Scott FaustAI, learning & software

Research, made inspectable / 01

Inside a learner map.

A response changes the evidence. The map makes that change visible.

My knowledge-tracing research asks how we can inspect a learner model’s state and reconstruct how it got there. Follow this small replay to see the mechanics—and where interpretation needs care.

Explore the replayResearch context

Read the map

Structure stays. Evidence changes.

This is a descriptive learner-state display. It does not choose instruction or demonstrate an educational outcome.

01 / Structure

Dots are concepts.

Lines are fixed relationships. The research system builds them from prepared concept relations; this example uses six invented concepts and equal-weight links. Neither the topology nor the layout changes during replay.

02 / State

Numbers summarize evidence.

Responses tagged to a concept update its correct and total counts. A prior keeps the direct estimate away from certainty after only a few observations.

03 / Context

Neighbors can move a value.

Optional smoothing mixes 80% of the direct estimate with 20% of the neighbors’ direct estimates. A smoothed change can occur without a new response on that concept.

Interactive replay

Follow one response at a time.

Synthetic demonstration. All concepts, links, responses, and times below are invented for explanation. They are not learner records or research results.

Under the surface

A small model, with a visible trail.

This replay implements the native map’s default count update and 80/20 smoothing. It is an explanatory reimplementation, not the full research pipeline.

Before → observe → after

Keep temporal order.

Record k’s response is unavailable to the state before record k. Step forward to observe it, then inspect the updated state. A question tagged with two concepts increments both counts once.

Direct estimate

d = (1 + s) / (2 + n)

Here s counts correct responses and n counts all responses on that concept. With no responses, d = 0.50 is the Beta(1,1) prior—not evidence of 50% mastery. Recent outcomes and last-seen record are displayed separately.

Neighbor estimate

g = 0.8d + 0.2 × mean

The mean uses neighbors’ direct estimates, not their smoothed estimates. These links have equal weights; the native system can use weighted links. With no neighbors, g = d. The native default does not decay counts with elapsed time.

Interpretation

A changing map is a question, not a verdict.

Check

Ask what changed underneath.

Was there direct practice, a different mix of questions, a shared concept tag, or movement in neighbors? Counts and recency provide context. Even a rising direct estimate can reflect easier questions rather than learning.

Separate

The benchmark is a different system.

The thesis also evaluates a separate predictive representation using a 70/30 mixture, additional history features, fitted correction, and calibration. That predictor is not integrated into this native map replay. These node values are not its calibrated response probabilities.

Bound

Inspectability does not establish validity.

This display does not validate mastery, diagnose a learner, establish causal learning gains, or demonstrate a tutor’s effectiveness. It shows how a specified model summarizes evidence. Human interpretation and educational decisions need additional evidence.

The broader research

From a visible state to a defensible claim.

The thesis studies technical auditability. The submitted evidence-to-action framework asks what further evidence is needed before model output can justify educational decisions. This demonstration sits at the representation and inspection stage.

Read the research overview

Public demo updated October 30, 2026. Research manuscripts, learner records, and full reproduction code remain private.