I started doing some math every day at the beginning of this year. I wanted to be working alongside the boys, and I thought it would help me understand their reality better if I was doing the same sort of work that they are. Plus, I’ll be their primary mathematics instructor as they progress, and it will be helpful if I go through a refresher on algebra and the like myself. Not to mention that my own math education stalled out after a basic trigonometry course in high school, and I thought it might be fun to pick up where I left off and see how far I could go!
I have been zipping right along, doing as many as four or five lessons per day. I was getting caught up to the point where I left off all those many years ago, refreshing my memory along the way. I had forgotten all the formulas for computing volume and surface area and the like, as well as concepts like the exponent “power rule”, etc. But picking that sort of thing back up has been pretty easy.
However, I finally hit a significant speed bump in the form of simplifying, adding, and multiplying rational expressions. For those who, like me, have largely forgotten 9th-grade mathematics, a rational expression, and the process of simplifying it, is pictured above.
For me, this is challenging because there is a lot to keep track of. It is not something I can perform both quickly and accurately. Throw some negative exponents into the mix, and it gets even more complicated. Then do a handful of these in a row, along with a score or so of other sorts of problems, and one’s head can start to get a bit full, especially when being interrupted every few minutes by one’s fellow students, whose mathematical needs outweigh one’s own. It’s easy to lose the thread of your thoughts and make errors.
So, I’ve had three or four lessons in the last 20 where I scored between 83 and 89, well under our standard of 95. I had one stretch where I did poorly enough twice in a row that it pulled my averages down to the point where I had to repeat a few lessons and a test in order to bring my scores back up to an acceptable level. Needless to say, I am down to an average of one lesson per day now, and it can be a pretty hard slog.
The boys have been glad to see me struggle a bit; it makes me a bit more human and fallible in their eyes. And it gives me the opportunity to show them how to endure through difficult work, to “try, try again”, and to do so with a good attitude.
This can be tough! I had a sinking feeling when I first realized I’d have to repeat lessons, and I right away tried to figure out how maybe I could get out of it. I realized this must be exactly how the boys feel when they run into a tough new concept and it slows them down. As a result, I am much more sympathetic with them than I used to be.
The boys and I are learning a lot together as we go through our math books. Sometimes we even learn math! I’m not sure who benefits from our study sessions more—the boys or me. Regardless, it is great to know we’re in it together. Nil desperandum!