What do Mathematicians look like?

Today, I ran two one hour sessions as part of a transition summer school being run with pupil premium money for upcoming Year 7s (11 year olds).  I wanted to get stuck into some problem solving activities first though, I wanted to dig into attitudes about Maths and Mathematicians.  So, I pulled out an old classic I’ve been using for years that I got from the amazing @PaulineMGaston.

I had students draw a picture of a Mathematician. I was really careful with my language here – I said “Draw a picture of a Mathematician and try to label it … for example your Mathematician may have a furrowed brow because they think really hard.”  (the labelling didn’t really happen this time)

We stuck them up with commentary from the artists and looked at them together:


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Some interesting things:  All these people are well dressed, wear glasses and are slim (when I asked one student whether all mathematicians were slim, she responded “Well, you are”).  I wasn’t wearing a suit – I was wearing jeans and t-shirt because it’s the summer holidays – but the other aspects could have been from me.

There was only one girl – @missradders and @JusSumChick reckon the second to last one is a girl, the student assured me it wasn’t but it is quite ambiguous.

Having chatted about the pictures, I asked them a series of questions and hit them with a cut up version of this so I could reveal it one at a time:

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We referred back to this at the end of the two problem solving activities to check which of these skills and attributes we used – helping them to realise that, yes, they are Mathematicians!

I really like this activity and do it at the start of the year with some of my classes.  I already have added @Rathematician ‘s suggestion of ‘Persist people’.

What else did I miss?  Mathematicians are ….

Orchestrating Better Discussions

41nct0yO-YLI can’t really understate how important I think discussion is in a Maths classroom, which is why the first teaching book I wanted to read this summer was this one – “5 Practices for Orchestrating Productive Mathematics Discussions” produced by the American NCTM.  I want to summarise briefly, give three good quotes and two things I’m going to take away from this.

Summary

This book looks at the key moves that a teacher can make to create a conversation in a classroom that has the potential to achieve meaningful learning.  I like the word orchestrate because that is what is involved.  After reading this book, I think I too often have students feedback after a rich task or investigation but don’t think enough about how I’m doing it.  This book gives a great structure to scaffold discussions: anticipate how the students are going to respond and answer, monitor how different students work and record this, intentionally select the approaches and students you want to share, sequence the presentations to be able to tell a meaningful story and connect the approaches to the underlying Maths.  The name of this blog is ‘joining up the maths’ and so this last point was really exciting to see.  I feel it is really important for students’ to see the links between concepts and subject areas and I think this book will help me facilitate more meaningful and productive conversations.

The authors also point out that for meaningful conversations there needs to be a meaningful task.  We can’t expect students to think deeply if we don’t provoke them and rather spoon-feed them algorithmic approaches.  As we more toward connecting our Maths curriculum more and more, we need to make sure we have good tasks that can help us do some of the heavy lifting (I’ll book more about that soon!).

Three quotes

“…the teacher’s role in discussions is critical.  Without expert guidance, discussions in mathematics classrooms can easily devolve into the teacher taking over the lesson and providing a ‘lecture’ on the one hand, or, on the other, the students presenting an unconnected series of show-and-tell demonstrations all of which are treated equally and together illuminate little about the mathematical ideas that are the goal of the lesson.” (p2)

“Sequencing is the process of determining the order in which the students will present their solutions.  The key is to order the work in such a way as to make the mathematics accessible to all students and to build a mathematically coherent story line.”(p44) Yes!! That!

“Although it is the thinking that goes into the preparation of a lesson that is important, creating some record of the decisions about the lesson is critical for two reasons.  First, the written plan serves as a reminder of key decisions so that teachers don’t have to keep all of the details in their heads.  It supports the teachers as they enact the lesson, reminding them of the course of action that they have set.  Second, the written plan serves as a record of the lesson that teachers can store for future use, revise, and share with colleagues.” (p82)

Take aways

I found this book through Fawn (@fawnpnguyen) and have really enjoyed her posts on deconstructing a lesson activity (part 1 and part 2). This book helped me think again about the moves I make while students are working that can help create more meaningful plenary and discussion.  I love the idea that by selecting and sequencing intelligently the students can tell the story and spot the links – I’m hoping this will reduce the need for me to tie together the threads in a deus ex machina.  I want to make sure I’m selecting and sequencing well and the anticipating and monitoring bit is vitally important if that is going to improve.  There was a suggestion of having a sheet that has the anticipated strategies and logging names and groups on it, so you could be prepared before hand knowing where the story is going to go.  While, I want students to be able to discover for themselves, there are particular threads I want to emphasise at various points depending on the learning goal.

The second takeaway is creating a future record.  I don’t keep anything meaningful in this way.  I have the student prompt sheet and the SMART notebook files but I don’t record any of my own thinking – so year on year I start from scratch.  As far as I know, this is the same for most Maths teachers in the England – maybe I’m just a slow learner!  But, as the rich tasks and investigations get added to, I want to record my anticipations and the student strategies that I didn’t think of to help develop my thinking and that of my team.

Conclusion

This is an expensive book, at almost £19, but I will be dipping into it and using it over the course of the school year.  I think it will make a difference to how discussions in my classroom will be used to more effectively achieve our learning intentions and gives me a framework to assess myself against.