Briefly summarized are results from a report on mathematics assessments in 32 states. The general trend in mathematics achievement is upward, since the mid-1970's in some states and the early 1980's in others. Patterns are noted for addition, subtraction, multiplication, and division with whole numbers; fractions; decimals; numeration; geometry; and problem solving. Major implications are noted, particularly the point that students are scoring relatively well on items dealing with computation with whole numbers, but scores on concepts and problem solving are not as high. Topics on which scores were below the 50 percent level are listed, with some comments on the five topics which occasioned the greatest difficulty. (MNS)