A fundamentally challenging question in K-12 education is about the effects of taking more advanced or challenging classes. It is particularly complex because students (and/or their parents) choose whether to enroll in these classes, making causal analysis challenging. In this paper, we begin to tackle this question by taking advantage of a novel dataset from a public school system in the US. This dataset records students' course enrollment decisions, prior academic histories, demographics, and subsequent outcomes around the time of a district-wide change that introduced optional open-enrollment advanced middle-school courses in subject areas. This is a rich observational dataset, but enrollment in advanced classes is driven by student characteristics and choices rather than random assignment. This creates a core identification challenge: the same factors that influence enrollment in advanced courses are also predictive of academic outcomes. As a result, simple comparisons between enrolled and non-enrolled students are confounded, and naive estimates may reflect underlying differences in student ability, motivation, or support rather than the impact of coursework itself. Our analysis shows that enrolling in advanced English courses has a net positive but modest effect on student achievement outcomes. However, these benefits are unevenly distributed: some students with relatively large predicted gains ("middle achievers" in prior years) are less likely to enroll than others. Some other groups (e.g. Black students and those with lower socio-economic status) also demonstrate significantly lower propensity to enroll. This gap between predicted benefit and observed enrollment illustrates how careful data analysis can extract actionable insights from large observational datasets, including identifying students who appear well-positioned to benefit but do not select into advanced options.
Figures & tables
Figure 1. Distribution of prior-year reading achievement among students in general education ELA classrooms before and after the introduction of the opt-in intensified coursework policy. The gray distribution shows the 2022–23 cohort prior to the policy change, while the blue distribution shows the 2023–24 cohort remaining in regular (non-intensified) ELA classrooms after high-achieving students opt into intensified courses. Overlaid density curves with prior reading achievement in z-scores on the horizontal axis and density on the vertical axis. The gray curve represents the 2022–23 cohort, and the blue curve represents students remaining in general education ELA in 2023–24. The blue distribution peaks to the left of the gray distribution and has less density at higher achievement levels, showing a shift toward lower prior achievement among students remaining in general education.
(0)
(1)
(2)
(3)
Baseline
VA Model
+ Extended Pathways
+ Demographics
Advanced ELA Enrollment β
0.205 ∗∗∗
0.086 ∗∗∗
0.086 ∗∗∗
0.063 ∗∗
(0.048)
(0.031)
(0.032)
(0.031)
Prior ELA Achievement
0.727 ∗∗∗
0.407 ∗∗∗
0.416 ∗∗∗
0.357 ∗∗∗
(0.037)
(0.048)
(0.045)
(0.045)
Math Pathway Indicators
No
Yes
Yes
Yes
Table 1. Value-Added Regression Estimates of Intensified ELA Enrollment
Figure 2. Distribution of estimated propensity scores for enrollment in intensified ELA coursework by treatment status. The shaded curves show the estimated propensity-score distributions for enrolled and non-enrolled students. Vertical dashed lines denote the trimming thresholds used in the main specification. Overlaid density curves with estimated enrollment propensity on the horizontal axis and density on the vertical axis. The blue curve for non-enrolled students is concentrated near zero, while the red curve for enrolled students is concentrated at higher propensity scores, peaking around 0.85. The distributions overlap across intermediate scores. Vertical dashed lines at 0.02 and 0.98 mark the lower and upper trimming thresholds.
Estimator
Propensity Trim
N
ATE
95% CI
Constant Effect (ATE-only)
LinearDML
0.02–0.98
1,481
0.071
[0.003,0.140]
Mean of Heterogeneous Effects (Causal Forest)
Causal Forest DML
0.01–0.99
1,583
0.068
[−0.019,0.155]
Causal Forest DML
0.02–0.98
1,481
0.064
[−0.074,0.201]
Causal Forest DML
0.05–0.95
1,289
0.071
[−0.022,0.164]
Table 2. Average Treatment Effects from Double Machine Learning
Figure 5
Figure 5. Enrollment rates in intensified ELA coursework by prior achievement band and socioeconomic status. Grouped bar chart showing observed enrollment rates across seven prior ELA achievement bands, with overlaid logistic trend lines. Green bars and a dark green line represent higher-socioeconomic-status students who are not eligible for free or reduced-price lunch. Orange bars and a dark orange line represent lower-socioeconomic-status students who are eligible. Enrollment generally increases with prior achievement and is higher for higher-socioeconomic-status students in most bands. In the highest achievement band, observed enrollment is approximately 87 percent for higher-socioeconomic-status students and 33 percent for lower-socioeconomic-status students, whose observed rate falls despite the rising fitted trend.
Figure 7
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
Construct
Generic definition
Use
ELA outcome
End-of-year ELA assessment score, standardized within assessment and cohort.
Primary outcome in the regression and causal-ML analyses.
Treatment
Indicator for whether a student enrolled in intensified ELA rather than regular ELA.
Treatment variable in all effect-estimation models.
Prior achievement
Prior-year standardized ELA and mathematics assessment scores.
Accounts for students’ academic starting points; also used to model treatment-effect heterogeneity.
Academic preparation
Prior GPA, prior ELA and mathematics performance levels, prior course pathways, and mathematics pathway information used in the regression models.
Captures differences in prior preparation and academic trajectory.
Demographic and program characteristics
Gender, race/ethnicity, disability status, English-learner status, free or reduced-price lunch (FRL) eligibility, and gifted identification.
Used as adjustment variables and for descriptive subgroup analyses.
Prior engagement
Prior chronic-absence status, absence and tardiness measures, and prior suspension status.
Additional pre-treatment controls in the causal-ML models.
Appendix
Table S1. Variables used across the empirical analyses.
Early detection of at-risk students and timely academic intervention pose major challenges in advanced mathematics education, where complex conceptual hierarchies and nonlinear learning trajectories often hold back students' academic performance. This study adopts multimodal data analytics to build a dynamic framework for learning behavior prediction and academic early warning. It constructs a hierarchical knowledge graph ontology, realizes adaptive edge weighting according to problem difficulty and student performance, and combines heterogeneous graph attention with temporal sequence modeling to capture students' evolving knowledge states. Empirical tests on semester-long multimodal datasets prove that this method can accurately identify high-risk students and effectively track error propagation. Targeted interventions greatly improve students' knowledge mastery and reduce academic risks. The results verify that integrating knowledge graph analytics with multimodal temporal modeling can deliver more efficient and personalized learning support for advanced mathematics education.
Liu Qiong, Li Zhengbo
Moutai Institute,, Renhuai, 564507, Guizhou, China
Despite the widely recognized potential of AI in education, most prior work has focused on individualized student assistance. In contrast, the majority of educational practice worldwide still takes place in collective classroom settings. To enable researchers to study AI assistance in collective teaching, we introduce Edustories, a dataset of 1,492 teacher-written case studies describing real elementary and high-school classroom situations involving challenging student behavior, pedagogical interventions, and their outcomes. Among many other applications, Edustories enables evaluating LLMs' ability to predict the success of teacher interventions, crucial for providing practicing teachers with useful feedback. Comparing the latest models from four language-model families against expert assessments, we find that current models fall short of human expertise in predicting classroom outcomes; the strongest models reach 58% accuracy compared to 64% of human experts. This gap highlights both the limitations and the emerging potential of AI as assistants for practicing teachers.
Michal Štefánik, Jan Nehyba, Jirina Karasova +4
Faculty of Education, Masaryk University, Czechia · R&D Center for Large Language Models, National Institute of Informatics, Japan
Existing predictive models in learning analytics often treat student academic history as a simple sequence, overlooking the concurrent nature of courses taken within a semester. This simplification can lead to inaccurate performance predictions, particularly for students with heavy or challenging course loads. This paper introduces a TRansformer for Academic Course-grade Estimation (TRACE) that addresses this limitation by jointly predicting both the set of courses a student will take and their corresponding grades for an upcoming semester. Our approach encodes courses on a per-semester basis to capture the effects of course concurrency and utilizes a novel loss function combining course-set prediction with grade prediction. We demonstrate that predicting courses taken in addition to the grades in those courses leads to significant improvements in prediction quality. Trained on ten years of institutional data, our joint prediction model reduces mean absolute error by nearly 50% compared to an identical architecture that predicts grades alone. The model also outperforms traditional LSTM-based sequential models, as well as graph neural network-based approaches, and offers natural ways to incorporate student attribute data. This work demonstrates the utility of modern neural architectures for creating interpretable models that can be adapted to new institutions via retraining and recalibration, as well as the importance of key techniques, such as predicting courses taken during training. We discuss how this model could be incorporated into early detection systems at institutions of higher education.
Paul Savala
Mathematics, St. Edward’s University, 3001 S Congress Ave, Austin, 78704, TX, USA. · S Congress Ave