A Theory of Achievement Growth Based on Vygotsky's Zone of Proximal Development

• In Event: Leveraging Nonempirical Quantitative Analysis for Theory Development and Exploration: A New Paradigm for Giftedness Research

Abstract

The physical sciences have made tremendous progress over the past century due in part to the quantitative nature of theories in those fields. Quantitative theories are unambiguous and allow for the specification of precise hypotheses that can be empirically tested. In contrast, educational theories are often qualitative, vague, and incapable of generating precise quantitative predictions. Theories that generate specific predictions facilitate scientific progress by allowing empirical data to arbitrate theoretical disagreement; the more specific the predictions generated, the more falsifiable and useful they are. We propose such a theory in this paper.
A quantitative revolution in educational measurement and methodology allows us to envision the development of quantitative educational theories in a way that was not possible a generation ago. Indeed, the empirical state of gifted education research is stronger than ever before. Quantitative researchers now have the tools and the data to ask and answer almost any question. What we lack are updated quantitative theories – new “arguments” – that these new tools can settle. This paper presents a quantitative model of achievement growth. The core concept is Vygotsky’s Zone of Proximal Development (ZPD, 1978). The model is presented in formal mathematical language. The model can be used to generate simulated growth trajectories that have strong resemblance with trajectories observed in real longitudinal data.

Mathematical formalization of the model. Let the ith student’s ZPD during interval t be defined as some function, ZPD(x). Let the school curriculum, if any, to which that student is exposed during the interval be defined as function SchoolCurr(x), and the extracurricular curriculum, which includes any non-school related educational experiences or skill practice, be defined as function HomeCurr(x). Further, the student’s learning rate in a particular domain (e.g., reading) is defined as LearnRate, and the decay (forgetting) in that domain during the interval is denoted function Decay. If interval t is sufficiently small, the student’s learning during t can be approximated using the fundamental characteristic equations of the model.

Learning = LearnRate * [Integral(ZPD(x)*SchoolCurr(x) + Integral(ZPD(x)*HomeCurr(x)] (1)

Achievement = Prior Achievement + Learning - Decay (2)

Growth trajectories can be simulated using this theoretical model. One finding is that growth during exposure to a fixed curriculum is heavily dependent on prior achievement, even for children who do not differ in their underlying learning rates. The model predicts curvilinear growth trajectories, where the nature of the curvature varies across individuals.

This paper will present simulated growth trajectories from this model. These trajectories will be shown to correspond with those discovered in recent longitudinal studies of reading and math achievement growth (Rambo-Hernandez & McCoach, 2015). It will identify specific predictions that can be tested against appropriate longitudinal datasets. Furthermore, the impact of various gifted education interventions – such as acceleration and enrichment – will be explored.

Authors

• Matthew McBee, East Tennessee State University

• D. Betsy Mccoach, University of Connecticut

• Matthew C. Makel, Duke University