Approximate Modelling of the Multi-dimensional Learner

Abstract

Abstract. This paper describes the design of the learner modelling component of the LEACTIVEMATH system, which was conceived to integrate modelling of learners' competencies in a subject domain, motivational and affective dispositions and meta-cognition. This goal has been achieved by organising learner models as stacks, with the subject domain as ground layer and competency, motivation, affect and meta-cognition as upper layers. A concept map per layer defines each layer's elements and internal structure, and beliefs are associated to the applications of elements in upper-layers to elements in lower-layers. Beliefs are represented using belief functions and organised in a network constructed as the composition of all layers' concept maps, which is used for propagation of evidence.

Learner Modeling for Integration Skills

“…In this way, remediation can directly operate at integration skill levels. This is di erent from granularity-based networks [8,9,32] including competency-based networks [33,35] where higher level nodes represent aggregation (not integration) of lower level skills and aren't directly connected to items. As a result, remediation can't directly operate at their higher levels.…”

“…Each noisy-AND gate uses a slip parameter to capture the the probability of accidentally failing a known item, and a guess parameter to capture the probability of correctly answering an item by chance. In this avenue of work, some use a hierarchical structure among skills, yet focus on either the prerequisite relations among intrinsically di erent skills [6,9,24], or granularity relationships (including competencybased networks) [8,9,32,33,35], where higher level nodes denote more abstract, more general, aggregated skills at which level remediation doesn't directly operate. They are substantially di erent from the integration relationship that we model and the level of remediation that we target here.…”

A Contingency Analysis of LeActiveMath’s Learner Model

“…Once all relevant information concerning an event is made available by LEAC-TIVEMATH, the first step in its interpretation by XLM consists in deriving a probability distribution from which a mass distribution standing for the evidence is generated [12]. Quite probably this step, which includes both the construction of the probability distribution and the specific algorithm used for its translation into a mass distribution, is unnecessary and may have a limiting effect on our use of belief functions as core knowledge representation formalism.…”

“…I2IIIisashorthand f or{I, II, III}) while a level name will be used to denote either a level or the set containing the level only, depending on the context. More details of XLM architecture, modelling framework, knowledge representation and modelling process can be found in [12].…”