Abstract thinking

Another big problem children face is that of abstract thinking. I once taught in a primary school on Humberside, where I was asked to tutor the problem child of a class. This little boy desperately wanted to learn and get approval, but wasn’t particularly able. As a consequence, he continually disrupted the class by demanding attention from the teacher, who with 25 other pupils to teach, couldn’t spend time with him.
This boy’s main problem with maths was his stage of mental development. He had not developed abstract thinking. This was evidenced by his inability to multiply 50 by 3 when asked to by his teacher. His attitude was principally “How can anyone do that?” Who learns their 3 times table as far as 50 times? Who learns their 50 times table?
I then asked him to draw a shape. What shape is a 50. He didn’t immediately understand me, so I drew an equilaterally curved heptagon (the shape of a 50p piece).
I then asked him what he would have if he had 3 of these. Without hesitation he replied that he’d have £1.50. I then explained that he’d answered the question. 3 lots of 50 was 150, just like he’d said it was.
Once the boy had converted the problem from an abstract one involving numbers, into a concrete one involving things (in this case three 50p pieces) he had no difficulty with the arithmetic.