Wodarz Maria N, Komarova Natalia L, Ma Timmy
University High School, Irvine, California, United States of America.
Department of Mathematics, University of California, San Diego, La Jolla, California, United States of America.
PLoS One. 2025 Sep 10;20(9):e0329296. doi: 10.1371/journal.pone.0329296. eCollection 2025.
It is well-known that income can correlate with the academic performance of K-12 students in the United States (U.S.). However, the mathematical relationship between income and K-12 performance, and how it varies across states, remains poorly understood. To help fill this gap, this study examines the relationship between K-12 student performance scores (defined as the percentage of students meeting or exceeding grade-level expectations) and median household income, across more than 12,200 public school districts in 42 US states. The study focuses on performance in English Language Arts (ELA) and Mathematics in 3rd and 8th grades during the 2018-2019 school year. A number of different mathematical functions are explored to quantitatively characterize this relationship, and the best fitting functions are determined statistically. It was found that in about half of the states, the proficiency rate increases linearly with the median household income, while in the rest of the states the increase is characterized by a saturating function. Further, the results reveal that less affluent states exhibit a steeper increase in performance with income compared to wealthier states. Additionally, grade-level and subject comparisons highlight disparities, including a pronounced decline in math performance from 3rd to 8th grade in most districts. These findings underscore the correlations between socioeconomic factors and educational outcomes and the variations between subjects, grade levels, as well as locations. By expanding our understanding of these relationships, this research offers potentially useful mathematical methodologies for developing evidence-based, quantitative approaches to studying educational equity.
众所周知，在美国，收入与中小学学生的学业成绩存在关联。然而，收入与中小学学业成绩之间的数学关系，以及这种关系在不同州之间如何变化，仍未得到充分理解。为填补这一空白，本研究考察了美国42个州超过12200个公立学区中小学学生成绩分数（定义为达到或超过年级预期的学生百分比）与家庭收入中位数之间的关系。该研究聚焦于2018 - 2019学年三年级和八年级的英语语言艺术（ELA）和数学成绩。探索了多种不同的数学函数来定量描述这种关系，并通过统计确定最佳拟合函数。研究发现，大约一半的州，达标率随家庭收入中位数呈线性增长，而在其他州，增长则呈现为饱和函数特征。此外，结果显示，与较富裕的州相比，较贫困的州成绩随收入增长更为陡峭。另外，年级和学科比较突出了差异，包括大多数地区数学成绩从三年级到八年级显著下降。这些发现强调了社会经济因素与教育成果之间的相关性，以及学科、年级水平和地区之间的差异。通过拓展我们对这些关系的理解，本研究为开发基于证据的定量方法来研究教育公平提供了潜在有用的数学方法。
