Writing Conferences and Maths Conferences

Currently I am reading a book called Conferring with Young Mathematicians at Work by Cathy Fosnot. It is a great book and has reinforced the importance of us being really familiar with the developmental progressions students move through when they are learning mathematical content. The books covers the critical conversations we have with our students in our maths session. Cathy compares these conversations to the conferences we have with our students in writing.

Now, probably my second favourite area to teach when I was in the classroom was Writing. So, this comparison really peaked my interest. 

I loved teaching writing and found having conferences with students about their writing to be a really powerful instructional strategy. We would talk through their plot, the characters, the language they were using, the structure of their sentences, the flow of the piece. I found it really valuable to run these conferences and the students really responded to having this time to refine their craft of writing with a more experienced writer (me)!

However, in maths, I never saw my chats with students as ‘conferences’.

It was more, as Cathy calls it in the book, a ‘product-based’ discussion.

I would generally ask questions like: “What have you been doing?”, “What strategies are you using?” or “Can you explain your thinking?” 

I would generally congratulate them on their work, take some anecdotal notes and move onto the next group.

My discussions were mostly based around students describing their ‘product’.

If we were to draw a comparison with a writing conference- I now see that this is basically the equivalent to a student reading their piece to me, and me walking away.

Cathy highlights in the book the importance of us having ‘process based’ discussions in our maths conferences with our students.

So, beginning by finding out what they have done, but moving the discussion on to nudge them to some deeper thinking. Like in writing we might say, ‘I notice how all your sentences are similar in length. Authors often use shorter sentence for impact, could you try this in the final paragraph?’

But to know where to nudge a student in maths requires us as a teacher to be very familiar with developmental progressions.

We have to know what is the next level of thinking we want the students to move towards. 

So, for example, if they're in Foundation (first year of school), and you've asked them to add two collections, and they are counting both groups separately, then counting the total, it is clear that ‘count on’ is the next strategy that you want to nudge them towards. In this video you will see an example of the actions of a typical 'count all' student.

In that moment we need to decide how we are going to nudge them towards that thinking? 

You might say something like: "that's a lot of great counting you are doing, but do we need to count the collections twice? how do you think we could use this paper plate to help us remember the amount in one of the collections?"

Another example might be a student is working out the number of chalk pieces in 5 of these packets:

They describe to you they are adding 12+12+12+12+12+12 to get the answer.

Again, it is in this moment that we as teachers need to use our knowledge of how students transition from additive thinking to multiplicative thinking to nudge them to think about “is there a more efficient way you could solve this?”, “is there another operation you could use?”

In these moments we, as the more experienced mathematician, are helping our students to see that there is a more efficient and elegant way they could approach the problem.  

Clearly, these conferences require us as teachers to have a deep level of pedagogical content knowledge. Having meaningful conferences with students in maths is not something we are born to do. It takes practice.

This week, I encourage you to have a go at trying to include a ‘nudge’ in your discussions with your students. Remember ‘nudging’ isn’t telling. Think of writing- we don’t tell them exactly where to include the shorter sentence, we nudge them to think and apply this tip themselves.

Think about the following:

1. Where are they?
2. What do they need to learn next?
3. How can I nudge them towards this thinking?

If you are looking for a resource that provides support in identifying what the next developmental step in various contexts is- this is an AMAZING resource from Doug Clements and team https://www.learningtrajectories.org/