Hypothetical learning trajectory based professional development programme in a web portal: The development of mathematics teachers in pedagogical concepts

Algeabra is not challenging only for students as a learning field but also for teachers during the time of teaching. In this research, we keep track of the pedagogical development of two middle school mathematics teachers in algeabra education and how they reflect their developments to their teaching. For this manner, we support teachers by giving hypothetical learning trajectories via a Web-based education portal which was developed by a research project with similar purpose. This process, which is designated as an action research, contains the preparations of learning trajectories and lesson plans by the teachers, the applications of these plans, and the revisions of learning trajectories and lesson plans along with feedback from us. We analyze the data collected from the documents available in the Web portal (such as teachers reflections, hypothetical learning trajectories, lesson plans and feedbacks), and videos recorded from lessons, and pre-and post-clinical interviews. We observe that the feedback given via the Web-based education portal extends the teachers' content and pedagogical knowledge. Thus, their abilities on preparing effective learning plans, promoting conceptual learning, moderating in-class discussions and using multiple representations are substantially improved. In addition, we conclude that this process improves the teachers' self-awareness and self-assessment ability which leads to a better tracking of the performance of students. Keywords: Mathematics Education, Professional Development, Web-Based Education Portal, Algebra Learning Area, Hypothetical Learning Trajectory