Practical implications for teachers
Are you just beginning, and want some starting points?
These are some practical ideas taking from discussions with teachers and also what worked
for us in our classrooms. Maulfry and I always say we wish we were teaching now, because
we know so much more. We know that each teachers' pedagogy is personal and that you will
find ways to open up mathematics in your classroom that suit you, and the children you teach.
There is no one way and no one pedagogy.
A useful blog by Cathy Gunn explains how she opened up the learning of mathematics after listening to my talk at the Early Education Annual Conference 2017.
"I wanted to explore graphical representation using an open maths concept so I tried it out during a day teaching nursery children. We had some polished stones in a tray and I modelled drawing some gridlines with a large marker pen on large paper. Some children wanted to draw their own grids with large pens and big paper. Others asked me to draw the grid. I was interested to see what the children did around representing the stones, or arranging them. It was open ended. I had no end product. My aim was to see where they took this infinite maths and how they built it upon their knowledge. There were many surprises. By not limiting and keeping it open, children wrote numbers: 200, 500, 10000…. One child wrote numbers 1-51 and could have continued further I think (something to follow up). Some children placed stones in each grid box in a pattern arrangement and others drew representations of the stones."
Cathy's enthusiasm is palpable and she continues,
"I was fascinated by the children’s graphical representation, their knowledge of number, their excitement and ability and their interest. Their confidence in big numbers and infinite maths makes me want to explore it more at home and in school."
"If you are less confident in maths and need inspiration, I encourage you to try it yourself."
To read the whole blog click here.
The importance of creating an Open Culture - Open Mathematics
Children's Mathematical Graphics thrives when the classroom culture is open and democratic.
In considering working in a way that encourages children's own mathematics, you have to seriously consider your classroom environment. How can you create a culture of mathematical enquiry?
"There are many aspects of Open Mathematics, but more than anything it is about creating a culture of mathematical enquiry where mathematics is woven through the day and not limited to a set disjointed activity. Problem-solving is at the heart of mathematics and linked to children’s own enquiries that arise out of their interests and every day happenings. Play is central to young children’s mathematics. Open Mathematics is underpinned by a democratic pedagogy where children and adults co-construct learning. Teachers and practitioners actively seek knowledge about children’s learning both from the children they teach and their engagement with a professional learning community."
For further information read the blog 'Open Mathematics - Open Minds' based on my PhD study (Carruthers, 2022).
Open Mathematics, things to try: What teachers say
Some things that teachers said they found useful:
"Children need free access to papers and pencils and other graphic tools. Observe and encourage
the children to put their thinking on paper. "
Another teacher commented "In our morning talk-time we set up the area sometimes with mathematical intent and see how the children engage. As well as mathematical resources, there are always paper and pencils and markers." One school used small whiteboards at the children's height and encouraged children to use them. The children used the whiteboards in many different ways.
"Nearly every day I write a message, comment or draw on the whiteboard. Often children will write on the board and use the space to discuss what they are thinking. Sometimes I have two standing whiteboards at children’s heights […] We model mathematical notation, drawings or tallies for the children to think about and this gives a focal point for discussion. Every group area of the nursery has a whiteboard at child height." (Nursery School Teacher)
Keep the mathematics open, ask open questions. The children will sometimes go beyond the curriculum expectations. They like large numbers. Follow and encourage their mathematics. One teacher said,
"Challenge children, ask a question that you know they will not know the answer to, encourage strategies and using their graphics to work out the problem."
Encourage children to ask their own questions about mathematics.
One teacher focused on children's questions. She created a culture of listening authentically
to children's questions. She advises:
- Listen to the children
- Value what they say
- Respond quickly to their questions
- Plan from the children
- Allow children to share their ideas
Outdoors, children have the freedom to use chalks and also have large areas for pretend play that can enhance mathematical thinking.