Problem-solving is a transversal mathematical skill that stands out significantly in current Portuguese curriculum guidelines for Mathematics in secondary education. However, its central role in the curriculum goes throughout all compulsory schooling, up to 12th grade. A good understanding of problem statements is essential for developing this skill; however, it depends on various factors, including the contexts in which the problems are formulated. This study aims to understand the difficulties experienced by 11th-grade students (16-17 years-old) in interpreting mathematical problem statements with different contexts and to identify their causes, seeking to answer the following research questions:
i) What are the main difficulties students face when interpreting problem statements?
ii) What are the causes of these difficulties? and
iii) What is the influence of context on the difficulties in interpreting problem statements?

Following a qualitative and interpretative approach, we selected six students, looking for diverse performance levels in Mathematics and different communication abilities.

The data were collected during the teaching of arithmetic and geometric progressions, and included:
i) audio recordings of three individual task-based interviews, designed on problems formulated in different contexts;
ii) audio recordings of a final semi-structured interview conducted in pairs; and
iii) participants’ written work produced during the interviews.

We identified two major sources of difficulties: gathering and organizing information from the problem statements, and interpreting the results in light of the statements after solving the problems. These difficulties may stem from several factors, including memorization of concepts and mechanization of procedures, lack of proficiency in the Portuguese language, and quick, superficial reading of the problem statements. The distinct contexts in which the problems were formulated seemed to influence the difficulties shown by the students: we found more difficulties in problems with real and semi-real contexts, probably due to students’ lack of experience in solving problems formulated in contexts beyond pure mathematics. The results of this study suggest that interpreting problem statements in different contexts should be a key concern in Mathematics education, giving particular attention to problems formulated in real or semi-real contexts. Such problems must be addressed in the classroom much more frequently, so that students can effectively develop their problem-solving skills. This is particularly important concerning the growing interest of modelling tasks in curricular guidelines for school Mathematics, namely at the secondary level.

Keywords: Problem-solving, interpretation, contexts, difficulties, mathematics secondary education, arithmetic progressions, geometric progressions.