Differential Return on Investment: Academic Growth Based on Initial Performance

• In Event: Who Gets to Learn? Student Achievement and Academic Growth

Abstract

Students vary in their initial achievement when they enter school and their rate of academic growth as they move through school. These differences have implications for classroom instruction and educational policy. Although previous research has examined initial achievement and growth differences, a gap remains in understanding how initial level of achievement interacts with subsequent growth as children move through school. Using Vygotsky’s zone of proximal development and return on investment as theoretical grounding, we examine how student initial academic performance relative to their school predicts their subsequent academic achievement. Specifically, we track the achievement of a cohort of students who start at or above their school’s mean at the beginning of third grade and test a range of hypotheses regarding their achievement and growth as well as which students show the greatest gains from their time in school.
Students who start at the highest levels of achievement show less growth over their time in school (Rambo-Hernandez & McCoach, 2015) than their average counterparts. Rambo-Hernandez and McCoach found that average students showed achievement gains during the school year but no gains over the summer. Conversely, initially high-achieving students showed less growth during the school year than average students, but their learning trajectory did not change during the summer— they showed as much growth when they were not in school (over the summer) as when they were in school (although there was some evidence of an uptick in growth in fifth grade).
Typically, if a group of students is not showing growth during an intervention, the question of whether that intervention is worth the investment becomes relevant. Moreover, with increased adoption of computer adaptive testing, previous concerns about the difficulty in measuring high performance in students (e.g., ceiling effects, measurement error; Lohman & Korb, 2006) grow less relevant. Still, it remains an open question: how much, if at all, are high-achieving students benefiting from school?
We examine de-identified data from all students from fall 2014 to spring 2017 in grades three through five from the ten US states with the highest participation for the Northwest Evaluation Association’s Measures of Academic Progress (MAP®) – a computer adaptive test of academic achievement in mathematics and reading. Because the MAP is taken at least twice per school year, up to six scores are included on mathematics and reading achievement for anticipated cohorts of an estimated 300,000 students. We built separate reading and mathematics three-level piecewise longitudinal hierarchical linear models (student repeated measures, nested within students, nested within schools) to model student growth from the beginning of third grade to the end of fifth grade (i.e., three academic years and two summers). Our results will show whether there is evidence of differential growth rates in reading and mathematics based on student initial distance from their school’s average score and whether those rates change over time. This manuscript has been accepted as a stage 1 registered report (in principle acceptance), and the authors have recently begun stage 2 (data analysis).

Authors

• Karen E. Rambo-Hernandez, Texas A&M University - College Station

• Matthew C. Makel, Johns Hopkins University

• Scott Joseph Peters, University of Wisconsin - Whitewater

• Cristina Worley, Texas A&M University - College Station