Each child had a sheet of paper with a grid of dots. On this they were supposed to draw a symmetrical pattern - as complicated or as simple as they liked. It seemed almost like a mapping of their mental activity. Or, as Mrs Peach more prosaically put it, “some of them don’t really understand the task. With them, that’s the first aim, to get them to realise the task. Others grasp the task immediately and they can learn about the concepts and develop them.”

She pointed to Alan’s work. Its quick mastery, fluent strokes and complicated exploration of symmetry matched exactly his exuberant progress through life. As a contrast, there was Gemma, who has recently lost her mother and whose disorganised scrawl, with the first few letters of her name draped haphazardly over the top seemed, in its purple search for shape, to echo her confusion.

Between these two extremes, other contributions showed a fascinating mixture of acuity and bewilderment. There was Bob, who had done all right at the two top corners but had then decided to go for joining the dots in order, a more familiar and safer activity. There was Teddy, who had typically disregarded the teacher’s instruction not to colour in and coloured in asymmetrical parts of his design. There was Fatima, who is very clever and had joined up different parts of her Rangoli in different colours, symmetrical on both sides. There was my Jake, who had tried to make his pattern into a symmetrical drawing of something and hence had two legs hanging down on either side: he much prefers everything to have a defined meaning. There was Regina, who hasn’t really got a clue though she is a sweetheart: she had just started a completely different drawing in one corner.

Many had remembered the previous week’s similar exercise in colouring shapes made out of dots and had made efforts to make geometrical shapes. A few had simply drawn a completely different picture. One boy, with special needs, had drawn isolated shapes at each end of the page. As well as grasping the task and developing and using the concepts, there seem to me to be other facilities mapped out on the Rangoli patterns. Has the child grasped the whole picture, using the entire area - and no more? Thus, do they have a sense of both the extent and the boundaries of any problem? Can they develop detail and correlate it from side to side - can they both control the concrete and abstract from it? And do they have a sense of proportion and rhythm - can they respond to beauty? Have they got the self-control to do what is asked and no more but the individuality to do it in their own way?

I was telling Tim about the Rangoli patterns. Tim is an artist whose canvases vibrate with power and meaning. He is an accomplished draughtsman who for the last several years has eschewed representational images for abstract or abstracted ones, often with densely poetic titles. “Isn’t it strange,” he said, “that we should easily be able to make these kinds of guesses about children’s minds but yet so many people say they are baffled by modern art? People don’t want to believe that they are seeing the inside of someone’s head.”

Of course, the danger with this kind of instant ersatz-Rorshach analysis is that we can easily get it wrong and, carried away by the thrill of our own interpretation, take speculation for proof. How if I didn’t know about Gemma’s mother? Might I not just think she hadn’t been paying attention? Perhaps Hank, a determined individualist if ever there was one, had only filled in one side of the paper because he forgot, rather than being determined to demonstrate that he had found his own way. But I think that’s all right as long as we approach the children’s work with good faith. Then we will believe, as loving parents do, that everything the child does expresses them, everything is worthy of consideration, everything is an opportunity.