National standardized tests database implemented as a research methodology in mathematics education : The case of algebraic powers

In this work we show the use of the INVALSI database as an instrument to collect organized data from national standardized tests in order to study students’ mathematical thinking on a large scale. It allows us to create appropriate correlations to single out the behavior of the students relative to a specific mathematical topic or a cognitive issue. In this study we have used the INVALSI database to study how grade 10 students work with powers in the domain of algebra. We analyze the quantitative data within a semiotic theoretical framework. Analyzing items taken from the INVALSI tests we are able to single out a general behavior that involves a population of Italian students and that persists in time. We interpret the results within our theoretical framework, thereby giving a quantitative validation to a theoretical perspective that has been proven consistent by qualitative investigations.