I. Purpose and Method In the preser;t study the author examines the developmental seqLrences of number concept and clarifles the congnitive characteristics of number in tetarded children. The experiments tried here consist of the following three fields. 1) Experiment I, to analyse the results frorn items concerning both mathematical abilities (i. e, naming number words, cduntings, the addition and subtraction operations, etc. ) and the logical operations of number (i. e, conservation). 2) Experiment II, to. examine the effects of the verbal instructions for countings, on the recognition of equivalences of perceptually different sets. 3) Experiment III, to practise an experimental education for equivalences of gioubs and examine the developmental aspects of acquiring conservation of number. We set the IS group of children (to be verbally instructed with the rules of conservation -reversibility and the Iike-), and the US group(not to be instructed with them) in this training in order to study the children's self-instructive behaviours. Heref children are generally taught equivalences of sets (consisting of the discrete and the continuous) by one-one corresponde.nces and counting. concrete objects. Tests are administered four times : pre-test, middle-test, post-test,and retention-test. Subjects are III retarded .children (morons) of specral classes (IQ 60-79, MA : 3 . 9) and 60 normal child.ren (in total). Main findings may be summarixed as follows.