Abstract:

There are two important challenges in mathematics teachers’ education in b-learning contexts: (i) the design of relevant curricular materials for developing the conceptualization of mathematics teaching and (ii) the design of learning environments for developing necessary skills to continue learning along life. The information and communication technologies (ICTs) provide tools for the design of these types of learning environments and curricular materials allow the development of ICTs skills (e.g. skills to participate in virtual forums, to interact with others to solve professional problems in virtual social spaces, etc.).
The teaching experiments represent a research method used in mathematics education that provide the context to analyze the development of the above mentioned skills and link the instructional design and the research about learning (Simon, 2000; Steffe y Thompson, 2000). A teaching experiment includes a “cycle of research” into three phases (Gravemeijer, 2004): (i) the characterization of a hypothetical learning trajectory: how teachers can develop skills when solving the proposed tasks and designing and planning instruction (the definition of learning objectives, the design of the proposed tasks), (ii) implementing the tasks designed and (iii) analyzing the experience from the theoretical framework that support the hypothetical learning trajectory.
The aim of this study is to design and analyze “teaching experiments” in the training of mathematics secondary school teachers focused on “learning the knowledge needed to teach the concept of proportionality” and analyze the influence of ICT. In the learning environments designed in the teaching experiments, we assume that there is a relationship between the student teachers’ interaction, the processes of knowledge construction, and the development of ICT skills.
A teaching experiment consists of several learning environments integrating four types of activities: watching videos, reading the theoretical content, and participating in virtual discussions and social interactions spaces defined by specific issues. Finally student teachers have to make a written report integrating different ideas and presenting a synthesis. The video clips allow student teachers to make explicit the cognitive references through which beginning to endow meaning to the teaching-learning situations. So they can learn to analyze what happen in mathematics classrooms as an aspect of developing teacher competences. In addition, the discussions generated in virtual interaction spaces when professional problems are solved, enable them the development of aspects of ICT competence. These learning environments are implemented in a b-learning context. In the face-to-face instruction student teachers work collaboratively in the professional tasks resolution. In the e-learning activities, student teachers participate in on-line discussions to finish the resolution of the problems and synthesize the ideas in a final report. The analysis of the interactions of pre-service teachers in the discussions provide us information about how we can characterize the relationships between forms of participating in the discussions and the cognitive engagement with the subject-matter to be learned, and about the development of ICT skills.

Keywords:

Teacher training, pre-service teacher experiences, blended learning, virtual learning environments (VLE), mathematics education.