Yesterday I wrote about the importance of physical, experiential knowlegde of physics: a sense of forces and flow; of motion and fields and angular momentum. I called it visceral knowledge – a type of hinterland knowledge, which I suspect some learners find easier to access and apply than others.
In this post, I am thinking about the writer’s technique called “the ladder of abstraction”. You see it in journalism all the time. You begin with a specific story, something very concrete, usually about a person. Then the journalist moves up the ladder of abstraction to provide a conceptual view, maybe with data, maybe with historical context. The article may contain photos or charts to provide a visual representation of the idea. The journalist will move up and down the ladder building a more compelling and complete narrative than abstract or concrete alone can offer.
Maths teachers have used the ladder of abstraction for years – they call it Concrete, Pictorial, Abstract (CPA). They start with concrete, physical objects – number beads, cubes, fingers, etc. before they represent the same concepts pictorially. Finally, the learners are ready to use abstract symbols to represent the same concept. It used to be a one way journey, putting away the number beads as the learners progress, but more and more I see the concrete ‘manipulables’ kept on the table so that a learner can make use of them throughout their learning. They move up and down the ladder of abstraction.
I think we do the same in physics. We’ll get the magnets out with the intention that everyone has a quick ‘play’ before they use the plotting compass. We get our students to pull springs beyond the elastic limit to feel what the deformation feels like. We develop a visceral hinterland.
And then we move up the ladder of abstraction. Learners draw magnetic fields, represent seesaws with triangular pivots, straight lines and rectangular masses. Finally, we move on to abstract mathematical representations.
We move up and down the ladder between pictorial and abstract in lessons and encourage the use of diagrams of various sorts to aid problem solving (see here). But we don’t always drop back down to the visceral.
Here are my recommendations (stolen largely from maths lessons).
- Keep the concrete examples available. If you are teaching about magnetic fields, try to make sure learners have access to magnets. If you are doing moments, leave seesaws and masses on the tables. (I appreciate there are many logistical issues to overcome!)
- Encourage your students to ‘have a quick play’ to model the situation in a question. Let them know what it feels like.
- Talk about the physical sensations. Help your students focus their attention on what they are supposed to be feeling.
- Point out the similarities and differences between the real situation and the pictorial and abstract representations.
- Doing is better than watching (here).
I’m thinking aloud here – I’d appreciate your thoughts.