This dissertation report follows a three-paper format, with each paper having a different but related focus. In Paper 1 I discuss conceptual analysis of mathematical ideas relative to its place within cognitive learning theories and research studies. In particular, I highlight specific ways mathematics education research uses conceptual analysis…

Connectivism, which has been argued to be a new learning theory, has emerged in the field of online learning during the last decade. On the World Wide Web at least, connectivism promises to establish learning spaces similar to those that Ivan Illich imagined in "Deschooling Society", through so-called massive online open courses (MOOCs).…

Concept comprehension is an important foundation for more complex thoughts. To enhance concept comprehension, teachers of traditional classrooms have been using instructional strategies and specific course designs, which have been proven effective. It initiates a hypothesis that integrating instructional strategies in the course designs of an…

This mixed-methods study probed the effectiveness of three kinds of objects (video, theory, metaphor) as common reference points for conversations between online learners (student teachers). Individuals' degree of detail-focus was examined as a potentially interacting covariate and the outcome measure was learners' level of tacit knowledge related…

Learning can be viewed as a communication process that puts the learner in contact with concepts created by others. A result of communication is that an act of interpretation starts, which invokes a process of conceptualization. According to Mayes, successful conceptualization will need the support of learning activities. Hence, machine mediated…