years, the one thing that I don’t regret is having worked diligently at mastering my basic math facts—becoming a math facts “expert”. It always seems to go back to those fundamental tools that I learned so very long ago.

For me, it’s simple, really. My children will achieve great things by becoming “experts” too. The efforts expended now will payoff later whether it’s in a field of math or science or some other field of their choosing. It will definitely be a skill they call upon in their everyday life.

When all is said and done, my children will have choices and be free to walk a path because it leads them to where they want to go and not because they had to settle for something less.


Brian said...

Love your blog. I have one observation that I feel has been terminally left out of this discussion.

My comment here ran way too long, so I put it up as a post on my blog at The Math Mojo Chronicles.

I'd be interested in a link exchange, too, if you think that would be appropriate. I find your writings thoughtful and intriguing. (Of course I would - a agree with about everything I've read here so far!)

I couldn't find your contact e-mail, so please contact me through my blog if your interested.


Brian at Mathmojo.com

Suma said...

math can be expertised by anyone who loves it..

suma valluru