weeks); for a student with an incoming rate of 25 WCPM, the expected weekly increase would be considerably larger ([125-25+ 30 weeks = 3.33 WCPM). Consequently, relying on cross-sectional normative data can result in varying standards for weekly rates of growth.
An alternative, more direct and perhaps appropriate, method of developing standards for weekly rates of growth is to monitor intraindividual student progress over time and to calculate normative data directly from students' weekly rates of improvement. Within the current educational reform, formative teaching systems such as CBM are most useful for indexing individual student growth over time -- to evaluate an individual's rate of progress and to assist teachers in developing better programs. Therefore, intraindividual norms for student growth, which describe students' weekly rates of improvement over time, appear necessary.
The purpose of this study was to provide intraindividual CBM norms for weekly rates of growth, or slopes of achievement. This normative slope information is critical to establish standards for formatively evaluating student growth toward satisfactory outcomes and developing instructional plans. This study makes an important contribution for three reasons. First and most specifically, intraindividual normative slope data should prove useful for CBM practitioners as they monitor student progress and use the information to develop instructional programs. Second and more generally, the methodology used in this study illustrates how other formative evaluation systems may develop norms; thereby, this study contributes to the development of a technology for measuring student change. Third and more theoretically, the resulting data can be interpreted in terms of models of student growth, which can enhance our understanding of human learning.
This database represents two consecutive years of investigation, with two samples of students, using standard CBM procedures in math, spelling, and reading in five school districts in the upper Midwest. The percentage of students receiving free or reduced lunches in these five districts ranged between 33 and 55, and the average normal curve equivalent on widely used, standardized commercial achievement tests was between 47 and 64.
In both studies (Years 1 and 2), every general education teacher within each participating school was included. In the Year 1 study, 24 teacher participants taught Grades 1-6 in three schools; each school participated in one academic area In Year 2, 51 participating teachers taught students in Grades 1-6 in five schools. Teachers in two schools participated in math; teachers in the other three schools, in spelling. In one school, teachers participated in both spelling and reading.
Students enrolled in the target schools participated. In Year 1, 117 students were included in reading, 252 in spelling, and 177 in math. In Year 2, 257 pupils were included in reading, 1,046 in spelling, and 1,208 in math. Any student with a disability, who was mainstreamed