Investigation of middle school students' skills and self-efficacies toward problem posing

The aim of this study was to examine the skills and self-efficacy beliefs of secondary school students towards problem solving. It was also aimed to determine the relationship between problem-posing skills of middle school students and problem-posing self-efficacy beliefs. In addition, it was investigated whether there was a relationship between problem-posing skills and self-efficacy beliefs towards problem posing of the participants and independent variables such as gender, grade level, academic achievement and education level of parents. The research was carried out as a mixed method study. The purpose of selecting the mixed method is to take advantage of the strengths of quantitative and qualitative research methods. The design of the study was determined as an explanatory design in which quantitative data were at the focus and supported by qualitative data. The participants of the study were 346 middle school students. In order to determine the problem-posing skills of the participants. Problem Posing Test prepared by the researcher was used. Problem Posing Self-Efficacy Scale developed by Özgen and Bayram (2019) was used to determine the self-efficacy beliefs of the the participants. Semi-structured interviews were conducted with 23 students selected among the participants and their opinions on problem-posing, self-efficacy beliefs and problem-posing skills were determined. In the interviews, Problem-posing and Self-efficacy Interview Form and Interview Form for Problem Posing Skills prepared by the researcher were used. Participants' gender, class levels, academic achievements, parental education status were obtained with the Personal Information Form. Finally, the rubric developed by Özgen, Aydın, Geçici and Bayram (2017) was used to evaluate the problem posing products of the participants. Quantitative data were analyzed by t-test, ANOVA and simple regression. Descriptive analysis and content analysis were used to analyze the qualitative data. As a result of the analyzes, it was found that the problem-posing skills of the participants were good and the self-efficacy beliefs about problem-posing were high. The participants were more successful in using the language of mathematics, language and expression than solvability, originality and presentation of a solution criterons. While the problem-posing skills of the participants do not differ according to gender, grade level and parental education, they differ significantly according to academic achievement. While the self-efficacy beliefs of the participants towards problem-solving did not show a significant difference according to gender, efficacy beliefs varied significantly according to parent education levels and academic achievement. It was also found that self-efficacy beliefs of participants were significant predictors of their problem-posing skills. There is a positive correlation between problem-posing skills and self-efficacy beliefs of participants. Findings from the interviews with the participants indicated that they found problem-posing activities easy and had high self-efficacy beliefs towards problem posing. Finally, the qualitative data obtained from the interviews with the participants were found to support the quantitative data of the study. In line with the results of the study, it may be suggested that problem-posing activities should be used more in educational processes. In addition, studies can be conducted to examine the self-efficacy beliefs of secondary school students.