Determination of 5th grade students' skill-based problem solving performances, types of errors they make in problem solving and reasons for making errors

The objective of this study is to ascertain the skill-based problem-solving performances of 5th grade middle school students requiring four operations with natural numbers, the variables affecting their problem-solving performances, the types of errors they make in problem-solving, and the reasons for these errors. An explanatory sequential design within the mixed research method was utilized in the study. The study's sample comprised 111 students (56 boys and 55 girls) enrolled in public secondary schools in the center, one district, and one village of Hatay province. The data collection instruments employed included the Student Identification Form, comprising eight questions, the Skill-Based Problems Achievement Test, encompassing ten problems, and a semi-structured interview comprising six questions. The students' responses to the problems in the Skill-Based Problem Solving Achievement Test were evaluated using the "Skill-Based Problem Solving Rubric," and the students' achievement scores were created. The achievement scores were transferred to the SPSS 26.0 package program, and t-test, Anova, Kruskal-Wallis-H test, and multiple comparison analyses were performed. The analyses yielded the conclusion that the skill-based problem-solving performance of fifth grade students was quite low. The investigation revealed that there were no substantial differences in students' skill-based problem-solving performances according to gender, school location, or the number of pages read per day. However, a significant disparity emerged when considering the daily use of technological devices for purposes other than academic pursuits. A subsequent analysis of the students' problem-solving solutions was conducted by employing Polya's (1997) problem-solving framework to identify the types of errors made in skill-based problems. To ascertain the underlying causes of these errors, semi-structured interviews were conducted with 20 students who had committed the identified error types. The analysis of these interviews revealed that the errors were primarily attributable to three factors: visual focus during problem-solving, incomplete utilization of problem-solving information, and inattention and misunderstanding of the problem. The study concluded that the predominant cause of these errors stemmed from a lack of comprehension of the problem. It was observed that students who lacked understanding of the problem were unable to formulate a suitable solution, while those who had partial or incorrect understanding of the problem arrived at erroneous results by employing incorrect or partially correct solutions. It was observed that some students who correctly understood the problem obtained erroneous results because they created a partially correct or incorrect solution path. In contrast, some students who correctly understood the problem and created a correct solution path obtained erroneous results because they performed partially correct or incorrect operations. It was further observed that students who correctly solved the problem performed all the steps of understanding, determining the solution path, performing operations, and finding the result correctly and completely. It was determined that these students demonstrated a comprehensive understanding of the problem, effectively utilized the provided visuals and information, and achieved the correct result through meticulous execution of their operations. Consequently, while a thorough understanding of the problem is paramount to identifying the correct solution, it is insufficient on its own. Keywords: Skill-based problem, new generation problem, problem solving, problem solving skills.