Investigation on Algebraic Thinking Processes in Geometry Concepts of High School 4th Grade Students

Abstract

The aim of this study is to analyze the thinking processes of fourth-grade high school students by using geometrical concepts regarding the components of algebraic thinking such as symbols and algebraic relations, different forms of representations and pattern generalization. For this reason, one Science class and one Turkish-Mathematics class were chosen. Van Hiele Geometry Test and algebra exam were administered to 38 students from the two classes. A total of 6 students-three students, scoring good, average and low grades from each class were chosen in accordance with the scores obtained from these exams. Interviews including 15 questions were carried out with these students. As a result of the research, it was determined that students often hesitated to solve problems in geometry by algebraic ways. Instead, it is observed that the way to remember the desired state (formula etc.) is used more. In addition, it was found out that students algebraic thinking skills were not sufficient to solve problems and the students' algebraic thinking skills changed according to their success levels or the departments they studied. On the other hand, it has been determined that there is a difference between the success levels of the students in the cases of transformation between impressions. It has been observed that the students with poor level have completed this process with less success than the other level students. This situation is interpreted as low level of algebraic thinking in students with low level of geometry.

The Effects of Educational Robotics Applications on Linear Equations about Algebraic Reasoning

“…At this point in the study, it was concluded that in the final test applied at the end of the teaching experiment, all participants were able to formulate all generalizations correctly, establish the relationship between the variables and convert them into equations. However, the result showing that students can reflect the rectangle"s side lengths and the distance between floors into the algebraic expression does not coincide with research made by Atasoy and Bulut (2018) and Dindyal (2004), both claiming that students had difficulty in interpreting the change in geometrical shape features and algebraic expression The algorithms they encoded in the coding process may have helped them to try this situation by watching them in the simulation.As a result, the fact that participants in this research can formulate generalizations can be said to be helpful in their utilization of algebraic reasoning in the coding process.. On the other hand, in the future studies, besides the algebraic reasoning of the participants, the development in algebraic thinking levels with coding can be examined. In the study, coding trainings start at kindergarten level in our country and in the world, starting from the development in the process of formulating generalizations and making sense of what these representations mean.…”