Introduction

Structure of ActiveMath's student model SLM represents each concept, rule, misconception and aggregations captured in the content in the structure (map) it generates. Every concept is augmented by various competency nodes each of which holds a stack for the last four evidences with a set of values indicating P(I), P(II), P(III), P(IV), i.e. the probabilities for the user being at a competence level I-IV for a competency related to that concept. Concepts can be related (prerequisite relation).

Update triggering

Events are sent from system components which include the following information/evidence: user's action (exercise step) ID together with the concepts (IDs) it is for, the success rate diagnosed by the system, if applicable the misconception diagnosed by the system, the difficulty and competence-level metadata of the exercise (step).

Propagation

Propagation of direct evidence of concept-competence nodes is triggered by incoming events and introduces evidence for the node(s) addressed by the event (concept it is for and event&apss competence). The updating result depends on the previous value, the difficulty level and the success rate in the event. In case of a negative evidence (wrong answer for the particular exercise), it is propagated to concepts that depend on the concept addressed by the exercise. In the case of a positive evidence, this gets propagated to the prerequisite competencies.

Competency Assessment

The competency level presented to the learner is the computed direct evidence for the particular concept. If no direct evidence is available, the indirect evidence (previously propagated as explained above) will be given. If neither is available the learner model tells the learner that no evidence is available.

The output of SLM:
Summarized probability value for each concept x competency.

Future work

Reasoning about tendency and inconsistencies of stacks.