Children's mathematical knowledge of division was examined in two different perspectives: performance on division problems and children's ideas about division. Eighty children (5-9 years old) were presented with two word division problems (partitive and quotitive). After solving these problems they were asked to define 'What is division?' during a clinical interview. Each child was classified according to their performance on division problems. Different types of definitions were found which varied from definitions without mathematical meaning to definitions that expressed mathematical meaning associated with division. The findings revealed a relationship between children's performance and their ideas about division; also the results indicated that the mathematical meaning associated with division appears before children can successfully solve division word problems. The results are discussed in terms of a developmental approach in which the relations between procedural knowledge and explicit knowledge are considered.
division; problems; definitions
