The Concept of Number Sequence in Graphical Representations for Secondary School Students

Abstract

<p style="text-align: justify;">The aim of this work is to characterise the understanding that students in compulsory secondary education (14-16 years old) have of number sequences in graphical representations. The learning of numerical sequences is one of the first mathematical concepts to be developed in an infinite context. This study adopts the focus of semiotic representations as its theoretical framework. The participants consisted of 105 students and a qualitative methodology was used. The data collection instruments were a questionnaire and a semi-structured interview. The results allowed for three student profiles regarding number sequences in graphical representations to be identified. These profiles may facilitate a possible progression in the learning of number sequences for students in compulsory secondary education to be considered. Therefore, the results presented in this study can provide information about the learning hypotheses of mathematical tasks related to numerical sequences and can help in the design of such tasks.</p>

How Students Generate Patterns in Learning Algebra? A Focus on Functional Thinking in Secondary School Students

“…They summed up the 𝑛, representing the independent variable, as the following dependent variable's value. The result supports previous studies (Bajo-Benito et al, 2023;El Mouhayar, 2018;Wahyuni et al, 2020) that secondary graders commonly recognized patterns by finding the difference between two consecutive terms and then adding them to a quantity in a given to produce the quantity in the next term. In this case, student's conceptual understanding of variables is limited to the specific unknown and not to the "variability" as it applies to the function (Usiskin, 1988).…”