It can be hard for children to understand even the early stages of arithmetic. If they don’t get these right, then anything subsequently involving numeracy will always be a struggle. One way to help, might be to link more directly the symbolic representations eg ‘9’, ‘two’ etc with counters of the type commonly used in primary schools.
Today’s invention is a game-like animated program which could run on eg any flavour of OLPC machine. Numbers would be represented as a queue of iconic people or bars or blobs (the child could decide). So something like 5+3 could be shown as equivalent to the joining of ||||| and ||| . These bars might bump into each other and swap positions, to provide some identification -and indicate commutativity. These counters would be animated in 3-D so that a scene containing them could be zoomed around at will. Operations like 131+255 which are scarily hard to visualise mentally could then be controlled and manipulated externally on the screen.
Higher numerical concepts such as the square root could be shown as a field of counters being reduced to a smaller square in one corner. This approach would help avoid obviously wrong numerical results by making them visually implausible and emphasise the importance of anticipating a calculation’s output. Reducing the importance of abstract symbol manipulation (algorithm execution), in favour of understanding the concepts would also be a good way to prime children for rational thinking in general.
