I find myself spending more and more time trying to get better at two things. Listening and asking the right kinds of questions that will push thinking. While I find that resources have helped me get better at asking the right questions, I have learned that listening is actually quite difficult. The quote below is something that made me really think and reflect on my own listening skills:
More about this in a minute…
A while ago I had the pleasure to work with a second grade teacher as we were learning how to do String mini-lessons (similar to Number Talks) to help her students reason about subtraction. After a few weeks of getting comfortable with the routine, and her students getting comfortable with mental subtraction, I walked into the class and saw a student write this:
What would you have asked?
What would you have done?
Did she get the right answer?
My initial instincts told me to correct her thinking and show her how to correctly subtract, however, I instead decided to ask a few questions and listen to her reasoning. When asked how she knew the answer was 13 she quickly started explaining by drawing a number line. Take a look at her second representation:
She explained that 58 and 78 were 20 away from each other, but 58 and 71 weren’t quite 20 away, so she needed to subtract.
I asked her a few questions to push her thinking with different numbers to see if her reasoning would always work.
Is her reasoning sound? Will this always work? Try a few yourself to see!
Typically, we look at subtraction as REMOVAL (taking something away from something else), however, this student saw this subtraction question as DIFFERENCE (the space between two numbers).
I wonder what would have happened if I “corrected” her mathematics? I wonder what would have happened if I neglected to listen to her thinking? Would she have attempted to figure things out on her own next time, or would she have waited until she was shown the “correct” way first?
I also wonder, how often we do this as teachers? All it takes is a few times for a student’s thinking to be dismissed before they realize their role isn’t to think… but to copy the teacher’s thinking.
Funneling vs. Focusing Questions
As part of my own learning, I have really started to notice the types of questions I ask. There is a really big difference here between funneling and focusing questions:
Think about this from the students’ perspective. What happens when we start to question them?
Please make sure you continue to read more about we can get better at paying attention to the pattern of our questions:
Questioning Our Patterns of Questioning by Herbel-Eisenmann and Breyfogle
Starting where our students are….. with THEIR thoughts
So I leave you with some final thoughts:
- Do you tend to ask funneling questions or focusing questions?
- How do we get better at asking questions and listening to our students’ thinking?
- What barriers are there to getting better at asking questions and listening? How can we remove these barriers?
- Is there a time for asking funneling questions? Or is this to be avoided?
- What unintended messages are we sending our students when we funnel their thinking? … or when we help them focus their thinking?
- What if our students’ reasoning makes sense, but WE don’t understand?
I’d love to continue the conversation about the subtraction question above, or about questioning and listening in general. Leave a comment here or on Twitter @MarkChubb3
What are your thoughts?
Thinking Mathematically 
I know the post is about questioning, and I completely agree with you that we listen out for the correct answer rather than using questions as an opportunity to find out what is happening inside the children’s minds; however, I am fascinated that this young person did not write her solution as a number line when this is obviously how she thought about and pictured this question. Is there a reason why she felt she needed to write the solution as a column subtraction?
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After spending much time with her, I believe she had a really strong sense of number and magnitude. However, she had seen others “stacking” numbers before and attempted to write her thinking similarly. Typically she would have used a model like a number line to show her reasoning, however, she attempted a different representation this one time.
What would you have done?
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I wonder if her desire to imitate stacking could merge with her strong number line reasoning and make 71 – 58 = 20 – 7 a good hybrid option for her. My temptation to destructively funnel would be reduced if I saw this on her paper and future algebraic reasoning would benefit.
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The subtraction method employed by the student is one I use as a means of using and applying negative numbers so I would be most congratulatory to a student who came up with this method by her own volition. What is really nice about her method is how she related it to shifts on an ‘empty’ number line. Also I suggest it it a ‘truer’ method than the “borrowing” and “paying back” method; this is because the latter, more traditional method creates a misnomer where a single column can hold more than one digit. This, in turn, makes a mockery of how the place value system works.
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I interpreted her thinking as 70 – 50 = 20 and 1 – 8 = -7, so 20-7= 13. I’ve seen kids do this before and as long as they can explain it, I celebrate their reasoning. Then I ask them to test it with other equations to see if it always works.
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It does make sense that 1-8=-7 however, being a grade 2 student and never having experiences with negative integers, her reasoning makes sense.
I too might have assumed she learned some “trick” or procedure, but after listening and asking questions about her thinking, I could see that she was visualizing the distance between the numbers.
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In this time of Common Core, in which we are supposed to be celebrating multiple representations and multiple solution methods, it makes sense that the teacher needs to listen to the student’s thoughts before offering her own. The Funneling versus Focusing really speaks to me.
Your 71-58 is a perfect example of this. Before engaging in a conversation about this problem, the teacher needs to LISTEN to the student’s thoughts in order to funnel rather than focus. Until I read the rest of your blog post, I assumed the student did 70-50=20 and 1-8=-7, therefore 20-7=13. As a result, any “help” I might have offered would have resulted in creating confusion in a student who already has great number sense.
Thank you for this!
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Thank you for the reflection and question!!
I find as I grow as a teacher that I need to stop ‘pushing my learning’ on my students. That is, I don’t need to make them ‘do it the way I do’. So many times when I stop and listen to how students process, I see my own learning paradigms shift to envelop theirs. Many times when I’m helping my students one on one, they hear me say “I’ll shut up now.” It’s my own verbal cue to be quiet and let them explain, to let them have that ‘productive struggle’ (and me as well) so they can own the problem and the problem-solving behind it.
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I like that you are saying that the struggle here is on both parties! Yes, it often takes our thinking in places we weren’t expecting when we really listen to understand. Thanks for the comment.
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Hi! Thanks for the great post. I’m an ESL teacher and your discussion of Funneling vs Focusing questions is super important for me too.
I think there is a time to ask funneling questions. There’s nothing at all wrong with saying, “Let’s work through the/my/the textbook’s process together.” (For me it’s most often in grammar or writing.) It just doesn’t suit every situation. “Tell me about your process” is different and also valuable. Perhaps more valuable, as the chart shows. I’d just change the top right box to “student and teacher engaged in cognitive activity” because the whole time the teacher is engaged in figuring out the student’s thinking.
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When my left-handed daughter entered kindergarten she was told that she needed special scissors to be able to cut paper successfully. They didn’t know that she was already remarkably skilled at cutting around complex shapes, using the Fiskars kids scissors we had at home. Of course no one asked her about her cutting skills, they just told her that she needed the special scissors. .When my daughter lost the special scissors they had given her, she was convinced that she could no longer cut paper, so she no longer even tried. This is was such a great lesson to me about how easily a child can be crippled by an adult with an agenda. Thanks for posting your story. A powerful reminder.
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Another great post, Mark; thank you! Number line thinking allows students to hold representations of magnitude in their visual space, and can become a flexible structure for thinking extending throughout many increasingly complex stages of number (decimals, fractions, integers, rationals, and irrationals). I really like how you consciously unpacked her thinking, a skill we all need to keep growing with!
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