This study was an attempt to investigate the relationship between the behavior patterns of mentally retarded children and their achievement level in arithmetic. The subjects were 18 male moronic children in a special class, who did not have gross neuro-motor symptoms. They were classified into the three main types according to observations of their behavior tendencies in daily life : A type, the basic type without emotional disturbance, B type, the excitable type characterized by hyperactivity and, C type, the inhibited type charecterized by hypoactivity. Test items were contrived according to the course of arithmetic study (1st grade-3rd grade). Each item was categorized into any of six fields : figure, measurement, addition, subtraction and using method of money. After each item was tested with each S individually, the index of attainment level of each S for each field=the number of the items which he passed×100/the total number of the items in the field concerned We found following results on the equal level of MA and IQ of the three types of children. As to the general attainment level in arithmetic the A type children were highest, and C type children were lowest. On the items which were resolved by simple mechanical operations, B type Ss attained considerably higher level, than on the ones wich contained reversible thinking processes. Also, the difference between comparative attainment on mechanical operations and on reversible thinking processes was greater in the B type group than in the C type group. With respect to MA, we found a significant difference between the MA of 6 and the MA7. Especially, MA 7chilren of A type showed the highest attainment level (to the 70% level).