Towards a characterization of algebraic competence: an exploratory study with students
DOI:
https://doi.org/10.15359/ru.36-1.40Keywords:
Algebraic competence, algebraic reasoning, algebraic tasks, mathematics education, university studentsAbstract
[Objective] The present article seeks to determine the algebraic competence displayed by a group of 27 university students in Mexico when they worked on an algebraic problem. A study framework is proposed based on the investigation of mathematical competence and levels of algebrization in three areas: solving, interpreting and validating. [Methodology] A qualitative and exploratory study with convenience-based selection of students was implemented during a regular two-hour class. The professor and the researcher were present when the task was carried out in the classroom. [Results] The results show that the students had difficulties in problem solving because they did not effectively manipulate symbolic-literal expressions, and did not achieve the expected level of algebraization. They were also inconsistent in interpreting the task – that is, they did not identify or connect knowledge about the properties of the operations necessary to solve the algebraic problem. When validating their responses, they provided descriptive proofs or verifications. [Conclusions] The findings suggest that most of the participants did not display a basic level of algebraic competence, and the necessity of formulating stages of development based on the three actions is discussed.
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