The credit for the main concepts behind this article are due to the superbly insightful book “How children fail” by John Holt, still going strong for nearly 50 years.
Little Jimmy walks to school with a pound coin burning a hole in his pocket. But not for long as he exchanges it for 2 fingers of fudge and 4 atomic blasters.
Sat in his chair in class a little while later, his teacher asks him what 2 + 4 equals. For once, he knows the answer – he bought 2 fingers of fudge and 4 atomic blasters for exactly 1 pound. So he confidently announces ‘one’.
His teacher is ‘teaching’ him arithmetic, and tells him his answer is wrong, and tells him the ‘right’ answer.
This ever common situation creates a cascade of problems, all damaging to the child, most of which are beyond the awareness of the teacher.
First, the teacher has failed to understand why Jimmy gave the answer he did – he fails to understand where Jimmy’s understanding of the world has gotten him to. In a class of 30, this is a very hard matter to resolve, I will readily admit, but that does not stop it being a problem.
Second, the teacher has used abstract symbols without even understanding that they are abstract. They are so familiar to the teacher that he cannot see them as a young child can. In essence, 2 + 4 = 6 is an algebraic equation with the algebraic terms missing (2x + 4x = 6x). It really means 2 of something plus 4 of the same kind of thing equals 6 of that kind of thing. This is implied, and thereby assumed by the teacher without making sure that the child has a matching understanding. Young children are very very flexible thinkers, unrestrained by years of reinforcement of what is correct, so to Jimmy, his answer was actually very correct. His algebraic terms were simply different : 2 of one thing plus 4 of another thing cost 6 of another thing again (2f + 4a = 6p).
This brings me to the third problem – that the clear and correct understanding of the problem from Jimmy’s perspective – was refuted. His world view was said to be wrong – without explanation as to why. This can and does shatter the confidence in children. And because the algebraic nature of the ‘correct’ answer is never explained, the child enters a state of confusion. Rather than embracing and learning about the world, he is propelled backwards.
The fourth problem is that he can grow fearful of the teacher – an authority figure who is apparently the proprietor of what needs to be known, but what is not properly understood by many, whose position cannot be questioned.
This in turn can lead to a fearful parrot-like mimicry of the ‘correct’ way of doing things. This is not learning – this is a transient memorisation of things not understood.
Teaching must only operate, if it is to be effective, on the basis of learning, not a mechanical absorption of ‘facts’. But if we insist on teachers being qualified to degree level, many levels removed from the mindset of the children they will teach, are we not in danger of filtering out the wrong type of teacher?