Three factors associated with arithmetical processes (sequence skills, arithmetical strategies, and information processing capacity) were measured in individual interviews with 35 first-grade pupils, aged 7.6 to 8.6, in one Finnish school. Mathematics achievement was determined from information supplied by teachers. Attitudes were assessed twice, with a 3-day interval, for 67 first and second graders. The findings are presented with discussion. Counting skills showed extremely significant development during the year. Pupils made an extremely significant transfer from the use of external aids to the use of mental strategies, but evidence was found to support the view that external aids are significant and indispensible in the learning and teaching of mathematics. The development of information processing capacity was also extremely significant. Sequence skills and arithmetical strategies accounted for 52% to 59% of the variance on the various components of mathematics achievement. Interrelationships of skills were found. Attitude measures were more valid as age and academic ability increased. A lengthy list of references is included with this English summary. (MNS)