The Geography of Mathematical (Dis)Advantage - An Application of Multilevel Simultaneous Autoregressive (MSAR) Models to Public Data in Education Research

Oct 15, 2026

Uploaded by Adam

Research on mathematical proficiency gaps links achievement differences to students’ and schools’ poverty indicators, yet neighborhood effects and spatial mechanisms are less commonly addressed due to methodological limits. This article jointly models test-takers’ socioeconomic standing alongside the nesting effects of schools and neighborhood structures. Using multilevel simultaneous autoregressive (MSAR) models and population-level data from 2.09 million New York State test-takers in Grades 3–8, results reveal a geography of mathematical (dis)advantage and spatial dependence across schools and neighborhoods.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages38

Reading Time1 h 36 min

AccessFree to download

Introduction

Mathematical proficiency and achievement gaps

Spatial and multilevel constraints in prior work

Study contribution and modeling approach

AERA Open January-December 2023, Vol. 9, No. 1, pp. 1–38 DOI: 10. 1177/23328584231198452 Article reuse guidelines: [sagepub.com/journals-permissions](sagepub.com/journals-permissions)[ ](sagepub.com/journals-permissions)© The Author(s) 2023. [https://journals.sagepub.com/home/ero](https://journals.sagepub.com/home/ero) The Geography of Mathematical (Dis)Advantage: An Application of Multilevel Simultaneous Autoregressive (MSAR) Models to Public Data in Education Research Manuel S. González Canché The University of Pennsylvania Research has shown that mathematical proficiency gaps are related to students’and schools’indicators of poverty, with fewer studies on neighborhood effects on achievement gaps. Although this literature has accounted for students’ nesting within schools, so far, methodological constraints have not allowed researchers to formally account for multilevel and spatial effects. I contribute to this discussion by simultaneously considering test-takers’own socioeconomic standing and the impact of their nesting schools and neighborhood structures. Multilevel simultaneous autoregressive (MSAR) models and population-level data of 2.09 million test-takers, whose standardized performances were measured at Grades 3–8 in New York State, revealed the presence of geography of mathematical (dis)advantage. Because mathematical performance is spatially dependent across schools and neighborhoods, moving forward, applied researchers should rely on MSAR to account for sources of spatially driven bias that cannot be handled with multilevel models alone. Full replication code and data are provided at [https://cutt](https://cutt). ly/N4zRstL. Keywords: achievement gap, data reproducibility, data science applications, econometric analysis, elementary schools, geographical network modeling, geography of mathematical (dis)advantage, hierarchical linear modeling, interactive data visualization, machine learning applications, multicolinearity in spatial or place-based indicators, multilevel simultaneous autoregressive (MSAR), observational research, performance assessment, regression analyses, research methodology, secondary data analysis, social class, social context, social stratification, spatial dependence, spatial socioeconometric modeling Introduction Mathematical proficiency is a gateway to academic and professional success. Mathematical proficiency predicts reading achievement more strongly than early reading performance (Duncan et al., 2007; Farran et al., 2006; Lerkkanenet al., 2005; Pagani et al., 2010) and is a better predictor of later school success than many other academic indicators (Duncan et al., 2007; Wright et al., 2020) . Relatedly, given the increasing relevance of science, technology, engineering, and mathematics (STEM) in the globalized economy (González Canché, 2017; Pearman, 2019; Rothwell, 2013), efforts to strengthen students’mathematical proficiency levels as early as possible would also affect students’prospects for economic and professional success (Aber et al., 2013; Pearman, 2019) . Mathematical proficiency levels, however, are not homogeneously distributed across student populations. Socialclass differences have been consistently documented to influence students’ prospects of mathematical performance as early as preschool and kindergarten (Case et al., 1999; Denton & West, 2002; Starkey et al., 2004) . Early competence in mathematics has also been shown to lead to later competence in mathematics, when “children who start ahead in mathematics generally stay ahead”(Siegler et al., 2012, p. 691) . Notably, because the effects of mathematical proficiency also lead to success in other academic, economic, and professional areas, early success in mathematics leads to positive spillovers, where success in mathematics begets success in mathematics and in other academic content, thus increasing the possibility of subsequent success in life (Aberet al., 2013) . Spillover effects based

FAQs

What problem does the article address about mathematical proficiency gaps?

It addresses how mathematical proficiency gaps relate to poverty indicators while highlighting that neighborhood effects on achievement gaps are not well handled due to methodological constraints.

How does the study model both individual and contextual factors?

It simultaneously considers test-takers’ socioeconomic standing and the impact of nesting schools and neighborhood structures using multilevel simultaneous autoregressive (MSAR) models.

What data and grade range support the findings?

The study uses population-level data from 2.09 million test-takers whose standardized performances were measured at Grades 3–8 in New York State.

Oct 15, 2026

Uploaded by Adam