It is nearly time to send home the report and portfolio. I hope this information helps you understand how your child learns. You will see examples in the portfolio. I have focused on our shape unit, but this applies to every area of maths and the curriculum.
It’s a bit long…. but I do hope you find it useful.
The poster shows a hierarchy of thinking and can be applied to any area of learning. Note that remembering facts is considered the easiest form of thinking, followed by understanding. Pages of addition sums where you remember and show some understanding would not be considered the work of successful mathematician. There is defiantly a place for remembering but we want more, MUCH MORE. We want successful creative mathematicians. We do not underestimate what young children can do. Our programme depends high level thinking.
We use the Primary Years programme maths document as the basis of our teaching. We can divide our teaching and learning into three parts. These stages are often shown in a circle; our learning knows no end.
Let’s see some examples from the class to help you construct your understanding.
Children use all their pervious experience to help them understand something new. This is best achieved by letting children use all their senses (touch, smell, taste, sight and hearing) to activate their brains. They need time to put their ideas into words as they discuss their findings with others. Now they can begin to make new connections based on past experience.
The children are constantly constructing their ideas about shape. I gave them as many shape manipulatives as I could find (manipulatives are things you can touch like blocks) and told the children to use them any way they wanted. I then gathered the children together and asked them:
- What is a shape? (some answers: circle, square, rectangle, diamond, arrow)
- Where can I find shapes? (Some answers: an ice cream is a triangle, the world is a circle)
Children use their own language to explain their learning. They may choose to write down or draw their findings, make models or act it. We would move to tradition forms of notation (+ – =) only when the children have shown their understanding.
The children meet the alien from space who does not understand shape. They had to explain their understanding of specific shapes they had sorted so the alien could learn to identify shape. I then gave them the mathematical vocabulary needed to describe shape e.g. children’s explanation ‘point bit’, mathematical term vertex or vertices.
Applying with understanding
This is where children show their understanding in new situations. They are applying skills and knowledge beyond their previous experiences.
The children have shown this by:
Using their knowledge and properties of 2D shapes to explain 3D shapes when they went for a walk to the shrine e.g. ‘It’s a cuboid, look rectangle and squares, makes the faces’
They can apply their understanding using patterns. Looking at the blank 100 squares and filling it in using numbers patterns they know, e.g. writing backwards from 100 because they know the pattern is 9- (- must be then be 9,8,7,6,5,4,3…).
They can make their ideas known, explaining and justifying their mathematical thinking and strategies, for example explaining the strategy they used to find a missing number in a line e.g. ‘I count backwards from 10.’