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Tuesday, 31 January 2017

Young Mathematicians At Work

Written by Rebecca Forchuk, Director of Staff Development
Cathy Fosnot Session: Young Mathematicians at Work 

During our PD day with Cathy Fosnot, she shared the process of Conferrals, which are intended to develop and support mathematical thinking…not about finding correct answers.  She stressed the importance of listening intently and asking good questions while conferencing with students where “every move [she] makes is about making the community move forward” (Fosnot, 2017). While she modeled what conferrals sound like with a group of 15 teachers, she asked the rest of the audience to write down the kinds of questions she asked. 

Here are the questions I heard.  While reading them, I urge you to:
1.     Reflect how these questions may be different than those we typically hear in math.
2.     If you don’t teach math, reflect on how these kinds of questions can be used and reframed in different subject areas. 
3.     Consider how these questions develop a safe, welcoming learning environment that is foundational to high levels of learning. 

Questions posed by Cathy Fosnot:

-How did you solve it?
-Can you share your thinking?
-How did your thinking from the last one help you with this one?
-What made you decide it was doubled?
-Is that what you’re saying?
-Turn and talk about the visual representation and see if you’re thinking about it the same way.
-Turn to your partner and tell your partner what you did.
-I was listening to your conversations and I found it interesting…What did you notice?
-Is that a conjecture you just made?
-Can we figure out why?!
-Can someone try to defend his answer? Who agreed?
-Let me see if we’re right…
-Are you seeing…?
-Are you suggesting a friendly amendment to the conjecture?
-Are we “cracking” division?
-Does anyone else have something interesting to add to the community?
-Is there something we can use to simplify…?
-Is there anything nice we can do with that?
-Is this the same as…?
-You had a question. Would you mind sharing your question because if  you’re going to ask it, so are others?
-Could we also write it as…..Turn and talk – is that true?
-You tell me if I get it right because it is your idea.
-What if I don’t have a ….?

As Cathy reiterated, these questions are about making strategic decisions when reflection is needed and to build the community’s understanding of a big idea in math.  The strings of numbers are carefully crafted; they scaffold using easier numbers to support development of big ideas, craft related numbers, and listen intently for those big ideas.  Last but not least, celebrate  student thinking!


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  2. Thanks Rebecca, looking forward in rephrasing some of my questioning with this article in mind.

  3. Thanks Becky! I loved the way she brought all learners into the community of mathematicians. By using the words "we" "turn and talk together" "friendly amendment", it was the ultimate in building a safe and caring learning environment. Kids are much more willing to take risks if they think that they are not just putting their ideas on the line but everyone is encouraged and willing to contribute and being right or wrong was not the purpose of the lesson but deeply understanding the process! It made me reflect on how we ask questions of students to probe deeper thinking for sure!