Questioning scenarios is a role-playing activity used in professional development to help teachers focus on questions that encourage students to respond with more elaborate answers. More information on questioning scenarios can be found here or in the full published article. Below are the five strongest scenarios:

Questioning Scenarios

This is actually our PD focus for this year! Will definitely be using these–thanks so much! Are there any questioning scenario resources available in relation to the primary grades?

Thanks! I have some but they aren’t particularly good so I rarely use them. I primarily stick with the Fractions, Ordering Decimals, and Median ones.

You are working with students on multiplication:

You put this problem on the board: 7 x 3 = 21

8 x 4 = ?

The student puts the answer of 32. They think the problem is 32 because one more than 7 (first problem) is 8 in the second problem. One more than 3 (second factor in the first problem) is 4 in the second problem so they think the pattern is one more than the first problem and they get 32. Right answer but wrong reasoning.

Woh. That would be brutal, Dottie. If you use it, please let me know how it goes. I’m not sure I would have ever realized a student had a misconception like that.

I am finding that without LISTENING to students, they have Waaaaayyyyy more misconceptions than I can ever think up. I am learning to be better at my questioning to get to their misconceptions so that we can address them. Thank you for the PD idea about this. I work in a K-8 school so I will be looking for more elementary examples that could be used.

I notice this too. Sometimes, I find questions on assessments that have these possibilities. I assume it is done intentional to see if the conceptual understanding exists, however, my supervisor says we would need to give credit for the correct answer, even if it is achieved through inaccurate reasoning. I am looking for data to support NOT doing this. I find it frustrating…unless I am wrong.

Thank you for sharing these. So many of my teachers focus on students getting the answer correct, but don’t ask them to explain how they did the work. The Fraction, Ordering Decimals, Median, and Area example will be great for my elementary teachers.

Here one I use :

(I don’t write / on the whiteboard I write the division symbol)

13 /4 =

16/5 =

19/6 =

22/7=

25/8 =

31/10 =

and the teachers (who teach students) will say to me 3 remainder 1 so I write 3 r 1 next to all of them. Then I ask what is the problem with teaching that? Answer: the 1 is shared differently each time so has a different value eg 1/4, 1/5 1/6 … and then I ask which is actually equal to 3.1? and I write the other decimals that are easy (3.25, 3.25, 3.125)

This is a common (mis)conception even in adults – I often ask 60/7 and the answer I receive is 8.4 ie 8 ones and 4 left over which must be .4!

Very nice. Thanks for sharing!

Love these scenerios, Robert!

I’m wondering if you have any you could share with more of a primary focus…like multiplication, addition, subtraction. If so, would you be willing to share those as well?

Thanks so much!

I wonder if being careful about problem selection would benefit students and teachers more. Yeap Ben Har tells us that each problem given to a student should help us address a new and different misconception.

I might find it more useful to use professional development time to develop a good set of problems to address misconceptions at a rate of 1 per misconception. Teachers would have the opportunity to identify common misperceptions (together we can find more than one person working alone) and develop student problems that would address the misconception.

That is also very valuable Ellen. I am simply providing this for anyone looking specifically for an activity to improve question asking.

Good idea Robert! It is indeed fruitful. Please add more to it!

For those of us who need help with questioning that will elicit more elaborate answers/greater depth of thought from students, do you have a list of sample questions that can be asked for each scenario?

Joel, maybe you can start with this? https://robertkaplinsky.com/the-art-of-questioning-in-mathematics/

I thought of this the other day. A student had a really convenient misconception. It was something like this

-3x+7x-x and he said 3x. I almost moved on, then asked how he knew. He said “there are 3 x’s (counting each term, not the coefficients).

I added it to my list for this PD.

I haven’t used questioning scenarios is for-EVER. But yeah, this is a good one. I would not have ever expected that reasoning. But yes, any odd misconception tends to make for a good questioning scenario.

There are many scenarios that I present to students and then ask for justification for its use. My favorite is “Keep-Change-Flip”. How does that make any sense?… multiplication where there was division; 3/2 where there was 2/3. Mathematics education students often reply that they learned that it always gets them the correct solution. They show little, if any, understanding of the mathematics behind the scenario and for the most part they seem “okay” with their lack of understanding. After all, isn’t the point to come up with a correct solution? After we have completed a lot of work using fraction tiles, drawings and discussions… many students find that the light bulb of understanding shines brightly. Despite this new deeper understanding, most teacher candidates seem to form an alliance and have expressed that it is just much easier to teach “KCF”… After all, they know they will be assessed, in part, on their future students ability to “get the right answer”.

I remember being in the same position as your students: I had the skills to divide fractions with essentially no conceptual understanding of why what I did actually worked… and no real sense that this was a problem either. Glad you’re finding ways to talk about this with your students.

Great discussion! I find it interesting to give students the problem and then the answer and ask them to show (write) their reasoning/method/thinking/working. That leads to interesting class discussions too! I am always talking to my students that the aim is to ‘tell the mathematical story clearly and accurately’.