A design framework for instructional activities based on structuring geometric knowledge

Geometry is a branch of science that examines abstract concepts such as point, triangle, circle and the relations between them. It is inevitable that there will be differences while structuring these concepts in the human mind, depending on many reasons such as individual differences and applied teaching methods. To operate and reason by using these concepts, they need to be embodied. With the embolization, abstract geometric concepts are represented and geometric shapes are formed. Geometric information is also created by using shapes. Many studies have been conducted on how geometric knowledge is formed in the mind of the individual. It is seen that the results obtained from the studies are guiding all the stages from the design of the teaching activities to the evaluation. However, it is generally accepted that there is a gap between the theoretical results obtained from mathematics education research and the reflection of these results in practical teaching practices. The main purpose of the study is to create a bridge between theory and practice in order to design teaching activities by combining research to explain the structure of geometric knowledge. Based on a synthesis of the literature and the results from the research, a design framework to be used in teaching activities for the construction of geometric knowledge was developed, refined and evaluated. In the study, which was designed according to the qualitative research approach, data diversity was used, grounded theory and document analysis were used together. The grounded theory process was carried out with determined geometry educators. From the results obtained, the dimensions of the design frame were revealed. During the document analysis process, textbooks, annual-daily plans and curriculum programs for geometry education were examined. The results were combined and the frame was finalized.