Difficulties in learning among secondary school students: implications for university

Abstract

In order to analyze the impact of higher education students’ knowledge of selected mathematical concepts previously studied in secondary education, a cross-sectional study was conducted with 160 students enrolled in various academic programs at the University of Veracruz, Mexico. Employing a mixed-methods approach, the study examined students’ performance on a written assessment consisting of verbal problem statements and two key secondary-school learning domains: equations and geometric figures. Through content analysis, evidence was found of persistent difficulties in both the qualitative understanding of problems and the mastery of concepts and ideas that had been addressed during pre-university education. Regardless of their level of academic progression, students relied similarly on procedures supported by a limited source of meaning, which proved insufficient for applying algebraic generalization processes at the university level. Regarding geometric figures and solids, students had not fully appropriated the defining characteristics and underlying concepts associated with geometric forms, resulting in difficulties in recognizing them when presented in non-standard representations. The findings suggest that secondary-school instruction does not necessarily guarantee the adequate construction of mathematical concepts and ideas and, consequently, students do not attain the level of knowledge required to solve problems independently. Finally, recommendations are provided concerning instructional practices and specific pedagogical actions that may strengthen mathematics teaching and learning in higher education.