And, as usual, the #MTBoS came through. Here are just some of the replies I received:
I answered the question thanks to the great replies I got. But it was not until a student asked me how to solve the question that I realized that, despite knowing that many students would struggle with this question, I did not plan out what I would say when they asked for help. My answers ended up being just like those given to me on Twitter - "this is how you start it" which really took some of the fun out of solving this "puzzle". So I am now wondering what a good question would be to help move my students' thinking forward without giving away the solution. I should have at least asked "What do you notice?", but am not sure that would have been enough to get them going. Please tell me if I am wrong! This is the question I came up with in the van ride to take my kids to Jiu-Jitsu:
I am wondering what you would ask - what would your best question be? Please let me know in the comments!
One of my go-to questions is "What's the most annoying bit? Why is it annoying?" and "Would you know what to do if it was different?"
ReplyDelete1. "Does this remind you of something that you've seen before? How did you solve that?"
ReplyDelete2. "What makes this problem difficult for you? Is there a way to remove this difficulty?"
3. "Can you rewrite each term in a different way that might help?" (That seems a bit opaque, but I'm envisaging 2 times 1/x rather than 2/x.)
Can't come up with a *best* question, but I'll keep brainstorming :).
I'm with Amie. I make a big deal about how a recurring theme in math is trying to take a new problem and make it into a problem you have done before. So I would ask "Is this similar to something we have done in the past? How is it different? Now - how do we attack that difference?"
ReplyDeleteWhat would a similar question look like that you COULD solve?
ReplyDeleteAlong the same lines, perhaps actually provide a similar problem from the past. Substitution seems to be the best method to consider, so maybe tell them to consider a problem along the lines of ... solve ' sin^2x + 2sinx + 1 = 0' or '5^2x + 2*5^x + 1 = 0'. Now can you apply a similar logic?
ReplyDeleteOr give a similar problem in two dimensions, like a "rate" question where 1/x tends to appear. (Bob can paint a fence in 6 hours, Larry can paint a fence in 8 hours, if they work together, how long will it take... granted, there's other ways to solve that, but there's probably other ways to tackle this one too...)
This is a really interesting approach. I would not have thought of tying it back to other times it made sense to substitute. Thanks for getting me thinking further!
DeleteI sometimes start with: What do you wish it looked like?
ReplyDeleteHow fun is this. Sorry I missed the first shout out!
I love this idea, Amy. Looking forward to trying it out.
Delete