Robert Kaplinsky ran a great session yesterday at TMC on asking questions to see what students actually understand. His title was: Improve Your Questioning Skills to Formatively Assess Student Understanding. We took turns going through a really fun role-playing protocol, where a teacher tried to probe a student’s understanding to see what they are actually thinking. There was great discussion about different types of questions that do a great job of probing understanding and asking students to elaborate on their thinking, rather than just saying yes or no. I was lucky to be partnered with Alex Overwijk and Christopher Danielson, and I ended up with a great new tool for getting students talking about their thinking.
So a student has solved a problem, and I suspect that they don’t understand what they’re doing — they got it wrong, or maybe they got it right for the wrong reason. I often end up going dwn this rabbit hole with the student. Even if I ask great questions, they tend to 1) realize they got the question wrong and 2) not want to relive it and answer all my questions. Each of us used a similar move where, when we realized there was something about the student’s thinking that didn’t work, we gave the student a short task to do to reveal that thinking, rather than continuing to probe and dig through the evidence we already have.
In the first scenario, a student draws this picture of 1/3:
You can make a pretty good guess at the misconception to probe student thinking, and Al started with a few quick questions asking Christopher to explain his thinking. He then asked Christopher to draw a new picture of what 1/3 might look like. Christopher drew this:
That reveals a lot more thinking, and also puts some more of the thinking on the student. We didn’t get into what to do next — the goal was to see where the student was coming from — and I loved that choice of a questoin.
In the second scenario, I was asked to order the decimals 0.52, 0.714, and 0.3. I ordered them as:
0.3, 0.52, 0.714.
Christopher tried to dig into my thinking, and I was very confident I was right. He then asked me to order two new numbers: 0.15 and 0.30. I now had:
0.3, 0.15, 0.30, 0.52, 0.714.
That forced me to do some mathematical thinking, and pretty clearly revealed my misconception. He didn’t stop there, though, asking me to write some new numbers that were larger than 0.714. I stuck with my student personality and gave him 0.715, 0.716 and 0.900. I loved this approach — rather than picking an argument with the student over the answers they already had — and were very confident about — getting some new information to reveal that thinking.
In the third scenario, Alex needed to find the median of the set of numbers
3, 7, 4, 2, 9
Alex said that the median was 4. I asked him a bit about his thinking, then, copying their moves the first two round, gave him a new set to find the median of:
2, 7, 3, 4, 9
Alex picked 3. Golden.
I don’t know what to call this move, but I really like it. It worked great for us, and I think would work even better with a student. I hate ending up in the situation of doing a “post-mortem”, forcing a student to relive a question, and this technique gets just as much or more information, but shifts the student’s attention to a new task.
There was lots more to Robert’s session that I’m skimming over, but this was my big takeaway, and it’s something really concrete that I hope to put into practice within the next few weeks.