Indicadores de niveles de razonamiento algebraico elemental en educación primaria en la resolución de tareas de proporcionalidad con tablas de valores

In Middle Education, proportionality is often modeled using tables of values. The use of these tables is conditioned by the mathematical objects involved. In this research study, indicators on the operational and discursive use of these objects are determined according to the algebraization levels. These indicators are used to assess the level shown by students, 11-12 years old, who solve proportionality tasks modeled using tables. The responses given are coded through operating variables. These variables are analyzed in an isolated way using elementary descriptive statistics and in a relational way through similarity analysis as well as implicative statistical analysis. Based on the results of this research, we can conclude that in order to reach the level of algebraization expected at this grade level, it will be essential to implement a teaching method based on an essential constructivist approach rather than an objectivist approach. Furthermore, results also suggest possible didactic interventions based on the indicators of the level of algebraization previously identified.