A contact has sent me an interview with a Maths’ teacher published in the weekly parents’ magazine at one of the renowned International Schools for 3 – 18-year olds in a major German city – the type of expensive, independent school sought out by English-speaking foreigners on the continent ... and maybe just the sort of establishment which Gove would praise and seek to emulate.
These are extracts of comments made by the senior graduate teacher with 16 years’ teaching experience who has responsibility for coordinating the maths programme within the primary sector.
" I would like parents of our young children to know the importance of students developing conceptual understanding. In maths, conceptualization means students are able to understand numerals are symbols for a quantity. They develop concepts of number by hearing, seeing, touching and experiencing numbers. To learn the concept of three, for example, students need to understand “3” as a symbol of three fingers, three steps, three apples, etc. They use all of their experiences with three ‘things’ to make the transition to what the numeral “3” represents. Young children need hands-on experiences with lots of conversation to understand concepts, whether it is tables or numbers.
" If children learn their times table or number facts only by rote, without having conceptual understanding, then it is like packing lots of tricks into a suitcase. If I travel and forget the suitcase, then when I need what’s inside, I have nothing to fall back on. In maths, if my bag of tricks only includes rote-learned facts without understanding, I can easily get stuck. I need good conceptual understanding to be able to think through a problem so that I don’t need to rely on tips and tricks to get an answer. I need to be able to work it out from what I understand.
" Children who memorize answers to equations are not doing mathematics. Memorizing numbers is not the same as thinking through maths. For maths in the Primary grades, a solid conceptual understanding built through lots of exposure to using numbers in real settings and problems means that when the children have more complex problems to work with, they have a solid base to build towards solving them. Primary students need to have a good conceptual understanding of numbers from our maths programme so that they can apply maths skills more confidently later.
" The foundation for competence in maths is a good conceptual base and that takes a long time to develop. "
I am not a mathematician by any stretch of the imagination but these paragraphs make total sense to me. Would Gove and his acolytes, however, begin to understand what this teacher is talking about? Would they be able to see that these arguments apply equally to other subjects?