In this study, we applied the technique of piecewise linear regression to a total of 144 schools with the third to fifth grades, aimed to search for a turning point at each grade level in terms of the effects of school renewal on school reading and mathematics achievement. We did find a turning point for each school subject at each grade level, with two rather distinguished phenomena of patterns. In the climbing pattern, the effects before the turning point were not statistically significant but the effects after the turning point were statistically significant. In the fading pattern, the effects before the turning point were statistically significant but the effects after the turning point were not statistically significant. For both patterns, the effects before the turning point were statistically significantly different from the effects after the turning point.