OK, so we can see straight away that if we take a general overview of this domain lark, there is an obvious ROD DOMAIN, an ARITHMETIC DOMAIN and an ALGEBRAIC DOMAIN. Each of these have associated ‘mark making’ activities on flat pieces of paper. So, at first glance, there are THREE main domains where we can be active plus their associated mark-making activities. Not surprising children (and adults) get confused is it? Inside the ROD DOMAIN we have various sub domains as described previously. Same with the others. Maybe we are getting a bit too pernickety with these domains. Maybe we’re getting a bit too philosophically mathematical. On the other hand, maybe not.
Looking a bit more carefully at the rod domain, you can see that there is a PURE ROD DOMAIN where there is no mark-making on paper (unless the children decide to of their own accord and in their own way). This is where children can play. When I say play, I mean, totally pure, unadulterated play with no adult interference at all. You, as a teacher are not attempting to get them to do anything or see anything in particular, just let them play.
You might decide it is time to start saying something. In this case you will have entered the ROD SPEECH DOMAIN. You can start saying things like, “I bet you can’t make a chrono-synclastic-infundibulum?”, and so on… (Kurt Vonnegut-The Sirens of Titan. A CSI is a ‘kind of wormhole through space and time where all kinds of truth fit together….” Just what we really need, nicht war?
You might decide to say, “Can you show me half of an orange rod?” Or, “Which one looks most like a strawberry?” Or, “Could you make a monkey using one rod of each colour?”
An awful lot of very useful ideas which are purely algebraic can be accessed in this rod speech domain totally without writing anything down. In fact practically everything that is useful in arithmetic can be first seen here. THIS ALONE IS ABSOLUTELY AMAZING, JUST THINK ABOUT IT. MOST IF NOT ALL OF THE USEFUL ALGEBRA CAN BE ACCESSED IN THIS ROD SPEECH DOMAIN……………
The things seen don’t have to be perfectly understood before moving across to other domains, it just means that when they are seen in other domains there will be some memory trace of the ideas already present at least in the subconscious, maybe more. In addition it must be said that it is a VERY GOOD THING to make a very strong decision to do this TILL THE COWS COME HOME. I.e. do a great deal of it. Do not be in a hurry. This is another big issue that becomes an immense problem. If you move too rapidly to other domains there will be trouble. On the other hand, activities can proceed in other domains at the same time, but only if the child is ready… This is an area where skillful teaching decisions have to be made.