S-CURVE

S-Curve

S-Curve

The S-curve is a graphic of a frequency distribution that visualizes growth and change. The growth of most organisms follows an S-curve. Growth processes do not simply reach a limit and then stop. Instead, they often follow one of two configurations with respect to limits. The first is a pattern of exponential (even superexponential) growth up to a turning point and then a pattern of slowing growth. The pattern exhibits a slow-slow-quickquick-slow progression: an S-curve. When a young tree is very small, it tends to grow only a few inches each year, but as time passes, it accelerates in both height and girth, until it reaches its natural limit, declines, and dies.

The second growth pattern also resembles an S-curve, but it extends the upward growth by tracing another S-curve back down. The overall pattern becomes a bell-shaped curve and may indicate the phenomenon of overshoot and decline. An example might be population growth in many historic empires. The failing empires outgrow their capacity to provide food or energy and subsequently break down.

These generic patterns of growth were adopted in social science research to frame the diffusion of innovation theory. The French sociologist, Gabriel Tarde, carried out the original diffusion research in 1903 and plotted the S-shaped curve. Modern diffusion research is traceable to the 1943 study by two sociologists, Bruce Ryan and Neal Gross, of the diffusion of hybrid corn among Iowa farmers. Everett M. Rogers, more than any other individual, has been responsible for synthesizing the theories and findings of diffusion research and formulating a unified theory. Rogers discusses four prominent theories of diffusion. His rate of adoption theory concerns us here. This theory visualizes the pattern of the adoption of an innovation as an S-shaped curve, with potential for stabilization and/or ultimate decline.

The S-curve is a graphic of a frequency distribution that visualizes change process, growth, or achievement. The S-curve most often is used to represent what happens when change is introduced into a relatively stable or traditional system. Participants in stable or traditional organizations may range from those who want no change of any kind to those who feel that drastic change is needed. In a school, the reasons for change might range from mandated programs from the district or the demand from the state to raise low or falling standardized test scores to the desire of the school staff to implement an academic program that is more responsive to the needs of all the students in the school.

The S-curve characterizes what happens to an organization when unrealistic expectations impede a planned change effort. The program may run into serious community opposition or lack of teacher support or budgetary shortcomings or any of the other countless obstacles that can slow or kill a comprehensive change effort or even a single program. The change initiative hits what Michael Fullan calls the “implementation dip” and Karl Albrecht calls the “valley of despair.” Things go down rather than up because the existing culture of the organization has been ...