Wednesday 1 June 2016

What's Your Best Question?

Yesterday, before class, I tweeted this out:



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!

8 comments:

  1. 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?"

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  2. 1. "Does this remind you of something that you've seen before? How did you solve that?"
    2. "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 :).

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  3. 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?"

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  4. What would a similar question look like that you COULD solve?

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  5. Along 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?

    Or 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...)

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    Replies
    1. 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!

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  6. I sometimes start with: What do you wish it looked like?
    How fun is this. Sorry I missed the first shout out!

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    Replies
    1. I love this idea, Amy. Looking forward to trying it out.

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