I’ve never taught young kids before so learning how to communicate math ideas to the boys has been a challenge. A fun challenge, to be sure, and something I’m constantly trying to do better. One benefit of filming a little bit of work with them every day is that it helps me see where I might be able to improve.

I still feel that I get surprised way more than I did when I was teaching older students, though. That surprise might be something I thought would be difficult seems to come easy because of a connection I didn’t realize they’d make, and other times it is the opposite – something that I thought would be easy is pretty difficult. I’m particularly trying to improve my reaction to that second type of surprise this year. Two problems from earlier this week have had me thinking about ways to get better.

The first was with my younger son. The problem he was working on is from an old MOEMs test: How many multiples of 7 are there between 100 and 1000? The part of the problem he was struggling with was finding multiples of 7 near 1000. I didn’t anticipate difficulty with this part of the problem ahead of time, and since finding multiples of 7 near 100 didn’t seem to give him trouble while he was solving the problem, I was surprised in real time, too.

To see if any of concepts that we talked about at the time sunk in I had him redo the problem on his own this morning. It appears that what stuck with him was the answer rather than the method. Makes me realize that I need to emphasize more of the process than the end result in these situations:

With my older son the problem was a geometry problem from an old AMC 8. Problem #22 from the 1987 AMC 8 to be specific:

By coincidence we’d been talking a little bit about this type of geometry problem after looking at this Dan Meyer piece: Developing the Question (see here for the work we did: Reacting to Developing the Question ). That little bit of extra exposure to this type of problem helped him work through to the answer of but the answer choices were ranges rather than an exact answer. Finding a good approximation for gave him a little bit of difficulty.

As I did with my younger son, I asked my older son to walk through this problem again this morning. The results were similar – he remembers exactly how to get around the prior difficulty rather than the ideas that help. Once again, it seems that I’ve not done the best job communicating the idea.

I really hope that I’ll be able to do a better job of emphasizing ideas over answers this year – especially when I’m trying to help them through a difficult part of a problem. Although I’m not 100% sure what the best approach to improving in this area is, getting better at communicating ideas is a one place where I’m looking to improve.