Individualised counterfactual inferences estimate whether a specific student would have performed differently under different help conditions¶

Claim · All claims
Evidence · 1 study · design r2 · q2
Currency · newest study 2026 · not yet checked against its sources · not reviewed by a person · recheck by 2029: tool and model accuracy changes quickly

Subclaims¶

q2 i? For a student who solved Q5 at the 2D level with scheme help, the counterfactual probability of solving Q5 at 2D without help is one; for Q12 solved at 1D with scheme help, the counterfactual probability of reaching 2D with feedback help is between 0 and 0.76, indicating uncertainty. → Francesca Mangili 2026

Evidence¶

Francesca Mangili 2026¶

Francesca Mangili, Alessandro Antonucci, Rafael Cabañas de Paz. (2026). Causal Modelling of Support Interventions for Student Competency Assessment. arXiv. https://arxiv.org/abs/2608.24632 doi:10.48550/arxiv.2608.24632

q2 · i? · design · r2

Individualised counterfactual inference for a single student from the CAT assessment (109-student dataset), conditioning on the student's full set of observed answers and hint usage. For Q12 the counterfactual probabilities were [0,0], [0.24,1] and [0,0.76] for 0D, 1D and 2D, indicating uncertainty about performance with more assistance.

"The former yields probability one forQ 5 = 2D, i.e., we are certain that the student would have been able to use a 2D algorithm even without help."

Discussion¶

Related Claims¶

• Group-level marginal inferences identify population propensity and autonomy but are nearly vacuous for higher algorithmic skill levels — related
• Counterfactual probabilities of necessity and sufficiency quantify the causal effect of hints and skills on task performance — related
• Marginal luck probabilities diagnose question calibration, flagging questions 7–9 as prone to over-performance and question 12 as particularly challenging — related
• Formalisation of theory offers generative models, counterfactual reasoning, and optimal-performance yardsticks unavailable to verbal accounts — a broader claim this one bears on