The Dunning-Kruger effect or "I prefer to do it my way!"
There is not a maths teacher on the planet who has not come across many students (and the occasional parent or three) who will reject the teacher's method with the phrase, "I prefer to do it my way.". This happens sometimes, perfectly understandably, where a previous teacher has used a different method and it is important for all teachers to accept this as being fine. However, it also happens where "my way" usually gives the wrong answer. And in mathematics, "the wrong answer" is something to avoid. Sometimes a student will find a single example of their method working and believe that this is a persuasive argument in their favour, which it isn't. I received an email from the parent of one of my students, a few years back, complaining that I was teaching her daugher an incorrect method for solving linear equations. She even included "a correct method" for me to emulate. Her "correct method" contained no semblance of logic or mathematical understanding at all. And yet, she had the confidence to tell me, a maths teacher with several decades of experience, that I was wrong. Now my imposter syndrome is severe enough that I spent quite a bit of time with this particular Mum's email before I was prepared to laugh out loud in response and send it round the department so everyone else could have a giggle at this parent's expense. The email was duly printed out and spent quite a while pinned to a shelf above my desk, as a warning of how bad it gets from time to time. Retirement means that I no longer even need to be diplomatic with such folk and can use them as exemplars of how not to do things. Anyway, this article is about some research which speaks to this sort of problem.
The Dunning-Kruger effect is actually not really a thing, more an internet meme, as the research itself is way more interesting than the so-called effect. David Dunning and Justin Kruger are social psychologists working in the field of competence and perceived competence (or confidence) and whether these are the same thing.
I would suggest reading the Wikipedia entry on this, which is as good a place as any, to begin. Now I am not going to claim that the research is perfect or that it should be accepted completely or uncritically (no research should), however, it is an interesting way of looking at an observable phenomenon, which for educators is always a great thing to study. There has been criticism of the paper (which was published in 1999) particularly in the realm of cultural differences, and you should certainly look at all sides of an argument before settling down on one side of the fence or the other. I this article, I only wish to show how the observed phenomenon of "I prefer to do it my way!" among students can be placed into a slightly more academic footing than usual.
At the centre of their research is the following graph, which explains their findings.
The bit that people tend to focus on, as it the bit that gives the highest level of schadenfreude, is Mt Stupid. And while Mt Stupid is funny and clever, it is not the whole story, unless your motivation is simply mockery. In learning, this should not be our aim. At all.
The study showed that when students are starting out on an interesting/difficult new topic or concept, they will go through phases of different levels of both confidence and competence. It is the mis-alignment of these two things which is interesting.
What they found was that in the early days of learning a new skill, people tend to over-estimate their competence and show high levels of confidence when their actual levels of knowledge or skill can be shown to be quite low in reality.
This is the peak of Mt Stupid and this naming, I would argue, is why ordinary non-psychologists have latched onto the research and have often demonstrated the truth of the research by how they apply it to all and sundry, even when not appropriate. This is ironic (the genuine, rather than the Alanis sort! ) given what it is that they are over-confident about.
If you are an honest learner, you will, I am certain, be able to view your own learning at many points in your life, through this lens. I certainly can. So, if you are someone who is looking for someone to mock, watch out, as it may well be you next.
For me, it was learning to play music. I, like many nascent guitarists, felt that what I needed to do with my guitar was to play as fast as possible, prefererably in 13/8 time and for musicality to be far far down the list of priorities, far behind impressing other people (a stage I have never attained). I can remember clearly, when I plunged down from the summit of Mt Stupid, into the Valley of Despair, which is where I knew that I would never be able be the musician, I wanted to be. Of course, it is here that the learning really starts in earnest. For me, an amateur and not very good musician, who derives a huge amount of pleasure from playing badly, I have never made it out of the Valley of Despair, but it doesn't matter, as no-one has to listen to the awful racket I make when I turn my amp on.
For the committed learner, the climb up the Slope of Enlightenment is slow, arduous and ultimately satisfying. There are other areas of study where I have managed to climb that hill successfully and it is a hugely worthwhile enterprise, if exhausting.
It is the job of the teacher to encourage our students to get past Mt Stupid without making too many errors, and then out of the Valley of Despair without giving in to the overwhelming temptation to quit. Mathematics gives so many opportunities to learn this cycle that makes it such a tricky subject to master, even in the low foothill slopes where I (and most secondary school mathematics teachers) reside.
The Dunning-Kruger research has implications for the fallacious philosophical position, the just-world hypothesis, which has much to say on the subject of victim blaming and many of the social issues we grapple with on a day to day basis. But this is not the space to go into that. Maybe another time.