Eighteen months ago, I visited a London primary school hailed as exemplary in its maths teaching. A year 6 pupil (aged 10) showed me how she calculated 432 ÷ 12. She hadn’t been taught long division and used a method known as “chunking”. This involves deducting multiples of the divisor (12 in this example) from the 432 until all that is left is a zero or a remainder, like so:
432 – (20 * 12) = 432 – 240 = 192
192 – (10 * 12) = 192 – 120 = 72
72 – (6 * 12) = 72 – 72 = 0
The answer is derived from adding the 20, 10 and 6 to make 36. It is a form of repeated subtraction and its advocates believe it aids the understanding of “place value”. Ofsted, however, views this method as “cumbersome” and “confusing” and it did seem to take the pupil a long time to complete. A similar approach is taken to multiplication. Instead of learning and practising the long multiplication algorithm, numbers are deconstructed into their component parts and formed into a grid:
Imagine the size and complexity of the grid if you wanted to multiply a seven-figure number by 12.
These methods are now universal in our primary schools, with strong resistance to the teaching and practice of traditional algorithms amongst many in the educational establishment.
The Advisory Committee on Mathematics Education (ACME), for example, believes that “the details of longer algorithms are easily forgotten” and
dismisses their importance because they require time and continuous practice.