I've been having some fun working with teachers recently around brainstorming better questions to ask their students. I've noticed that we have a tendency to want to ask our students computational questions as opposed to conceptual questions. We've been working hard to turn the first type into the second. A few examples from the past week....

Paper Airplane Investigation

Some 6th graders were investigating the best type of paper to use when making a paper airplane...they had decided to compare construction paper, computer paper, and cardstock. After making each, throwing a few trials, and recording data, the plan was to have students fill in the following chart:
We started thinking that by including "average," it implied that this was the best way to make decisions about what was best in this case, forced the teacher to instruct on how to calculate an average before the students had made sense of the idea, and turned the activity into a computational one rather than a conceptual one. We thought about the small change of just giving students this chart...
...and then asking them to decide "which one is best" by inventing a method and justifying their reasoning.

Scientific Notation

One teacher had been thinking a lot about trying to create discussion in the math classroom. He had been working on scientific notation with his class and was thinking about using this question as a prompt to spark discussion:
We decided that if we wanted kids to talk, they needed to have something rich and complex to talk about and make sense of. After brainstorming some different options, we turned the computational question into a conceptual one by asking:
Of course, this also opens up a host of interesting extensions...
"what about the smallest product?"
"what if we divide instead? biggest result? smallest?
"what if one of the exponents was negative? both?"
"what if we move the decimal point?"
...and many others.

Let's commit to asking different questions and letting students share THEIR ideas with us and each other.
 


Comments

09/21/2013 1:59pm

So what's your job description lately?

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09/21/2013 2:05pm

This is some great insight. If you have any additional examples, please share.

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Bryan S Meyer
09/21/2013 2:36pm

Well, it depends on who you ask. Some would say "supporting teachers on implementing Common Core." I like to think of it more as "collaborating with teachers in creating rich learning environments where students create and share ideas with each other." But...doesn't exactly roll off the tongue like the Common Core nonsense. :)

It's just a one year position/leadership opportunity to work with teachers in our schools. Who knows what after that?!?

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Bryan S Meyer
09/21/2013 2:38pm

Thanks, Jim. Even better...give your own a try and share your experience with us here or elsewhere! Keep in touch.

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09/21/2013 6:03pm

<music>
Mathematical modeling and building number sense,
these are a few of my favorite things.
</music>
Good stuff. Thanks.

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09/27/2013 8:11pm

Thinking about "better questions to ask" is such a simple idea and yet so profound. I can imagine how "which one is best" could lead to discussions on the one that travelled the furthest, the average, cost of paper, durability, which one looked the best, etc. A completely different activity- one that was open-ended and allowed students to construct their own understanding. Great stuff

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09/27/2013 8:34pm

This is great! I will be using the scientific notation example this week. Asking better questions is a good challenge for all teachers.

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09/29/2013 7:21pm

Love the thinking involved in this rewrite. Thanks for the spark!

I just created a set of questions based on your idea. I added one slot, and asked students to use every digit 0-9. The addition of zero is intended to include the zero power, which can be tricky for students to wrap their heads around. I'm hoping that hearing the rules from other kids will help to cement the ideas.
-Nat

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Matt
09/30/2013 2:25pm

I really like the scientific notation question. Would you allow the use of a calculator for this or ask them to apply exponent properties and knowledge of decimal computation?

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Bryan Meyer
09/30/2013 2:55pm

Hi Matt...

Funny you should ask this question....my colleague and I were going back and forth on the same one. Originally, I was thinking it would be good to do without a calculator because we really wanted students to reason through their decisions to put numbers in certain places. The more I think about it, though, it seems that eventually students would HAVE to provide this sort of justification even if they were using a calculator (after all, they aren't going to check ALL of the possibilities). Maybe my thinking right now is, "its a rich question...so just pose it, get out of the way, and let them answer it however they want."

What do you think?

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Matt
09/30/2013 4:51pm

My original thought was that they would reason without a calculator by adding the exponents they placed on the 10's. But once they get to justifying the decimal portion the I would inevitably get the requests for calculators. I also have yet to show them how to use scientific notation with the calculators (but something tells me they would figure out the calc. display w/out any guidance).

The smallest product question is great too, but using 0-9 might be better to see if they remember to utilize the value of 10^0.

I'm thinking of doing this in groups of 3 with the students using oversized whiteboards in a sort of Socratic dialogue. What do you think?




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