Looking backwards and looking forwards

Tom Francome closed the ATM Conference this year with this talk, reflecting on the history of the ATM and thinking how we can draw on this history to move learning forwards. 70 years ago, on June the 28th 1952, 12 people attended the first ATM meeting (originally the Association for Teaching Aids in Mathematics). A number line with arrows at each end (Figure 1), or blurred ends, rather than fixed ends, foreshadows the idea that there are numbers smaller than zero or fractions that are greater than one and so on. Gattegno devised his tens chart as a means of harnessing the power of both the structure of the number system and of the learners themselves to notice things and generate new number names from their awarenesses. Teaching all fragments can lead to a fragmented view of mathematics and "too much teaching concentrate[s] on the acquisition of disparate skills that enable[s] pupils to pass tests and examinations" (Ofsted, 2012) - sometimes we want small steps and sometimes we want giant leaps that can be taken within structured wholes.