Differential return on investment: Academic growth in mathematics and reading based on initial performance

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 (ZPD) and return on investment as theoretical grounding, this registered report examined how students' initial academic performance relative to their school predicts their subsequent academic achievement. The stage 1 accepted registered report is available at https://osf.io/9zmak/. Specifically, we tracked the achievement of a cohort of students who started at or above their school's mean at the beginning of third grade and tested a range of hypotheses regarding their achievement and growth as well as which students showed the greatest gains from their time in school.

Using a large database of student academic achievement in the United States, this registered report included 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 were included on mathematics and reading achievement for effective samples of approximately 220,000 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).

For both mathematics and reading, average student achievement growth slowed as they progressed from third through fifth grade. From there, the findings diverged. In mathematics, student growth was mostly similar across achievement levels and grades from third through fifth. However, in reading, above-average students demonstrated slower growth than average students during the school year but faster growth during the summer. Also of note, at the beginning of third grade, the highest achieving students outscored average students in their school by more than 2 years in mathematics and 3 years in reading.

Our results may be able to be explained via a ZPD model, which posits development only occurs when students are placed in appropriately challenging environments. In mathematics, the observed pattern of relatively consistent growth across achievement levels suggests average students were just as likely to be in their ZPD as higher achieving students. In reading, as initial achievement increased, student reading growth slowed, which suggests the higher the initial achievement, the less likely students were to be in their ZPD. If a goal of education is for students to learn new things, our results suggest existing school offerings in reading are not meeting that goal equitably for students across the performance spectrum. Differential growth patterns should be considered when designing learning experiences for students who enter with a wide range of prior mastery.