An Automatic Group Formation Method to Promote Student Interaction in Distance Education Courses

This article proposes an automatic group formation method applying the particle swarm optimization (PSO) algorithm to boost the quality of students' online interactions. The groups were heterogeneous regarding their levels of knowledge and their interests, and three different leadership roles were distributed among group members. A case study with 66 undergraduate students was performed. Discourse analysis was applied using two coding schemes to measure the critical thinking apparent in the students' online discussions and evaluate the socio-cognitive aspects of group interactions. The results provided evidence that groups of undergraduate students formed by the proposed method achieved better scores in most categories analyzed when compared to the randomly formed groups.

Quasi-automatic semigroups

Quasi-automatic semigroups are extensions of a Cayley graph of an automatic group. Of course, a quasi-automatic semigroup generalizes an automatic semigroup. We observe that a semigroup [Formula: see text] may be automatic only when [Formula: see text] is finitely generated, while a semigroup may be quasi-automatic but it is not necessary finitely generated. Similar to the usual automatic semigroups, a quasi-automatic semigroup is closed under direct and free products. Furthermore, a semigroup [Formula: see text] is graph automatic if and only if [Formula: see text] with a zero element adjoined is graph automatic, and also a semigroup [Formula: see text] is graph automatic if and only if [Formula: see text] with an identity element adjoined is graph automatic. However, the class of quasi-automatic semigroups is a much wider class than the class of automatic semigroups. In this paper, we show that every automatic semigroup is quasi-automatic but the converse statement is not true (see Example 3.6). In addition, we notice that the quasi-automatic semigroups are invariant under the changing of generators, while a semigroup may be automatic with respect to a finite generating set but not the other. Finally, the connection between the quasi-automaticity of two semigroups [Formula: see text] and [Formula: see text], where [Formula: see text] is a subsemigroup with finite Rees index in [Formula: see text] will be investigated and considered.

An Automatic Group Formation Method to Promote Student Interaction in Distance Education Courses

This article proposes an automatic group formation method applying the particle swarm optimization (PSO) algorithm to boost the quality of students' online interactions. The groups were heterogeneous regarding their levels of knowledge and their interests, and three different leadership roles were distributed among group members. A case study with 66 undergraduate students was performed. Discourse analysis was applied using two coding schemes to measure the critical thinking apparent in the students' online discussions and evaluate the socio-cognitive aspects of group interactions. The results provided evidence that groups of undergraduate students formed by the proposed method achieved better scores in most categories analyzed when compared to the randomly formed groups.