Basic skills tests in which measurement of growth is defined in the context of national norms are discussed. An integral part of the construction of norms is the production of a trait or ability score which is normed. Test publishers define a multidimensional trait by including items which measure it. The trait as a construct is a distinct ability, rather than the sum of a set of discrete skills. To be useful, a normative scale must exhibit monotonic growth. Curves which provide the basis for unambiguous norms are illustrated, using achievement data from a trial of the DMI Mathematics Systems, which is a set of criterion-referenced tests in mathematics suitable for grades K to 8 and above. Objectives were developed to be consistent with current classroom practices, curricula, and textbooks. Two test booklets, each containing 42 items, were tried out in grades 6-10;, using over 2,000 students. The results for some skills showed decreasing characteristic curves from one grade to the next. It was concluded that items which result in non-monotonic increasing characteristic curves must be eliminated in order to have empirically based nonambiguous norms. When the norm-referenced trait involves growth, content areas that do not grow do not belong in its measurement. (GDC)