Personalized AI Practice Replicates Learning Rate Regularity at Scale

Jocelyn Beauchesne; Christine Maroti; Jeshua Bratman; Jerome Pesenti; Laurence Holt; Alex Tambellini; Allison McGrath; Matthew Guo

cs.CYMar 9, 2026

Personalized AI Practice Replicates Learning Rate Regularity at Scale

Authors: Jocelyn Beauchesne, Christine Maroti, Jeshua Bratman, Jerome Pesenti, Laurence Holt, Alex Tambellini, Allison McGrath, Matthew Guo,

Organizations: Campus AI

Abstract

Recent research demonstrated that students exhibit consistent learning rates across diverse educational contexts. We test these findings using a dataset of 1.8 million (366k post-filtering) student interactions from the digital platform Campus AI providing further evidence to the observation of regularity in learning rate among students. Unlike prior work requiring manual cognitive modeling, Campus AI automatically generates Knowledge Components (KCs) and corresponding exercises, both of which are validated by human experts. This one-to-many mapping facilitates the application of Additive Factors Models to measure learning parameters without complex cognitive modeling. Using mixed-effects logistic regression, we confirmed the core finding of prior work: students displayed substantial variation in initial knowledge ( $\text{IQR} = [2.78, 12.18]$ practice opportunities to reach 80% mastery) but remarkably consistent learning rates ( $\text{IQR} = [7.01, 8.25]$ opportunities). Furthermore, students using this fully automated system achieved 80% mastery in a median of 7.22 practice opportunities, comparable to the 6.54 reported for expert-designed curricula. These results suggest that automated, science-grounded content generation can support effective personalized learning at scale. Data and code are publicly available. https://github.com/Campus-edu-AI/learning-rate

Figures & tables

Type	Condition	Response
Category	Random variable types	Discrete or continuous
Fact	U wave on EKG	Late repolarization of Purkinje fibers
Rule/Plan	Eye focus during basketball shot	On the target (front or back of rim)
Concept	Contractual capacity	Legal ability to enter into a binding contract

Table 1: Examples of LLM-generated Knowledge Components across different types.

Clarity	%
Very clear	75.3
Somewhat clear	12.7
Not clear	11.9

Table 2: KC evaluation by instructors: clarity (n=361), relevance (n=359), difficulty (n=282).

Parameter	Population	Student Effect
	Effect	Mean	Q1	Median	Q3	SD
Initial Knowledge	0.686	-0.0169	-0.304	0.0221	0.314	0.461
Learning Rate	0.0657	-0.000262	-0.00555	0.000323	0.00516	0.0121

Table 3: Summary Statistics for Mixed-Effects Model Parameters

Figure 1: Observed learning curve versus statistical model predictions across practice opportunities on a Knowledge Component. The solid orange line shows empirical accuracy rates from student practice data. The dashed blue line represents the population-level prediction from a mixed-effects logistic regression model (iAFM framework). Students show consistent improvement from approximately 73% to 85% accuracy over 18 practice opportunities.

Panel of Figure 2 — Figure 2: Parameter distributions from the base mixed-effects logistic regression model (iAFM framework) for n=7161 students. Both distributions show the individual-level variation around population parameters, with initial abilities displaying greater heterogeneity than learning rates. Quartile boundaries (Q1, Q3) and 95% confidence intervals are marked for reference.

	Initial Knowledge			Learning Rate
Percentile	Log Odds	Percent Correct	Ops to 80% (Fixed Rate)	Log Odds per Opp	Percent Point Improvement	Ops to 80% (Fixed Knowledge)
25	$0.59$	$64.24$	$12.18$	$0.06$	$1.23$	$8.25$
50	$0.91$	$71.34$	$7.22$	$0.07$	$1.34$	$7.52$
75	$1.20$	$76.92$	$2.78$	$0.07$	$1.44$	$7.01$

Table 4: Median for initial accuracy and practice opportunities to reach mastery (

80\%

correct probability) for low (25) and high (75) percentiles of initial knowledge (assuming overall learning rate,

\delta

) and learning rate (assuming overall initial knowledge,

\theta

) for the base models.

	level	subject	kc type	$\theta_{\text{pop}}$	$\delta_{\text{pop}}$	$\mathbb{E}[\theta_{\text{s}}]$	$\text{SD}[\theta_{\text{s}}]$	$\mathbb{E}[\delta_{\text{s}}]$	$\text{SD}[\delta_{\text{s}}]$
model 0				$6.85e^{\text{-01}}$	$6.57e^{\text{-02}}$	$-1.69e^{\text{-02}}$	$4.61e^{\text{-01}}$	$-3.00e^{\text{-04}}$	$1.21e^{\text{-02}}$
model 1	✓			$6.94e^{\text{-01}}$	$6.82e^{\text{-02}}$	$-6.30e^{\text{-03}}$	$4.60e^{\text{-01}}$	$0.00e^{\text{+00}}$	$1.20e^{\text{-02}}$
model 2		✓		$6.86e^{\text{-01}}$	$6.56e^{\text{-02}}$	$-3.37e^{\text{-03}}$	$4.55e^{\text{-01}}$	$-1.00e^{\text{-04}}$	$1.20e^{\text{-02}}$
model 3			✓	$6.63e^{\text{-01}}$	$6.42e^{\text{-02}}$	$-1.97e^{\text{-03}}$	$4.59e^{\text{-01}}$	$-0.00e^{\text{+00}}$	$1.19e^{\text{-02}}$
model 4	✓	✓		$6.90e^{\text{-01}}$	$6.64e^{\text{-02}}$	$-1.93e^{\text{-03}}$	$4.55e^{\text{-01}}$	$0.00e^{\text{+00}}$	$1.19e^{\text{-02}}$
model 5	✓		✓	$6.86e^{\text{-01}}$	$6.63e^{\text{-02}}$	$-1.41e^{\text{-03}}$	$4.59e^{\text{-01}}$	$0.00e^{\text{+00}}$	$1.19e^{\text{-02}}$

Table 5: Results of ablation comparing population-level and student-level parameters across model variants. Each model includes different combinations of course level, subject, and KC type effects. Population effects (

\theta_{\text{pop}}

\delta_{\text{pop}}

) represent fixed intercept and slope, while student-level statistics show the distribution of random effects across n=7161 students. Initial knowledge values are in log odds; learning rates are in log odds per practice opportunity.

	$\mathbb{E}[\theta_{\text{kc type}}]$	$\mathbb{E}[\delta_{\text{kc type}}]$	$\text{SD}[\theta_{\text{kc type}}]$	$\text{SD}[\delta_{\text{kc type}}]$
KC type
association	$1.42e^{\text{-02}}$	$8.95e^{\text{-04}}$	$1.76e^{\text{-03}}$	$1.32e^{\text{-04}}$
category	$7.16e^{\text{-02}}$	$4.53e^{\text{-03}}$	$5.11e^{\text{-03}}$	$4.25e^{\text{-04}}$
concept	$1.83e^{\text{-02}}$	$1.16e^{\text{-03}}$	$5.39e^{\text{-03}}$	$3.67e^{\text{-04}}$
fact	$2.80e^{\text{-02}}$	$1.77e^{\text{-03}}$	$3.52e^{\text{-03}}$	$2.62e^{\text{-04}}$
principle/rule/model	$-6.89e^{\text{-02}}$	$-4.34e^{\text{-03}}$	$6.52e^{\text{-03}}$	$3.30e^{\text{-04}}$

Table 6: Comparing Intercepts and Learning Rates for the KC Types factor, expected value and standard deviation are computed over results from model 3, 5, 6 and 7.

Figure 3: Scatter plot the course subject factor effects, Average $\theta_{\text{course subject}}$ against $\delta_{\text{course subject}}$ averaged across ablation Models 2, 4, 6, and 7.

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May 20, 2026

Faster Completion, Less Learning: Generative AI Reduced Study Time on Math Problems and the Knowledge They Build

How much have students' ordinary learning processes shifted in response to generative AI, and how does that affect their durable learning outcomes? Self-report surveys show little change, while small-scale behavioral studies report widespread AI use without the scale or duration to measure learning consequences. We address both questions using a ten-year panel of

3.2

million ALEKS learning interactions for investigating time-on-task, complemented by ALEKS PPL placement-assessment data for examining proctoring and learning outcomes, with a quasi-experimental design exploiting variation in tasks that are more susceptible to AI (text-based word problems) and less susceptible to AI (interactive graph-based problems). Learning time on AI-susceptible problems declines

2.8\%

per quarter among college students after ChatGPT's release, cumulating to

26.9\%

over eleven quarters; high-schoolers show

31.3\%

, middle-schoolers

9.0\%

, and Grade 5 students no detectable change. Among college students, the post-ChatGPT divergence vanishes entirely under proctoring, ruling out broad efficiency gains as the likely explanation. Logistic fixed-effects models on randomly assigned proctored retention items yield a

25\%

cumulative decline in odds of correct response; the same estimator on non-proctored assessment produces a large opposite-signed increase -- inconsistent with any platform, cohort, or curriculum explanation. These results are among the first large-scale behavioral and outcome evidence that generative AI has altered how students study and the knowledge they build -- the population-level indicator of cognitive surrender, with direct implications for educational research, assessment governance, and AI policy.

Sina Rismanchian, Hasan Uzun, Jeffrey Matayoshi +2

University of California, Irvine · McGraw Hill

Mathematics Education Generative AI in Education Cognitive Offloading

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Jun 12, 2026

LessonBench-V1: A Benchmark Dataset for Evaluating AI Lesson Generation Agents

Large Language Model (LLM) based AI educational content generation systems are increasingly being developed, yet no standardised benchmark exists to systematically evaluate them. This study introduces LessonBench-V1, a benchmark dataset comprising 647 human-written lessons paired with LLM-based reverse-engineered lesson plans across 240 STEM topics spanning mathematics, physics, chemistry, and computer science. The lessons are drawn from 97 trusted open sources, including LibreTexts, Brilliant.org and GeeksForGeeks. Each lesson plan is human-reviewed and produced through a pedagogically grounded methodology that synthesises Bloom's Taxonomy, Gagné's Events, Merrill's First Principles, and the 5E Instructional Model. The lesson plans capture 3,620 learning objectives with pedagogical metadata, enabling systematic, reproducible evaluation of lesson-generation AI agents and supporting further research. The study further proposes a three-dimensional evaluation pipeline for use with the dataset.

Ravidu Suien Rammuni Silva, Ahmad Lotfi, Isibor Kennedy Ihianle +2

Department of Computer Science, Nottingham Trent University, Nottingham, UK · Department of Physics and Mathematics, Nottingham Trent University, Nottingham, UK

Educational Assessment Generative AI in Education AI Agent Benchmarks Text Generation Generative AI Evaluation Education

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Sep 23, 2026

StudentBench: AI and human tutoring yield equivalent GRE learning gains

Artificial intelligence offers an unprecedented opportunity to augment human capabilities, yet progress at the frontier has focused primarily on advancing model capabilities. We introduce StudentBench, a suite of AI teaching evaluations and a public platform that enables large-scale data collection with over 175,000 student-AI messages to study whether large language models (LLMs) produce learning gains equivalent to human tutoring. Using StudentBench, we measured learning gains on Quantitative and Verbal GRE questions across 2,383 human participants receiving AI tutoring, human tutoring, or no tutoring. We establish that AI tutoring is statistically equivalent to expert human tutoring for GRE learning gains (p = .015), and in five of the seven GRE domains, the best performing AI tutor surpassed the human tutor, on average. In a second study, expert human tutors compared LLM-generated lesson plans and practice problems through 2,028 pairwise rubric evaluations. Together, the two studies clearly separate AI tutors across: (1) lesson planning, (2) practice-problem creation, (3) conversational pedagogy, (4) cost, and (5) engagement. Surprisingly, one AI tutor achieved learning gains equivalent to human tutoring (p = .044) at 918 times lower cost (USD 0.0052 for AI versus USD 4.81 for human, per percentage point gained). For Quantitative GRE sessions, faster AI replies correlated with more student messages, more messages with more correct practice, and more correct practice with larger learning gains (all p < .002). To support future research, we open-source the de-identified data collected in our studies.

Curtis Northcutt, Inaara Hasmani, Kevin Feng +3

Intelligent Tutoring Systems Generative AI in Education Education

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Abstract

Education

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