I cannot recommend this highly enough: have your kids bring in questions for you to answer in class.
As I mentioned in the last post, I asked my kids to do this, and this week they responded with some really great questions, most of which I had never seen or tried to solve before.
I gave each problem about 5 minutes of time in class, just thinking through it out loud, trying an idea or two to see where it would lead. For a few of the problems the initial idea was fruitful and I was able to solve on the spot in class. For others, the initial idea was off the mark and I needed to start over and try something else. I think the kids enjoyed watching me squirm a bit too much on these, but in a way the whole point was for them to see me struggle, be wrong, try again, make a silly arithmetic mistake, go back to an idea that had been previously discarded, and so on. And for a couple of the problems, I needed to take it home and work it through that evening, returning with an answer the following day.
I wasn’t able to take a problem every day in every class, just because of other things going on (a tornado drill on one day, for example), but I was able to do so a couple times in each class, and by the looks of it they got the point. A few kids told me outright that they got a lot out of the discussion around these questions. Also, there was a little more “I’m not sure if I’m right, but I’ll put what I’ve got on the board” by the end of the week. By seeing me be imperfect right there in front of them, there was a little more understanding that I’m not looking for them to be perfect, but instead I’m looking for them to learn from their imperfections. And by the end of the week, one of the first statements made in each class as the kids were walking in was, “I’ve got a questions for you to try today,” so if nothing else I know that the kids are enjoying the discussion and that we have at least a couple more weeks’ worth of exercises ready.
One of the students was intrigued enough by one of the problems that we had a short conversation on Twitter about it that evening, which for me was one of the highlights of the week: a student doing math for the sake of solving the puzzle and for the learning, and more importantly not for the sake of the grade. It also got me thinking about possibly putting a student-posed problem of the week online for the kids to discuss, just for the sake of having the discussion. The difficulty, of course, is that communicating mathematics online is cumbersome, at best, but it may be worth the try to see what creative ways the kids come up with to overcome the difficulty.
Another thought that crossed my mind was that this idea would have merit in other disciplines. Having students bring in a poem for the teacher to analyze in English class, an article for the teacher to translate in Spanish class, or a document for the teacher to explore in history class would be a great exercise for both the teacher and the students, as would the resulting discussions.
So, nothing but a positive update to last week’s post. Nice to have this happen every once in a while.