This thesis reports an investigation into numerical errors
of six- and seven-year-olds, with special reference to two
aspects of subtraction.
A method was found for categorising children into four levels
of attainment. Teaching programmes were then devised to help
them proceed forward to their next level. The first
programme, using concrete aids, had a highly significant
success rate. The children on the second programme,
involving symbolism, achieved only partial success. Children
who failed even the first programme were studied in depth
and a sequence of special remedial work was devised which
proved very successful. This, could be adopted widely by teachers to help children understand and enjoy work on
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.