On the Origin of the Matthew Effect: Insights From a Quantitative Theoretical Model

• In Event: Are Excellence Gaps the Unavoidable Consequence of Expanded Opportunity for High-Performing Students?

Abstract

A quantitative theoretical model of academic achievement, based on the concept of the Zone of Proximal Development (ZPD), has proven capable of reproducing the results of several empirical, longitudinal studies of achievement. This paper applies the model to understanding the origins of variance in achievement (at the individual and subgroup mean level of analysis), and the effect of gifted education initiatives on that variability. This model has been implemented in the ZPDGrowthTrajectories R package.

The goal of this paper will to describe the psychological underpinning of the Matthew Effect as well as its limitations. The model clearly illustrates how underlying individual differences in learning rate, the educational favorability of the home environment, and the forgetting rate produces variability in student achievement. However, the model also indicates how additional variability results from the interaction between the students’ dynamically changing ZPDs with the unfolding school curriculum. The advancing content presented over the course of the school year works much like a wave that rapidly propels high-readiness students to greater levels of achievement, while often failing to engage the highest and the lowest achievers.

We will examine the effects of many types of curricular interventions that are designed to benefit the most capable students. We vary the boundaries, depth, and pacing of curriculum as well as the educational “dose." We even consider the impact of interventions that increase the baseline learning rate (such as enrichment, by increasing student engagement and motivation), provide intensive summer instruction, or generally increase the educational impact of the child’s home environment. The advantage of this approach is that the effect of many potential interventions can be explored quickly, without the cost and delay of experimentation, and without the risk of harming students. Further, the results are uncontaminated by measurement error or sampling error.

The Matthew Effect does not automatically result from all of these interventions. However, when it does not appear, the cause is always related to curricular insufficiency at high levels of achievement. In many cases, removing educational ceilings in early grades simply creates them later. The effective removal of inappropriately low curricular ceilings – at least when this is done in a general, non-targeted manner – always results in the Matthew Effect. We will also examine the effects of targeted interventions. In some cases, counterintuitive behaviors are noted.

This paper will conform to open science principals; all simulation code will be made publicly available in order to facilitate the checking of results for accuracy as well as future exploration of the model dynamics.

Authors

• Matthew McBee, East Tennessee State University

• D. Betsy Mccoach, University of Connecticut

• Matthew C. Makel, Duke University

• Natasha Lynn Godkin, East Tennessee State University