Learning Algorithms Reference

Learning Algorithms Reference

Last Updated: 2026-02-15 | For: Developers and advanced content authors

This page explains the learning-session scheduling logic currently implemented in MoFaCTS and ties it to relevant literature.

Practical Summary

MoFaCTS currently uses:

• a logistic probability model (LKT-style in spirit, not full Bayesian KT), and
• a selection policy (unitMode) that decides which item to show next using those probabilities.

In learning sessions, the most important selection mode is distance, which picks the item closest to an optimal target probability in logit space.

Where This Lives in Code

• Probability calculation and item selection: mofacts/client/views/experiment/unitEngine.js
• Author-facing tooltip definitions for unitMode and calculateProbability: mofacts/client/lib/tooltipContent.js

1) Probability Model

Default model

If a unit does not provide its own calculateProbability, MoFaCTS uses a default logistic model (defaultProbFunction):

y = -2
  + 0.458 * logitdec(recent outcomes, decay=0.974)
  + 0.29  * stimSuccessCount
  - 0.09  * stimFailureCount
  + 6.14  * recency(stimSecsSinceLastShown, d=0.2)

probability = 1 / (1 + exp(-y))

Inputs used

The model composes multiple signals from practice history:

• recent correctness history (decayed),
• per-stimulus prior successes/failures,
• recency (time since last shown),
• additional contextual history available in p.* when custom probability code is provided.

Why this is "stripped-down LKT"

• It predicts correctness probability using logistic skill/performance signals (similar to KT-family and PFA-family models),
• but it is not a full hidden-state Bayesian Knowledge Tracing model with explicit learn/slip/guess transitions per skill.

2) Selection Policy

Once each candidate item has a probability estimate, unitMode determines selection.

distance mode (primary learning-session mode)

distance computes:

dist = | logit(p_item) - logit(p_optimal) |

and picks the item with minimum distance, subject to eligibility constraints (canUse, spacing rules, hidden-item filters).

Interpretation:

• p_optimal is the desired challenge level (from delivery params or item parameters),
• choosing minimum distance aims to keep practice near an instructional sweet spot.

thresholdceiling mode

Picks the highest-probability eligible item that is still below a ceiling threshold.

3) Worked Interpretation of Distance

Suppose target probability is 0.80.

1. Compute each candidate item's current p_item.
2. Convert both p_item and 0.80 to logits.
3. Pick the item with smallest absolute logit gap.

Compared with plain probability subtraction, logit-space distance behaves better near probability extremes and matches the model's logistic form.

4) Relationship to Literature

The current implementation aligns most directly with this lineage:

• Knowledge Tracing tradition: student knowledge/performance inference from sequential responses.
• Logistic performance-factor modeling: correctness predicted from prior successes/failures and related factors.
• Spacing/recency effects: timing between practices matters for retention and scheduling.

MoFaCTS currently operationalizes this as a pragmatic, configurable engineering model (custom calculateProbability supported), rather than a single locked research model.

References

1. Corbett, A. T., & Anderson, J. R. (1994). Knowledge tracing: Modeling the acquisition of procedural knowledge. User Modeling and User-Adapted Interaction, 4, 253-278. https://doi.org/10.1007/BF01099821
2. Pavlik, P. I., Cen, H., & Koedinger, K. R. (2009). Performance Factors Analysis - A New Alternative to Knowledge Tracing. In AIED 2009. https://doi.org/10.3233/978-1-60750-028-5-531
3. Cen, H., Koedinger, K. R., & Junker, B. (2006). Learning Factors Analysis - A General Method for Cognitive Model Evaluation and Improvement. ITS 2006. https://doi.org/10.1007/11774303_17
4. Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., & Rohrer, D. (2006). Distributed practice in verbal recall tasks: A review and quantitative synthesis. Psychological Bulletin, 132(3), 354-380. https://doi.org/10.1037/0033-2909.132.3.354

See Also

• Learning Sessions
• Developer Architecture
• Content Creation Reference Tables
• Settings.json Reference
• Troubleshooting