As teachers we sometimes think we are being helpful when we break a concept down into little parts - teach each part separately and then try and put the picture together at the end. This rarely works. People need to understand where they are going to stand a chance of getting there.
One of the key features of teaching for understanding is not to stand inbetween the pupil and the 'thing' that is being taught. Giving pupils the 'big picture' about what they are trying to learn is an important part of teaching mathematics effectively. From helping them understand what mathematics is ... every lesson, no matter what topic, pupils can be reminded about what mathematicians do and how they discovered, created a particular concept in mathematics. Before they learn about one of the number operations they can learn about the concept of number operations ... (there are numbers and numbers can be operated upon.) (There are also shapes and shapes can be operated upon as well.) By understanding the infinite nature of the subject they will then know it is normal to discover something and then move onto another depth of understanding. If we can find a way of introducing the nature of the whole topic we are teaching when we teach a part then this will improve students understanding overall. Time can also be spent at the end of the lesson thinking about where what they have learnt fits into their big map of mathematics.
When considering adults' thinking skills, it is useful to have in mind a matrix of possibilities:
| |
visual |
verbal |
| holistic |
* |
* |
| sequential |
* |
* |
Whether having a visual or verbal preference, learners who think holistically will prefer to have presented to them the bigger picture first. This may be as simple as a verbal overview or link to a real life context, or it may involve detailed planning via a mind map of where the topic is going.
The next time you are planning to teach a mathematical topic, think where it stands in the 'big picture' and prepare an introduction for pupils that helps them understand what the topic is all about. Put your ideas in context.
Do you know if you think holistically or sequentially? Do you prefer lists and story boards (sequential) or narratives and mind maps (holistic).
Observe youradult learners and see if you can work out who thinks in which way.
A while ago I observed a class of lower attaining Year 6 children work on linking decimals and fractions. One of the girls was clearly not sure of what she was doing or why. She asked the teacher why the class were learning about this aspect of maths and the teacher gave a really good explanation of where they were heading with this work and also why this would be helpful in a real life situation. As soon as she had, the girl was satisfied that it was a valid and important task and was able to move forward in her learning.
This example stressed to me the importance of giving children the big picture of their learning and also its relevance to real life.
When training teachers to provide learning support to adults with dyslexia we worked on using mind maps. One particular trainee showed extreme reluctance to mind map, saying she could never get on with it. However, hearing from me that I was also a reluctant convert (being a compulsive list maker!), she persevered. She was astounded with the difference it made with introducing a new topic with an adult learner, who was receptive and showed a quicker grasp of the issues.