Investigation of 10th grade students' inquiry in the process of building hierarchical relationship of special quadrileterals

The main goal of this study is examining the 10th grade students' inquiry process when they construct the hierarchical relationship of special quadrilaterals. Mathematical inquiry community approach was adopted to examine the inquiry process of the students. This approach has 7 sub-components: (1) Developing understanding of mathematics through dialogue, (2) Collaborativelly problem solving, (3) Self-reviewing and correcting mistakes (4) Taking risk, creating a working environment, (5) Suggesting alternative approaches, (6) Reviewing the procedures of inquiry (7) Doing mathematics like mathematicians. This classification was adopted as the conceptual foundation of the study. The study was designed considering the case study design, which is one of the qualitative research paradigms In this context, 10th grade students' wxisting knowledge regarding the definitions and properties of special quadrilaterals as well as their inquiry process related to hierarchical relationships of special quadrilaterals were examined in the study. Additionally, how their existing knowledge of special rectangles affected their inquiry process were examined as well. Participants of the study were four 10th grade students. While choosing the participant group of the study, purposeful sampling method was used because it gives detailed information about the situations that need to be investigated in depth. In the study, firstly, inquiry-based questions were developed within the scope of quadrilaterals and interviews were conducted considering those questions and students' inquiry processes were examined. The video recordings of 10th grade students taken during the 6-week and the answer of question sheets constituted the data of the study. In the study, the recorded videos were analyzed using the video methodology, and the sheets were analyzed using the document analysis method. In this study, it was observed that students mostly used the act of developing mathematical understanding through dialogue in the inquiry process. After the dialogue action, the actions of taking risk, collaboratively problem solving, self-reviewing and correcting mistakes, doing mathematics like mathematicians, and suggesting alternative approaches emerged. The act of reviewing the procedures of inquiry did not occur during the process. The results of this study showed that the mathematical inquiry community was effective in establishing or developing the students' existing knowledge about the hierarchical relationship of quadrilaterals. In addition, it is thought that creating inquiry communities that allow students to establish connections between concepts by themselves will strengthen mathematics learning.