Learning Sequences
| dc.creator | Eppstein, David | |
| dc.date | 2008-03-28 | |
| dc.date.accessioned | 2026-07-07T09:29:07Z | |
| dc.date.available | 2026-07-07T09:29:07Z | |
| dc.description | We describe the algorithms used by the ALEKS computer learning system for manipulating combinatorial descriptions of human learners' states of knowledge, generating all states that are possible according to a description of a learning space in terms of a partial order, and using Bayesian statistics to determine the most likely state of a student. As we describe, a representation of a knowledge space using learning sequences (basic words of an antimatroid) allows more general learning spaces to be implemented with similar algorithmic complexity. We show how to define a learning space from a set of learning sequences, find a set of learning sequences that concisely represents a given learning space, generate all states of a learning space represented in this way, and integrate this state generation procedure into a knowledge assessment algorithm. We also describe some related theoretical results concerning projections of learning spaces, decomposition and dimension of learning spaces, and algebraic representation of learning spaces. | |
| dc.description | 37 pages, 15 figures. To appear as a chapter of J.-Cl. Falmagne, C. Doble, and X. Hu, eds., Knowledge Spaces: Applications in Education | |
| dc.identifier | https://arxiv.org/abs/0803.4030 | |
| dc.identifier | http://arxiv.org/abs/0803.4030 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157669 | |
| dc.subject | Discrete Mathematics | |
| dc.subject | F.2.2; G.2.1; K.3.1 | |
| dc.title | Learning Sequences | |
| dc.type | text |