The investigation of the relationship between eighth-grade students'geometryself-efficacy perceptions and geometric reasoning skills

In this study, the relationship between geometry self-efficacy perceptions and geometric reasoning skills of eighth grade students was investigated. In this study, which the quantitative research approach was adopted, the correlation model, one of the relational screening models, was used. The population of the study consists of 3055 secondary school students in the 8th grade of Kırşehir Provincial Directorate of National Education in 2018-2019 academic year and 346 (female: 188; male: 158) secondary school students. In the selection of the schools, stratified sampling method, which is one of the probability-based sampling types, was used. Students' perceptions of geometry self-efficacy were examined by Self-efficacy scale for geometry consisting of 25 item and developed by Günhan and Başer (2007). "Positive self-efficacy belief", "Use of Geometry knowledge", "Negative self-efficacy belief". Students' Reasoning skills were investigated by Sırtmaç (2018) with a test consisting of 8 open-ended questions prepared to measure four sub-skills such "Analysis", "Generalization", "Synthesis and non-routine problems", "show a reason". Analytical rubric was used as the graded scoring key in the analysis of the answers given to the test. In order to make descriptive analysis of data, frequency, mean and standard deviation values were calculated. Students' perceptions of geometric self-efficacy and geometric reasoning skills at .05 significance level differed statistically according to gender t-test for independent groups; ANOVA test was used to determine whether the school is differentiated according to the success level of the school. The relationship between the students' self-efficacy perceptions of geometry and their geometric reasoning skills was examined with Pearson Correlation test. In addition, simple linear regression analysis was used to determine whether the students' self-efficacy perception scale for geometry significantly predicted their geometric reasoning skills; multiple regression analysis was performed for the degree of predicting the geometric reasoning skills of the subscales of the scale. As a result of the analysis, although there is no statistically significant difference between the sub-dimensions of the scale and gender for self-efficacy perceptions of students; there was a statistically significant difference between the scale and gender in favor of male students. In addition, it was found that both female and male students' geometric reasoning skills were partially sufficient. On the other hand, high school students' perception of geometry self-efficacy is high; it was found that the students who were educated in high-performing schools were low. As a result of the analysis, it was determined that the geometric reasoning skill levels of all students were partially sufficient depending on the variable of school achievement level. In addition, it was found that there was a statistically significant relationship between the students' self-efficacy perceptions about geometry and their geometric reasoning skills both in the general and sub-dimensions of the scale. It was determined that students' self-efficacy perception about geometry positively predicted geometric reasoning ability. It was seen that 5% of the geometric reasoning skill was explained by self-efficacy perception towards geometry. On the other hand, the variance explained by the sub-dimensions of students' perceptions of geometric self-efficacy related to geometric reasoning was found to be statistically significant and when the dimensions of the self-efficacy scale related to geometry were taken together, it was found that 9% of the total variance related to geometric reasoning was explained. Keywords: Reasoning, Self-efficacy, Teaching Geometry