Introducing alien methods
Every so often a visitor from the planet Marlo comes to our classroom. The Marlon often visits when the class has been discussing and learning a new concept. The Marlon can be any visiting adult who can understand the "rules". Most of the time she is my team teacher. She usually arrives when I need to ensure that those children who are gaining in confidence have acquired the intended degree of understanding, and when some children are having difficulty in understanding, or in expressing their understanding of the concept.
I work with dyslexic children and my current research is in the field of specific learning difficulties and mathematical understanding. The language of mathematics is of prime importance in mathematics lessons and learning. Dyslexic children often have some difficulty in acquiring mathematical concepts and in understanding and using algorithms.
It is important that children acquire understanding through concrete experience and they need to demonstrate that understanding in a variety of ways before the teacher can be sure that they have really grasped the concepts being taught.
Dyslexic children often have poor motor skills, coding and sequencing problems and many have difficulties with short-term memory. There is much one can do to help children to organise their work. They can be helped to remember procedures and to develop methods of working to suit their own particular needs.
One of the most important ways for any person to demonstrate understanding is for him to explain his thinking to others. Politicians argue their case by setting the scene and describing actions and consequences; manufacturers of cars sell their products by describing the specifications of their cars and comparing them with other cars; travel agents describe destinations and facilities in detail in order to sell holidays. Ask a child to describe his latest computer game and he will probably be able to do so. Ask him to tell you what happened in Home Alone or Neighbours and he will do so.
How often do we ask children to describe what they did in their maths lesson? How often do we ask them to tell us about the mathematics they used? For many children this is a common experience and is a challenge they can meet, while children with specific learning difficulties do not find this easy. However, the development of their use of mathematical language helps them to clarify their ideas.
Discussion and reflection is a vital component of the teaching and learning of the dyslexic child. While it is important that they be given the tools to cope with a mathematical curriculum, it is equally important that they be given the opportunity to discuss and describe. They should be asked to define, and define and define until they have told the listener and themselves everything they know. In this way they refine, broaden and reconstruct their own knowledge.
This is where "Marlon Maths" comes in. When the Marlon arrives in the classroom she wants to know what the children have been doing. The Marlon has acquired some knowledge of the English language, but there are many words and concepts that she does not know. The children can only find out what these are by talking to her. The first time the Marlon came to my classroom we had been looking at 2-D and 3-D shapes. I asked the children to tell the Marlon about 2-D shapes.
John: 2-D shapes are squares, triangles and circles.
Marlon: What is a square?
John: It is a shape with four sides.
Marlon: Is that a square? (She points to a chair that has a top, a bottom, a front and a back.) John: No! A square is something you draw.
Me: Maybe the Marlon can draw it on the board. Would you like to try Marlon? Marlon: Yes, please!
Me: Jack, can you start?
Jack: A square has four sides and you can draw it.
Marlon: Like this?
Jack: No! They have to all be joined up.
Marlon: Like this?
Emma: The lines have to be straight.
Marlon: How about this?
Ben: Let me tell you. You need four straight lines and they join up but don't cross each other.
Marlon: Ah! I understand.
Jack: No! Start again. Put your marker on the board. Now draw a line straight across.
Jack: No! It should be straight.
Marlon: It is straight.
Me: Marlon is right. What do you want her to do?
Claire: Look, draw a line that is as level.
Marlon: Level with what?
Claire: The edge of the board.
(Chorus of approval.) Me: Can anyone think of a way of describing how and where you want this line drawn without mentioning the edge of the board?
What do you call a line that is this way? And what do you call one that is this way up?
Think of maps.
(After more discussion we arrive at the words "vertical" and "horizontal". ) David: Right. Draw a vertical line with a horizontal line going down from the end of it.
Marlon: Like this?
David: No! They must both be the same!
Marlon: The same? But they are different lines.
David: I mean the same length.
Marlon: Oh, I understand!
Jack: Yes! Now draw another vertical line from the bottom of the horizontal line. It must be the same length as the others.
Marlon: Like this?
Jack: No! Rub out that line. It has to be under the first horizontal one.
Marlon: Like this?
John: Now join the end of that line to where you started.
(The Marlon completes the square.) Me: Now, can anyone explain exactly what a square is?
Jack: It is a shape with four straight sides which are all the same length and they join up but do not cross each other.
Me: Mm.... yes, but can you be a bit more specific. Can anyone say anything about the sides opposite each other?
Philip: Well two are horizontal and two are vertical.
Me: I am going to draw a square on a piece of paper. (I do so and hold it up.) Is that a square?
Me: (I turn the paper through 90 degrees.) Is that a square?
(Some hesitation and not all think it is. A lively discussion ensues at the end of which it is agreed that a square is a square no matter what way you turn it, just as a boy is a boy no matter what way you turn him, as we demonstrate!) Me: Well, there must be some way of describing these lines which means that they are opposite each other but not necessarily vertical or horizontal.
(No one knew the answer to this. I introduced the concept of parallel lines.)
This was not the end of the discussion. I use this for all aspects of our maths work. Children have to explain symmetry to the Marlon. Explaining our money system brings in early ideas of decimals. Explaining measurement helps children revise their ideas and discuss or explain the meanings of the terms used.
Marlon Maths can be used at any stage. Ask the children to explain a 100 square to the Marlon. Ask them to explain the meaning of words like add, plus, subtract, divide. Ask them to explain an algorithm. The Marlon (with a few hints from the teacher) knows some words and not others. The teacher knows when to accept a definition and when to press for clarification.
Our Marlon has a hat (a card headband with a shiny head green circle attached to the front) so we all know when she has arrived. Maybe creatures from other planets can visit classrooms all over the land. We have had a lot of fun with our Marlon and the children have been learning at the same time as the Marlon and I have expanded our knowledge of how children think mathematically. It has helped me to assess how much the children have understood of the lessons we have had and to clarify my own teaching methods.
Mel Lever is a teacher of dyslexic children at Fairly House School, London and is currently researching into maths and dyslexia at Kingston University. The names of the children in this article have been changed.