Lusage de la compensation additionner-soustraire et multiplier-diviser par les eleves de onze ans

A class of 32 11-year-olds (grade 4) was given three written tests, each followed by an interview. As students of grades 1–3, these children used text-books with numerous instances of explicit use of inverse operations (e.g. 3×2=6, 6:2=3, 6:3=2). The purpose of the research was to examine the extent to which these students understood and used relations between inverse operations in order to simplify computations. Samples of results:

A majority (21 students) was not able to find the value of 28+75?75 or 14×15:14 without performing all the operations.

About half fell in the preprogrammed traps writing e.g. that 100?19+100 equals 19 or 3×3/4?3/4 equals 3.