Differential Return on Investment: Academic Growth Based on Initial Performance

• In Event: 25.073 - Truth and Consequences: Different Reference Groups in Gifted Identification

Abstract

Recent research has illustrated that up to 35% of students in the U.S. demonstrate proficiency at least one year above their current grade level before that year even starts (Peters, et al., 2017) and students who start at the highest levels of achievement show less growth over their time in school (McBee, et al., 2018; Rambo-Hernandez & McCoach, 2015). Vygotsky’s zone of proximal development provides a framework for examining student achievement in school with simulation studies showing that students who have academic needs most closely related to classroom instruction are likely to demonstrate the most growth; as student academic needs deviate from the curriculum, growth suffers (McBee, et al., 2018; Vygotsky, 1937/1980).

This study assesses how much students at varying levels of initial achievement benefit from school by comparing high achieving students’ growth (a) during the school year and the summer and (b) to typical student growth. We use summer growth as the baseline for academic growth in the absence of school. Summer growth simultaneously accounts for multiple out-of-school influences on student achievement (e.g., parental involvement, SES, motivation, and participation extra-curricular activities; Downey, et al, 2004). The difference between school year growth and summer growth is attributable to the effect of school. Thus, students provide their own counterfactual. We pre-registered hypotheses compared to typical students, students with higher initial achievement will show: (a) slower academic growth during the school year, (b) a smaller difference between their school and summer growth, and (c) less growth during the school year.

To test these hypotheses, we examine Northwest Evaluation Association’s (NWEA) Measures of Academic Progress (MAP®) reading data from all participating elementary schools in 10 states with the highest MAP® participation rates from the 2007-2008 academic year to the 2016-2017 academic year.

We use four level hierarchical linear modeling (student repeated measures, nested within students, nested within schools, nested within districts) to model student growth from the beginning of third grade to the beginning of sixth grade (i.e., three academic years and three summers). Student initial achievement is based on their relative standing within their school at the beginning of third grade. Additionally, we only use students who start at their schools 50th percentile or higher. Students will be identified in terms of how many standard deviations they are above their school’s average with students at the 50th percentile serving as typical. The simplified two-level model is illustrated below:

Level 1: Repeated Measures
γ_tijk= π_0ijk+π_1ijk (time in school)+ π_2ijk (time in summer) + e_tijk
Level 2: Student
π_0ijk= β_(00jk )+β_(01jk ) (st.initial achievement SD) 〖+ β〗_(02jk ) (st.initial achievement SD) + u_0ijk
π_1ijk= β_(10jk )+β_(11jk ) (st.initial achievement SD) 〖+ β〗_(12jk ) (st.initial achievement SD) + u_1ijk
π_2ijk= β_(20jk )+β_(21jk ) (st.initial achievement SD) 〖+ β〗_(22jk ) (st.initial achievement SD) + u_2ijk

Although not illustrated above, we will also include quadratic of time on student growth in school and summer, and we will include quadratic effects of initial achievement in standard deviation units to account for potential deceleration of growth as student initial achievement moves away from their school’s initial achievement.

Authors

• Karen E. Rambo-Hernandez, West Virginia University

• Matthew C. Makel, Duke University