Thinking Mathematically

Questioning the pattern of our questions

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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?

Summarized by Annie Forest in her Blog

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:


 

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?

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