TL10 How do I facilitate non-mathematical discussion in the maths classroom?
This vignette illustrates how one teacher used specific questioning techniques to help her pupils focus on effectively filling in the maths skills table. She had an observer in the class, whose notes are italicized.
In this Task, I wanted to try to have the pupils realise how many different maths skills that they had actually used throughout the case. I was hoping that they would be able to gain some appreciation of how relevant maths is, to help solve every day problems.
Having asked the pupils to turn to the Maths Skills Reflection sheet in the last page in their booklets, I asked a pupil to read out the instructions at the top. Then I waited, expecting them to get instantly to the Task without hesitation. Some pupils immediately started writing; some asked their friends for clarification of the Task, others appeared to lose interest almost immediately.
After a few minutes, thus giving the pupils some time to try to understand the Task, I realized that I would need to give them a little more direction. I refocused the group so that we could take an example and fill in the first row together.
Observer notes: Pia asked the class, “As an example, what sort of maths did you use in the Task?” A boy casually said, “Graphs”. Pia jumped on that and said, “What did you do with the graphs?” Then she led the pupils through, by questioning the class as a whole, the sorts of things that they might write to complete the table about how they used graphs. This was good because then the pupils could complete the rest of the table as they had a sense of what was needed.
I then asked the pupils to Think/Pair/Share the activity – I gave them a few minutes to work in silence and to Think individually of as many maths skills they could. Whilst they were thinking, I intermittently asked them to try to remember back to what we did in Lesson 1,2,3,4. I was hoping that this would help them organise their thoughts. They were then asked to share their ideas with the person sitting next to them (sharing in groups of 2 – Pair). There was a lot of discussion between the pupils and additions to their tables. Some pupils erased their previous work and rewrote a better example. Others discovered that they had misinterpreted the Task and thought that they needed to reflect on the whole year’s work. They asked for a new worksheet. I asked the pupils to Share their ideas with the rest of the group on their table. All pupils were engaged on the Task. Some were quite excited about identifying skills that others had not written down. Other pupils wanted to discuss their ideas with me, or were keen to show me their completed work.
Following is an example of how a teacher can stimulate and sustain reflection. These are teacher comments, leading questions.
“Sally, would you please read out the instruction at the top of the table? (Teacher then slowly reads out heading of each column of table - no explanations necessary yet)
We have used many different maths skills the last 4 lessons. I want you to think carefully and quietly for the next 20 seconds or so about what skills you think you have learnt. Think about Lesson 1……2……3……4…..
Who would like to share an idea with the class………(wait 5 –10 seconds)…..…Peter?
Great idea Peter – we did use Graphs – so let’s all write graphs in the table (teacher also writes on board)
Now, next column says, ‘where I used it’, so where did we use graphs?…….(wait 5 – 10 seconds) ……Natalie?………excellent ……can you repeat that Natalie so that everyone can hear?…….(teacher writes Natalie’s idea on the board)
I am sure that you all have lots of other great ideas about how we used graphs …..(wait 5 seconds)……..Jonathon?………Andy? …..Alice?……..
OK, I want you all to write your own idea about how we used graphs ….…..which part of the table do I write in?……..good..…..off you go
For the next column, we need to give an actual example of where we used the graphs………yes, Matt,………. it can be a picture or it can be in words.
Who would like to give an example of a picture on the board?…....thanks Nick
Who would like to give an example of a sentence on the board?…..…thanks Alessia
Now, the last columns asks us to write if we understood the skill….Y….N…AB….Peter……you gave us the idea of Graphs at the start, how well did you understand the skill?...........great……..
Now everyone, put your hand up if you are going to write Yes…….A Bit……..No……..
What should you do if you have written ‘A Bit or No?’………..
Why is this an important question that I have just asked you?......