In the last couple of posts, I have fallen down a rabbit hole burrowed by the Education Endowment Foundation and others. I don’t think a knowledge-rich curriculum is something that can easily be tested and found to work or not to work, because it relies on the slow accumulation of knowledge across a variety of domains. It also brings into question what we are doing all of this for. If a child knows lots about the solar system but this does not aid her standardised reading performance this year then should we conclude that knowing about the solar system is useless? I don’t think so because I want students to know lots of stuff. In this sense, for me a knowledge-rich curriculum is more of an aim than a method.
Yet I do think that a knowledge-rich curriculum should help improve reading comprehension over the long term due to my understanding of how reading works. This is provided, of course, that students actually learn some knowledge as a result of the curriculum i.e. that the curriculum is effective in its own terms. And I also think that knowledge has a central role in all creative and problem solving endeavours.
I am using a relatively loose definition of knowledge here. We can easily slip into high-minded discussions about the Western literary canon and whether it is representative of our diverse societies, but that’s only a small part of what I am referring to.
For instance, in the 2018 Northern Hemisphere Maths Methods VCE paper – bear with me – there was a question about discrete probability distributions that was set-out in an unusual way. Students needed to recognise that it was equivalent to the more standard version. This is something they could perhaps work out, creating new knowledge for themselves, or it could be something they learn via making a mistake and receiving feedback. In both of these cases, the knowledge will be more like a memory of an event – “remember that time when they asked that question where…” Alternatively, a teacher could explicitly teach this different presentation in class. This is the kind of tiny, grain-sized piece of knowledge that nobody gets excited about, but that can make all the difference.
And while I don’t believe in the existence of generic, trainable skills such as creativity or critical thinking, I do think that some kinds of knowledge can be effective across a number of different domains. Knowledge of logical fallacies, for instance, can help you evaluate lots of different types of argument based upon their form. However, I would contend that the more generic a strategy is, the less useful it is. A person may commit a logical fallacy and still be essentially correct about something. You need relevant domain knowledge to evaluate this correctness.
Similarly, back in the days when physics questions came without diagrams, the heuristic, ‘always draw a diagram’ had some utility for problem solving across the entire subject, from mechanics to electronics. Yet if you did not know the physics involved in a particular situation then drawing a diagram wouldn’t help much.
At the extreme end are heuristics such as ‘effort counts’ or ‘look at things from different perspectives’. You’ll only get marginal gains from applying them and then, only if you have something more substantial to build upon.
What does this knowledge do?
According to cognitive load theory, there are basically two ways to solve a problem. The first is to apply knowledge you already possess, either because you have generated that knowledge yourself or you have obtained it from others, or to randomly generate solution steps and test them to see if they move you closer to your goal.
This sounds as if experts and novices must operate in the same way when they are tackling novel problems, but it’s not quite like that. I would suggest that we ride the knowledge wave as close to the goal as possible before we resort to randomly generating and testing new steps. For relative experts, the wave of knowledge projects them far closer to the desired goal than relative novices and so they are much more likely to be successful. As Isaac Newton wrote, “If I have seen further it is by standing on ye sholders of Giants.”
Low knowledge individuals have to start guessing when they are still a long way from the goal.
Higher knowledge individuals begin the process of trial and error far closer to the goal.
Notice that we could mount an entirely equivalent argument about creativity, with the goal state in the case of creativity being a unique yet valuable product. Creativity is essentially a form of problem solving that precludes known solutions.
Novel problems do not stay novel for long. As successful solutions emerge and are communicated, they become subsumed into the knowledge base of individuals.
If this picture is accurate then there is little point in practising a ‘skill’ of solving novel problems or of being creative, because that is just practising the random generate-and-test stage. It is like practising rolling dice in order to become better at rolling sixes.
However, I don’t think this gives us the full picture. There is an emotional impact of wrestling with novel problems and students probably do need some training in order to learn how to cope with that and develop robust dispositions. Such training would have to be done well, however, because it could backfire. Similarly, a small amount of training in the use of intermediate level heuristics that apply across a range of situations is probably worthwhile.