Tonight I happened to catch #MSMathChat for the first time in a long time, and the topic was one near and dear to my heart – ratios and rates. The funny thing is that ratios and rates are a topic I loathed up until a couple of years ago.
I loathed them mostly because I didn’t understand them that well. When I was in school growing up, I was one of those kids who was great at math as long as I could be shown a procedure and then follow it. Meaning rarely entered into the equation. Unfortunately, ratios are really all about meaning – about relationships between quantities – and I never got that. I just saw them as two numbers separated by a colon, and that was about it.
A couple of years ago, I had to start writing math lessons on ratios and rates, and I felt like a fish out of water. Since I didn’t have much choice about writing the lessons, I started digging in to the topic. I’m particularly thankful for this book for challenging me to think and reason more than I ever had to growing up. Some of the problems in the book were flat out hard, but I was so proud of myself whenever I came up with the correct answer.
Another challenge in the book was understanding how students had solved the exact same problems I solved. I loved reading over their solutions, trying to figure out what they were thinking and what they were trying to say. I felt just as proud when I would finally piece together how some of these students solved problems completely different than me, but in creative and elegant ways.
I don’t know if I’d go so far as to say that I’m a pro at ratios and rates now, but I do understand them finally, and I love what they represent. During our Twitter chat tonight, I suggested some ideas that I couldn’t really elaborate in bursts of 140 characters, so I’ve taken to my blog to try to flesh them out a bit more.