MATHEMATICAL PROBLEM-SOLVING DIFFICULTIES AMONG FIRST-YEAR MIDDLE SCHOOL STUDENTS: AN EMPIRICAL ANALYSIS BASED ON THE PÓLYA MODEL

Problem solving is at the heart of mathematical activity, but observations in the classroom show that most students, whatever their age, have difficulty with this discipline. Even if the lessons learned are the same, not all pupils manage to solve the same problem, and some don\\\'t even manage to go beyond a certain level of resolution. This research aims to identify the particular difficulties encountered by first-year middle school students when solving mathematical problems, based on George Pólya\\\'s (1945) four-stage model (comprehension, plan development, plan execution, verification).To achieve our objective, we adopted a qualitative approach, using case study as our main research method, proposing a “problem” exercise to students, with the students\\\' answers analyzed and compared with a standard solution. The results of our research indicate a heterogeneous distribution of difficulties: 7% of students fail at the problem comprehension stage, 14% encounter obstacles during plan development, 79% experience major difficulties during plan execution (calculations, application of strategies) and 72% omit or fail to check the solution, a crucial step in validating their approach.