Representations in the Learning of Sequences and Regularities by Third-Grade Portuguese Students

Abstract

Due to their abstract nature, representation of mathematical concepts through different registers favors their understanding. In the case of ‘‘sequences and regularities’’, it becomes propitious the exploration of different registers of representation in the institution of topics, such as term, order, formation law, and generating expression. Considering these assumptions, a teaching experiment was performed to understand the contribution of multiple representations in the learning of ‘‘sequences and regularities’’ by 3rd-grade students. The study adopted a qualitative methodology and the findings of the study reveal that students initially presented a smaller variety of representations, which increased during the teaching experience. Students showed a greater preference for pictorial representations and made explicit connections between different representations throughout their resolutions. Pictorial representations and tables allowed close and distant generalizations, the determination of the formation law, and the generating expression. The greatest difficulties of the students resulted from the interpretation of the statements of the proposed tasks, which were also evident in the representation (natural language), showing a greater number of incorrect answers. This result shows that some students still have difficulties in justifying their reasoning, either in writing or orally.