  In this paper, we apply the Logistic PCA (LPCA) as a dimensionality reduction
tool for visualizing patterns and characterizing the relevance of mathematics
abilities from a given population measured by a large-scale assessment. We
establish an equivalence of parameters between LPCA, Inner Product
Representation (IPR) and the two paramenter logistic model (2PL) from the Item
Response Theory (IRT). This equivalence provides three complemetary ways of
looking at data that assists professionals in education to perform in-context
interpretations. Particularly, we analyse the data collected from SPAECE, a
large-scale assessment in Mathematics that has been applied yearly in the
public educational system of the state of Cear\'a, Brazil. As the main result,
we show that the the poor performance of examinees in the end of middle school
is primarily caused by their disabilities in number sense.
