Abstract:

In the field of mathematics’ education, we find not many but some proposals that use on-line forums as main strategy to learn mathematics. Most of the investigations in this field are related to the analysis of the students’ interactions, the roles of the teachers and students and the obstacles on using the online discussion forums in the context of problem solving. But, there is less research about which are the students’ patterns of participation when they are solving authentic problems.
Those investigations about the analysis of the discursive process and their effects on mathematics’ learning are based on sociocultural perspectives. They consider the mathematical knowledge as a social construction, and they centre the investigation in the analysis of the processes where this social construction takes place. Furthermore, the Gordon Pask’s Theory of Discussions gives us information about the importance and relevance of the kind of questions planed and the kind of knowledge constructed. In the case of mathematics, the main characteristic of the mathematical discourse is the enormous linguistic richness that it is different from the everyday language. The use of symbols, the density of concepts, the use of logic connectors, the adjectives and prepositions are more important than in a normal online discourse. It means that students can encounter difficulties when applying discursive strategies to communicate mathematical knowledge. In order to solve these difficulties, Salmon (2007) suggests adopting a five-stage model when planning online discursive activities that are: access and motivation, online socialization, information exchange, knowledge construction and development.
In this paper we present the case study of the activities of the stages information exchange and knowledge construction when solving authentic geometrical problems. The themes of the four online forums presented are: what doubts do you have, analytic geometry and everyday life with four subthemes: the uses of the geometry analytic, why the wheels are round, the applications of the conics when launching a satellite to the space, what are the geometrical places.
There were 29 students participating in both forums, grouped in two groups, with different questions and instructions of work. The quantitative and qualitative analysis of the online forum discussions developed in a Moodle environment let to interpret the students’ participation in function of their acting. Actions as reading others posts, publications, actualizations of publications, answering other students, open new lines of discussion.
The quantitative analysis allows identifying the patterns of participation of the students when reading and publishing. In each forum there were analysed all the post, in order describe the density of words for publication, actualization or line of discussion and the number of graphics.
We can conclude the existence of a participation pattern in the different forums: no participation, silent participation that means only reading but not publishing, and a communicative participation with the post of answers, new lines of discussion and the actualization of the posts.

Keywords:

On-line discussions, mathematics, geometry, participation.