应用与计算数学杂志

Application of Markov Chains to Analyze and Predict the Mathematical Achievement Gap between African American and White American Students

Abstract

Vivian R Moody and Kanita K DuCloux

A stochastic, mathematical model known as a discrete Markov Chain was used to show how to estimate the probability that the mathematical achievement gap between African Americans and White Americans would close during a particular calendar year. The implications of race in the achievement of mathematics in the United States are profound and well-documented in mathematics education research literature. The authors used historical data drawn from the National Assessment of Educational Progress (NAEP) to examine trends of mathematical achievement between African Americans and White Americans during the assessment years of 1973–2012. The authors provide a discussion of NAEP data in the context of the discrete Markov Chain model and describe how specific properties of the Markov process were used to estimate the probability that the mathematical achievement gap will close within the next 50 years.