Dan Meyer, one of the foremost proponents of fuzzy maths*, has written a couple of blog posts (here and here) where he argues against calling a mathematical mistake a ‘mistake’. He illustrates it with an example where a student makes an error filling in a tedious linear function table. The student has assumed that the interval in the first column is constant and has filled in the second column accordingly.
That’s a mistake, right? However, Meyer would prefer us to see it as the right answer but to a different question:
“If I label it a mistake, even if I attach a growth mindset message to that label, I damage the student, myself, mathematics, and the relationships between us.”
This doesn’t make any sense. The idea of encouraging students to adopt a ‘growth mindset’, an idea based upon the work of Carol Dweck, is not without challenge. Recent systematic reviews of growth mindset interventions have shown little positive effect, but the basic idea of encouraging students to view mistakes as a normal part of the learning process seems reasonable enough.
Yet the students of a teacher following Meyer’s advice will not be able to do this because their mistakes will be covered-up by the teacher. Meyer seems to recognise this later in the post but can’t quite extract himself from his own quicksand.
As a student, I would have hated to be patronisingly informed that my answer would be correct if the question were different, but I have a deeper objection than just this. I think we should be honest with students. There is something manipulative and sneaky about this kind of approach.
So what is going on? It makes more sense when you see fuzzy maths as part of the progressivist tradition. One broad element of this tradition is the tendency to see education as the process of drawing something out of a child rather than putting something in. It is as if the correct maths lies within the child in the manner of a set of tangled-up Christmas tree lights. The teachers’s role is to help the child unwind them.
Of course, this is absurd and that is why fuzzy maths has such a poor track record.
But what if those who go about promoting fuzzy maths do not themselves recognise it as a product of progressivism? Does that invalidate the argument? Not really. Curiously, given the preoccupation of progressivism on students figuring things out for themselves, the cultural transmission of ideas is powerful and ideas thus transmitted may persist long after everyone has forgotten their origin. Peter Ackroyd describes this effect in medieval England in his The History of England Voume I:
“Customs could be an inexplicable mystery. If the king passed over Shrivenham Bridge, then in Wiltshire, the owner of the land was supposed to bring to him two white domestic cocks with the words ‘Behold, my lord, these two white capons which you shall have another time but not now’.”
We are all unaware of the origin of many of the ideas and practices that we hold to and assume are just common sense.
*Fuzzy maths goes by many names such as Reform, Constructivist, Discovery, Problem-Based and Inquiry-Based Teaching. I use “fuzzy maths” as a catch-all