Multiple Representations and Meaningful Learning in Mathematics Education During the Transition to Higher Education

Source abstract

The transition from secondary education to higher education represents one of the major challenges in students’ mathematical development. During this stage, many first-year university students experience difficulties in understanding fundamental mathematical concepts due to limited connections among different forms of mathematical representation and the predominance of procedural learning approaches. In this context, the present study aimed to analyze the contribution of multiple representations to meaningful learning of mathematical concepts among first-year university students. A mixed-methods approach with a quasi-experimental design was employed, involving students enrolled in introductory Mathematics and Precalculus courses. The instructional intervention was grounded in Duval’s theory of semiotic representation registers and Ausubel’s theory of meaningful learning, incorporating activities that promoted the integration of algebraic, graphical, numerical, tabular, and verbal representations. The findings revealed significant improvements in conceptual understanding, graphical interpretation, coordination among representation registers, and mathematical problem-solving skills. In addition, students reported positive perceptions of the instructional strategies, emphasizing that the use of multiple representations facilitated content comprehension and supported the construction of meaningful knowledge. The study concludes that multiple representations constitute an effective pedagogical strategy for enhancing meaningful learning in mathematics during the transition to higher education. Furthermore, they contribute to the development of mathematical reasoning, conceptual understanding, and the application of knowledge in diverse contexts. These findings provide relevant evidence for the design of educational practices aimed at improving mathematics teaching and learning in the early years of university education.