I have been taking a MOOC called How to Learn Math. The course is for teachers, homeschoolers, parents, and anyone else involved in teaching children math. I'm taking it because I have a son who delights in math, and as a homeschooler I want to be sure I'm never the one to take that joy away from him. What I love about these courses is their flexibility. You can engage at whatever level you have time for or interest in. What you get out of it depends entirely on what you put into it.
The first session was quite interesting. There was a lot of discussion about the math anxiety so prevalent in our society and the negative messages we pick up (and pass on) about math. It really made me think about my own education in math, and how it has affected my attitudes towards math. Lockhart's essay A Mathematician's Lament has been incredibly thought-provoking for me since Alice (our PEI resident homeschool math expert) first introduced me to it back in May, and I'm so glad the course included it. I think I can safely say that though I don't agree with everything in it, it has completely changed my perspective on math.
Here's a copy of one of my assignments for the course: a concept map.
I was rather fortunate that my childhood experience in math did not leave me with a fear of math. Other than the fact that all the drill was frustratingly boring in the elementary years (pages and pages of long division, ugh!), I did well and got good grades. Then high school came, and algebra and geometry were introduced. I loved these. (for all the wrong reasons, according to Lockhart. I think maybe he could have been more open to allowing us non-creative logical/analytical type thinkers to enjoy math in our own way. Not that I don't wish that I had more training in problem solving and creative mathematical thinking as he describes it.) Though I did well with math as a child, there was no joy in it, no exploration and discovery, no creative problem solving. It was all a matter of being a "good student" and following directions well.
And yes, I did think I was smart because I could "do" math. I remember telling Stephen about an incident where my younger sister, who did not enjoy algebra the way I did, exclaimed in frustration "But why?" I replied, "It doesn't matter why. It's like a puzzle...just go through the steps and you'll get the right answer." Stephen was shocked by my reply..."You mean you did it all without understanding it?" And yes, I guess I did. He described how he could visualize a problem, which was a totally foreign concept to me (I am so not visual. I don't even understand being a visual thinker. The closest I come is the way I can usually tell how a recipe is going to taste when I read a recipe.). So maybe I'm not as smart as I thought...
Lockhart's music analogy really spoke to me. When I was a young child, we had an organ in the house. My mother taught me the bare basics of reading music, and from then on I was on my own. I played with the organ all the time. I learned to play hymns quite fluently, though I always thought the ones without sharps or flats were the easiest to play. I can remember figuring out that I could play anything I wanted without using black keys by simply moving my hands up or down the organ from where the written notes indicated I should play. I worked out a whole system where I counted the sharps or flats and figured out how many notes up or down I had to play to get into the key of C. Of course, I knew nothing at all about keys...I just knew that if I did this I could play without using black keys. I can still remember the moment when my "cheating" was discovered. I think my guilt that I wasn't playing it "right" the way it was written colours my memory of the experience. More likely the girl who found me out was simply surprised that I was confidently playing in a key other than what was on the page in front of me. At one point, my parents decided to give me organ lessons. They took me every week, then watched as my interest in playing dropped to near zero. Wisely, they stopped the lessons before permanent damage was done. Later, as a young teenager, I bought my own piano. I played and played, and gradually got better at it. I met someone who could play by ear, decided to learn how to do that, and did. Perhaps I would have learned more if I had had lessons. I could have learned to use the right fingers on the right keys. I could have gained some fluency if I had practiced some scales. But as it was, every minute of playing the piano was purely for the enjoyment of it.
So what's my takeaway for math? Because of my "unschooled" experience with music, I believe that unschooling in math could have its advantages and disadvantages. The biggest advantage (and this is huge!) is that, given the right resources and challenges, the joy of discovery and learning is never quenched. The disadvantage is that without disciplined application at the right time, children may not gain the fluency and facility that would enable them to continue to discover and enjoy at a higher level. On the other hand (as Lockhart expressed so well in his essay), the "drill and kill" method so common today is much worse. Even when it is "successful" and children do well according to the tests they take (as I did), they may never explore the wonder of the order and patterns that God built into His creation and gave us the ability to appreciate and enjoy. They may never experience the joy of successfully figuring out a challenging and complex problem. I did not, but now I am so looking forward to discovering all that is wonderful about math and to passing it on to my children.
I believe the approach expressed in Charlotte Mason's philosophy is the best. "Education is an atmosphere, a discipline, a life." It is also a "science of relations" (Lockhart spoke of that, too, when he referred to the importance of historical context in the study of math.). Unschooling emphasizes the atmosphere and life, Classical education emphasizes the discipline, but I think Charlotte Mason brings a needed balance to both.
How do I see this working in my home? SA's natural enjoyment of numbers and measurement is what first set me on the path of finding a better way of teaching math, one that would not take away his joy. First, I will try to provide an atmosphere in the home that fosters learning. This is a bit difficult for me when it comes to math, given my own experience and gifts (or lack thereof -but at least I'm still learning!). I have found that a book like Family Math can be a real help if everyday math situations are not your strong point. I want to provide a rich variety of resources and challenges that will continue to stimulate SA's interest. I also want to teach him the discipline of taking on a difficult challenge and persisting until it is solved. Of course, we are just starting out. I'm sure real life will give me a lot more insight than I have now! This course is looking promising, too.
So there it is...long and rambling and only a fraction of all I've been thinking about lately. How would you describe your math experiences as a child? How did they affect the way you feel about math today? If you're taking the course, has it given you any insight or sparked any thoughts so far?