Computation Routines Prescribed by Schools: Help or Hindrance?

Fifty Brazilian children between the ages of 7 and 13, all number conservers, were individually given seven addition and four subtraction exercises. The children were asked to write down and do each exercise and then explain how the answer was reached. The results showed that: (a) counting was the preferred procedure; (b) the use of school-taught algorithms was rather limited; (c) some children decomposed numbers into tens and units and then worked at both levels, combining results subsequently; and (d) children rarely referred to previously obtained results when doing related exercises. Mathematics educators could profit from a knowledge of the procedures used naturally by children and the specific difficulties related to natural and to school-prescribed routines.