There is an important way to think about what we are trying to achieve in education and this involves making a distinction between the types of knowledge and skills that we want children to learn.
The distinction that I have in mind is between biologically primary knowledge and biologically secondary knowledge. In the book, ‘Cognitive Load Theory,’ Sweller, Kalyuga and Ayers draw upon the work of Geary to explain how this distinction underpins their theory.
Biologically primary knowledge and skills are things that we have evolved to learn. For instance, few people need instruction in learning to walk. Similarly, children just ‘pick up’ their native language. Clearly, we don’t have the vocabulary coded into our brains because children can grow up to speak any language. Instead, we have a natural way of learning this.
Humans have been around in our current form for about a million years (very roughly) and the immediate precursors to homo sapiens could certainly walk and may well have had some form of language. This gives evolution by natural selection the time to work on these capacities. We have literally evolved to learn them.
Another biologically primary skill is the use of means-end analysis to solve problems. We all have this strategy at our disposal: comparing the current state of a problem with the desired outcome. It is pretty much the only universal problem solving strategy – unlike the sorts of sometimes-useful heuristics such as ‘draw a diagram’ – and we don’t need to be taught it. Similarly, you acquire a personality without being instructed in it.
Biologically secondary knowledge is the stuff that we generally have to be instructed in. These are the kinds of knowledge and skills that came late to the party. For instance, writing was only invented a few thousand years ago and, for much of the time since, only a few members of the elite would learn the skill. This means that we cannot have evolved a capacity to learn how to read or write.
This does not mean, of course, that we cannot learn these things by ourselves. A good textbook can provide a form of instruction. Given the time and inclination, we can even learn through discovery. But because these are not ‘natural’ things to learn, the process is always characterised by hard work and it can be arduous. This is why explicit forms of instruction work. They limit the number of things that a learner might pay attention to and so make the process more efficient.
Schools have traditionally tried to deliver both kinds of objective. The village school seeks to teach children the biologically secondary skills of reading, writing and reckoning whilst the playing fields of Eton were created to develop young men’s character and leadership; biologically primary mixtures of inclination and personality.
The extent to which we succeed in doing the latter is debatable. It is much harder to measure someone’s character than their ability to read and so it’s hard to find the evidence. However, I think we confuse ourselves in the way that we think about this. Imagine a Swiss finishing school that aims to teach ladies how to walk. The school is clearly not doing this. It is teaching people to modify the way that they walk; a small alteration to something that they can already do in order to meet a questionable aesthetic.
I worry that when maths teachers seek, as a primary goal, to make students resilient so that they ‘never give up’ then we have lost sight of the biologically secondary learning that we are mainly employed to bring about. Such ideas are always deeply flawed when thought about in the abstract. Should we really never give up? Perhaps sometimes giving-up is the most rational course of action. I am sure that we have all seen the wastage caused by the sunk cost fallacy and I am sure that this is rampant throughout society, wherever egos are at risk.
To really explore a child’s individual relationship with failure would require a kind of therapeutic relationship quite unlike anything that maths teachers are capable of providing. I wouldn’t even want them to try. It’s icky.
However, bringing students to a sense of achievement by having mastered difficult concepts and procedures is to implicitly teach them something about the value of hard work. I think it best that we focus on that.