Seventh Grade Students' Learning of Angles Technological Environment: Cultural Historical Semiotic Analysis

The goal of this research was to analyze students’ gestures when they learn the angles topic, in addition to their symbolic and graphical writings. This analysis enabled us to examine the different learning processes that students perform when they learn a geometric topic in a technological environment, in our case using GeoGebra. To do so, we used the knowledge construction theory of attention (Posner & Peterson, 1990) and awareness (Allport, 1988), and from the other side the objectification framework (Radford, 2003, 2005, 2008, 2009 ). This study answered two questions: (1) what are the characteristics of students’ building of knowledge according to Posner and Peterson, and to Allport, when they learn the angles topic in a technological environment? (2) What are the characteristics of students’ objectification processes according to Radford, when they learn the angles topic in a technological environment. The research participants were selected from seventh grade students in governmental schools belonging to Nablus city Directorate of Education, on condition that the participants' marks were 85 or more. The participants studied the angles unit using GeoGebra. The researcher observed the participants' use, in the process of learning, of bodily and hand gestures, and different types of verbal, algebraic and graphical symbols. In addition, she videoed the learning of the research participants. This learning was analyzed using the previous analysis frameworks. The research results showed that students' attention emerged during their preparedness and adaptation to the mathematical situations and their exploration of the mathematical objects and relations. Regarding awareness, it appeared as a result of students' change of behavior and through their telling about the relations or some of the concept properties, but not all of them. The research results showed also that the students went through three stages of knowledge objectification: the factual stage, the contextual stage, and the symbolic stage. In the factual stage, the students expressed the geometric relations in gestures, or through special cases or through figures. In the contextual stage, the students expressed the geometric relations using a language that was not precise, but they coordinated between their gestures and talk, where their language included deictic terms. In the symbolic stage, the students expressed the geometric relations using precise language, where their use of gestures lessened and their use of the concepts in new contexts increased. It is recommended that the teaching practice in the classroom increases the use of teachers' questions, group discussion, and using technology, where recent studies show the contribution of these teaching practices to the development of students' mathematical understanding, exactly as the results of the current research show. It is also recommended that more qualitative studies be done to analyze students' mathematical understanding using the theoretical frameworks that the current research used. Finally, it is recommended to use GeoGebra in teaching students mathematics, where the results of the current research showed that GeoGebra supported the students in preparing for the mathematical situation, for exploring this situation and for objectifying the mathematical relations in the angles topic.