Using Learning Progressions to Design Vertical Scales that Support Coherent Inferences about Student Growth

Abstract

The concept of growth is at the foundation of the policy and practice around systems of educational accountability. It is also at the foundation of what teachers concern themselves with on a daily basis as they help children learn. Yet there is a disconnect between the criterion-referenced intuitions that parents and teachers have for what it means for students to demonstrate growth and the primarily norm-referenced metrics that are used to infer growth. One way to address this disconnect would be to develop vertically linked score scales that could be used to support both criterion-referenced and norm-referenced interpretations, but this hinges upon having a coherent conceptualization of what it is that is growing from grade to grade. In this paper, a learning-progression approach to the conceptualization of growth and the subsequent design of a vertical score scale is proposed and illustrated in the context of the Common Core State Standards for Mathematics.

Keywords:

• growth
• vertical scaling
• learning progressions
• educational accountability

Notes

¹ See, respective of titles, Kolen, 2006, pp. 171–180; Kolen & Brennan, 2004, pp. 372–414; Young, 2006; pp. 469-485.

² Indeed, the second author of this paper, who taught high school mathematics in Colorado as recently as 2012–2013, was completely unaware that math scale scores in Colorado had been linked vertically until informed of this by the first author. This even extends to personnel at the Colorado Department of Education who work in the educational accountability group, who on one occasion in correspondence with the first author insisted that Colorado’s tests were not vertically scaled.

³ http://www.corestandards.org/Math

⁴ http://www.corestandards.org/Math/Content/introduction/how-to-read-the-grade-level-standards

⁵ What we show here is a snapshot view of the full learning progression, which is too large to fit on a single page and is much easier to convey on a website. For the full learning progression, please visit http://www.colorado.edu/education/cadre/learning-progression

⁶ In the mathematics education literature, the term learning trajectory is typically used in place of learning progression, and the work of Confrey and colleagues also invokes the trajectory terminology. However, for the sake of consistency, we use the term progression throughout.

⁷ We thank an anonymous reviewer for bringing this to our attention.