The Learning Curve: Revisiting the Assumption of Linear Growth during the School Year

Abstract

Important educational policy decisions, like whether to shorten or extend the school year, often require accurate estimates of how much students learn during the year. Yet, related research relies on a mostly untested assumption: that growth in achievement is linear throughout the entire school year. We examine this assumption using a dataset containing math and reading test scores for over seven million students in kindergarten through 8th grade across the fall, winter, and spring of the 2017–18 school year. Our results indicate that assuming linear within-year growth is often not justified, particularly in reading. Implications for investments in extending the school year, summer learning loss, and the development of racial/ethnic achievement gaps are discussed.

Keywords:

• Learning trajectories
• hierarchical linear models
• summer learning loss
• linearity

Acknowledgments

We are grateful to Angela Johnson and Beth Tarasawa for their feedback on the paper.

Notes

1 To ensure, results were not sensitive to the sample used, we also replicated analyses for the first research question using only students who tested at all timepoints, and results did not change substantively.

2 We define the population of schools as the set of US public schools in the 50 states plus the District of Columbia that reported enrollment of at least one K-8 student during the 2017–2018 school year within the CCD data file.

3 We also calculated standardized gains estimates accounting for within-person correlations across terms and results were highly similar.

4 Learning gains under 9-month and 10-month school year and the extra expected gain from lengthening the school year are calculated in an analogous fashion for the piecewise model.

5 As a supplemental analysis, we also present a conditional piecewise model in Appendix Table A6. Results tell a similar story to the quadratic model.