The role of auxiliary elements in the process of solving multiple solution geometry problems

The purpose of this research is to examine the strategies used by first-grade students in the elementary mathematics education program during the process of solving multiple solution geometry problems and determine the role of auxiliary elements in these strategies. This research, designed based on the fundamental qualitative research design, was conducted with 8 students during the fall and spring semesters of the 2021-2022 academic year. The data of the study consisted of clinical interviews conducted with all students in four sessions lasting an average of 45 minutes each. The data of the study were obtained from worksheets presenting four multiple solution geometry problems, video recordings where students explained their thought processes, and questions asked beneath these problems. Thematic analysis was used to analyze the data obtained for the purpose of answering the research questions. In the four problems examined, it was observed that students tended to apply the Pythagorean and Euclidean theorems when encountering right angles. Additionally, it was observed that students were not comfortable with making additional drawings in the problems and refrained from doing so to avoid making mistakes. When making additional drawings, students sometimes made random drawings, disregarding geometric constructions. As a result, it was observed that some drawings that students believed to be correct were geometrically impossible. However, it was found that attempting to make additional drawings focusing on different points of the problem in order to increase the number of solutions provided significant contributions to students' development of mathematical thinking and problem-solving skills in multiple solution problems, highlighting the importance of auxiliary elements.