Teachers' Knowledge For Integrating Dynamic Geometry Software Into Mathematics Lessons: Contrasting Chinese And French Cases

Due to the development of the use of new technologies such as computer science in the teaching of mathematics,it is important to study one of the critical aspects which conditions the practice of teachers in the classroom: teacher knowledge.There is a great deal of research into the description and definition of what teachers' knowledge is or what kind of knowledge they need.Several of them point to the important role of technology in describing teacher knowledge.Teacher knowledge can be reflected in their classroom activities.In this research,I have selected one of the most important technologies in the teaching of mathematics: dynamic geometry software,in order to study teacher knowledge involved in their class practices.· Taking instrumental orchestration(Trouche,2004)as a theoretical framework,this research is based on the observation of mathematics lessons from 5 Chinese teachers and 1 French teacher in order to analyze the knowledge they demonstrate in their practice with the technology.Instrumental orchestration takes into account all aspects of teaching practice,from lesson preparation to class conduct.Many works have dealt with dynamic geometry and have characterized how teachers use it.For example,dynamic geometry software plays two distinct roles in mathematical tasks and problem solving: that of amplifier or that of generator(Laborde,2001).This type of software also affects teacher-student interaction(Hollebrands ?Lee,2016).Finally,by using software,the teacher shows whether he focuses rather on mathematics or rather on mathematics related to software(Hollebrands ? Lee,2016).· Focus on technology· Focus on technology to notice mathematics· Focus on mathematics with use of technology· Focus on mathematicsThe assumption that we made is that· Teacher knowledge is revealed in their instrumental orchestrations with dynamic geometry and that we can characterize and describe them by contrasting the cases of Chinese and French teachers.· More precisely:· What can we learn from the analysis of the roles of dynamic geometry in the mathematical tasks selected by the teachers?· What can we learn from the organization of tasks by contrasting the teaching practice of Chinese teachers and French teachers?· What can we learn from the teacher-student interaction by contrasting the French and Chinese cases?In total,11 lessons from the 6 teachers in the study were observed and recorded.They were also interviewed before and after the observed math class,in order to understand in depth their opinions on dynamic geometry.The result is that most teachers see software as an amplifier for presenting content during the teaching process,although software can change learners' strategies for solving tasks.During class and during interaction with students,most teachers focus on mathematical content regardless of technology,although they use different instrumental orchestrations during lessons.The interviews reveal that for teachers,there are many factors that can affect the use of software by teachers,such as: the physical configuration of the class,the capacity of the students,the educational objective,the exam.These considerations require further study.For example,if the teacher conducts a lesson in a computer lab,allowing each student to use dynamic geometry individually,then the teacher can use the software more to create new learning situations for students,while he can control it more in general class.