I continued to work with J and K today on attempting to become 'more conscious' while working on problems. I put 'more conscious' in inverted commas, because it doesn't quite seem to encapsulate what I mean, or rather, is a rather vague term that I am using to stand for lots of things.
I presented some problems for J and K to work on, but before doing them, I asked them to read the following blurb:
Remember what we/I have said about being conscious, of concentrating, on each problem. Use your initiative.
Don’t leave this work until the last minute - it should take quite a long time. Don’t just work through the questions, trying to get them finished as quick as possible - work on them. Take your time. Read the question out loud to yourself. Try to articulate what you know, and what you need. Could you explain to someone what you are going to do, and more importantly why you are going to do it? This is not always possible, but don’t just do things without thinking about what you are doing.
Is your first idea the most useful one? Are you about to make the same mistake you ‘usually’ make (is this a habit)? Take a moment. Is there something else you could try? If you are stuck, look at the question again ‘as a whole’. Is there something you have missed? If there is a diagram, what is it telling you? Could you create a diagram that tells you something? Very often, a ‘reasonably accurate’ diagram can tell you something that you hadn’t realised, or give you an image that helps you realise what to do.
Don’t just work through the problems, work on them. Each one is an opportunity to learn something. Think about what you can learn from each one. When you have finished a question, don’t move quickly onto the next one. First, find a way to check what you have done. Do you have any nagging doubts about what you did?
Then, if you think it will be useful, make notes. You might not need to, if you found the question easy. But if there is a question that you are really stuck on, what is it about that question that is making it difficult? If you get stuck, or if you got unstuck, make a note of what happened. What do you think is making it difficult for you to solve problems ‘like this’? Is there something you can practice, perhaps using the textbook?
Bring all of this to next lesson, and we will talk about it.
If you get tired, take a break and come back to it when you feel fresh. There’s absolutely no point working through the questions for hours, making lots of errors, getting annoyed, with none of it ‘going in’. Work for a while, and when you feel your brain has stopped working, and the quality of your work is getting worse, stop for a while, have a cup of tea and a biscuit, and start again later.
It seemed as though this had some effect; J and K seemed to become more deliberate in their working. J commented that he recognised himself in 'leaving it until the last minute'. He said that every week he set himself to do his homework earlier, but rarely did so. We have talked about this quite a bit this year. Gurdjieff called this the 'disease of tomorrow'. [I have also been talking about the difficulties in setting oneself to do something differently with a group of teachers that I am working with on noticing.]
Both had problems with part (a), and moved onto part (b). K solved this part correctly, and J got the partially correct answer (3/2, 9/2). Interestingly, J paused as he did not think this answer was correct. I asked him how he could check his answer. It is not easy to see how this could be checked. One way is to go back through working, but this is rarely beneficial in my experience. Usually a more fruitful approach is to return to the question as a whole.
I directed J's attention back to the diagram and asked him if his answer looked right. Looking at the diagram, he could see that the y-value should be 3, "because it is half-way". He had substituted the x-value (3/2) into his function for the area, because "this is what we normally do, we substitute the value for x back into the function", but could now see that it was the function 6 - 2t that he should have substituted his value for x into.
I suspect that 'doing what we normally do', without considering the features of the specific problem being worked on, is one of the key factors that leads learners to work less consciously.
We then returned to part (a), which they were stuck on. I asked J and K to read the question again, out loud. They were reticent, but J started reading. As soon as he had finished reading the first sentence, K said that we needed to find the equation of the line through (0,6) and (3,0), which lead to a solution.
It is easy to skim the first few sentences, thinking they are only saying something about the diagram. But we have found time and again that reading the question out loud after having worked on the problem brings affordances that were not present upon a first reading to oneself. I think this is because the second or third reading brings the realisation that we have ignored parts of the question, it draws attention to the whole. It is often the case that the relevance of certain parts of the question only become apparent after having worked on the problem for some time.
I wonder if/when this will become an action that comes to mind for J and K?