Agentic education · Learning science

Actionable companion · Learning design & outcomes

Learning with agency: Tracking with (Un)Certainty

AI-assisted editorial implementation guide, separate from the original research. Proposed actions are not claims or recommendations attributed to the source authors. No independent peer review of this guide is asserted.

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Evidence and context

Title and abstract screening; stage labels describe reported settings, not verified numerical ages. Design labels require full-text appraisal. Reported stage(s): Age / stage not established. Verify the participant population and task before transferring the findings.

Original authors’ abstract, reproduced under the linked source license:

Abstract One of the highest ambitions in educational technology is the move towards personalized learning. To this end, computerized adaptive learning (CAL) systems are developed. A popular method to track the development of student ability and item difficulty, in CAL systems, is the Elo Rating System (ERS). The ERS allows for dynamic model parameters by updating key parameters after every response. However, drawbacks of the ERS are that it does not provide standard errors and that it results in rating variance inflation. We identify three statistical issues responsible for both of these drawbacks. To solve these issues we introduce a new tracking system based on urns, where every person and item is represented by an urn filled with a combination of green and red marbles. Urns are updated, by an exchange of marbles after each response, such that the proportions of green marbles represent estimates of person ability or item difficulty. A main advantage of this approach is that the standard errors are known, hence the method allows for statistical inference, such as testing for learning effects. We highlight features of the Urnings algorithm and compare it to the popular ERS in a simulation study and in an empirical data example from a large-scale CAL application. Keywords: computerized adaptive learning systems, student modelling, tracking, statistical inferences

What kind of evidence is this?

Intelligent tutoring & adaptive learning · Design requires full-text appraisal

Stage: Age / stage not established. Screening labels describe reported context and study-design language. They are not a risk-of-bias rating or proof of effectiveness for an age band.

Study methods · source passage

We start by restating the Rasch model as a game of chance in which both the player and the item are represented by an urn. These urns are thought to have an infinite number of green and red marbles. The proportion of green marbles in these urns equals the (inverse logit of the) player ability and item difficulty. The game proceeds as follows. Two marbles are drawn -one from the urn of the player and one from the urn of the item- until they are of different colors. The player wins (i.e., a correct response is given) when a green marble was drawn from the player’s urn and a red marble was drawn from the item’s urn, and the player loses (i.e., an incorrect response is given) if a red marble was drawn from the player’s urn and a green one from the item’s urn. See Algorithm 1 for an algorithmic representation of this game of chance.

Design the system before the pilot

Document the learner model, mastery rule, hint sequence and adaptation signal. Compare adaptive routing with the same content in a non-adaptive sequence. Check whether early errors lead to persistent low-expectation pathways.

  • Specify a measurable learning objective, a comparator and a task without tool assistance before adopting a system.

A 90-day district pilot

  1. Days 1–15 · Appraise. Have the curriculum lead and a teacher read the methods and limitations. Record the study design, sample, comparator, outcomes and evidence gaps. Define a local question that the study can help inform.
  2. Days 16–30 · Design. Treat the paper as background evidence until its population is verified in the full text. Do not assign an age-specific intervention or extend adult results to children. Name an accountable owner and set the baseline, success threshold and budget before implementation.
  3. Days 31–60 · Test. Start with a small voluntary cohort, preserve an accessible non-AI route and require teacher review. Use synthetic or de-identified examples; approve data handling and tool terms through district processes.
  4. Days 61–90 · Decide. Extract the participant ages or education stage, recruitment, task and comparator before selecting a local pilot. If these cannot be established, retain the paper for design discussion rather than age-band efficacy claims. Compare with baseline, document uncertainty and stop or revise if learning worsens, access is unequal or critical errors persist.

The board decision brief

Report the learning problem, evidence quality, participating population, total cost including review time, measured benefit, errors, access differences and remaining uncertainties. Make a dated recommendation to stop, revise or expand. A positive perception survey alone does not establish learning improvement.

Attribution and reuse

Abe D Hofman; Matthieu J S Brinkhuis; Maria Bolsinova; Jonathan Klaiber; Gunter Maris; Han L J van der Maas. Tracking with (Un)Certainty. Journal of Intelligence (2020-03-03). https://doi.org/10.3390/jintelligence8010010

Companion prepared 2026-10-30. Original authorship and DOI are preserved. The abstract is an attributed source extract; the implementation plan is new AI-assisted editorial material, offered under the same CC BY 4.0 license. This guide has not undergone independent peer review.