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.
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.