Two-Dimensional Knowledge Model for Learning Control and Competence Mapping

The paper presents two-dimensional model for knowledge representation with volume as one variable and ability as another one. This makes possible describing current state of learner’s abilities and integration for higher level parameters e.g. grading related to course or other entities. Both values are related to atomized knowledge elements (competences) with volume interpreted as credit units and ability levels are formed during learning with application of forgetting. This model makes possible characterization (grading) of knowledge based on real abilities independently of predeclared courses and for ‘drop-outs’. So, on that bases one can obtain grade for some course if proper knowledge has been obtained in different courses and schools even when courses had not passed. Also this model helps to build connections between courses as using courses in the role of prerequisites becomes less usable. Not wasting knowledge obtained in MOOCs is another example with high drop-out levels where classical passed-failed model does not work.