An adaptive Theory of Computation online course in ActiveMath

Abstract

A standard Theory of Computation course for undergraduates spans three important topics that are at the core of the computer science (CS) curriculum: automata and languages, computability, and elementary complexity theory. The level of abstraction makes the course demanding to teach, but also to learn. The traditional static "one size fits all" textbook, or e-textbook, cannot adapt to different students according to their background knowledge, experience, personal preferences, and learning goals. In response to these shortcomings, we report on the design and a prototype implementation of an adaptive e-textbook for the undergraduate course Theory of Computation in ActiveMath. The main challenges are to develop an ontology for the core concepts suitable for the semantic knowledge representation of ActiveMath, which is the basis for the adaptivity, and then to actually create the course content, i.e., the definitions, theorems, proofs, examples, exercises, and interactive visualizations according to the constructivist approach to teach this course.

Interactive Concept Maps in Ontology-Oriented Information and Learning Web-Systems

“…У статті [4] пропонується використання карт понять у навчальних середовищах для вивчення математики для навігації та кращого засвоєння матеріалу (рис. 2).…”

An Intuitionistic Fuzzy Approach to Classify the User Based on an Assessment of the Learner’s Knowledge Level in E-Learning Decision-Making

“…The numbers of such concepts represent the teaching domain and selected granularity. For example,a domain 'introduction to finite automata' is divided into smaller concepts like basic definitions, deterministic finite automata, nondeterministic finite automata, finite automata, etc., which can be described as C={c1,c2…., cn} where 'n' is the total number of domain concepts [16]. Learning dependencies amongconcepts are represented by the ordered prerequisite relation 'R,' as given below:…”