Mathematical indicators as propaganda tools: the INVALSI “implicit dispersion”
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6 October 2025
When an educational phenomenon is described through a weak construct, theoretically unfounded and scientifically unvalidated but expressed by a numerical indicator, that indicator will easily turn into a weapon of mathematical destruction. This is the case of the pseudo-concept of implicit dispersion: introduced in 2019 by INVALSI and today become a multifaceted indicator, assimilable, depending on the circumstances, to functional illiteracy, educational poverty, skills deficit, fragility of student learning, up to being configured as a measure of a presumed individual and social risk. A construct entirely internal to the INVALSI metric and its evaluation procedures, now automated and inaccessible. The results of the INVALSI tests are not verifiable, debatable, or falsifiable: not even by the student obliged to take them, and who now finds the INVALSI certification directly in their digital curriculum.
When an educational phenomenon is described through a weak construct, theoretically unfounded and scientifically unvalidated but expressed by a numerical indicator, that indicator will easily turn into a weapon of mathematical destruction.
This is the case of the pseudo-concept of implicit dispersion: introduced in 2019 by INVALSI and today become a multifaceted indicator, assimilable, depending on the circumstances, to functional illiteracy, to educational poverty, to skills deficit, to fragility of learning of students, up to being configured as a measure of a presumed individual and social risk.
At the Ambrosetti Forum in Cernobbio, Minister Valditara first highlighted the drop in the school dropout rate (which today is preferably called explicit dispersion: 8.3%, ahead of the European target of 9%) attributing it to his policies within the framework of the PNRR (Agenda Sud and Caivano Decree). He then drew attention to implicit dispersion, declaring:
“Impressive results; it is no coincidence that the OECD invited me in connection with Paris to illustrate this data [the reduction in the percentage of implicit dispersion from 2022 to 2025 in the southern regions], because it is the first time that a country has managed to tackle the problem of implicit dispersion so drastically.”
That the OECD asks the Minister for explanations sounds rather incredible, first of all because this indicator does not exist in the international debate, indeed, it does not exist outside INVALSI data.
What is implicit dispersion?
The INVALSI President defines it as “(share of) students who do not reach the minimum level of competence required. Those who, even obtaining the diploma, do not reach level 3 in the Italian and Mathematics tests and do not even reach level B1 in reading and listening in English” (2019, invalsiopen).
He then adds that implicit dispersion is “a measure to support the identification of fragility in learning”, that is, “an indicator of fragility that allows early identification of students most exposed to the risks associated with school failure” (Tuttoscuola, 2022).
It would therefore be the percentage of students, measured by INVALSI year after year, who do not reach a threshold of adequacy in the tests, a threshold established by INVALSI itself. A construct entirely internal to the INVALSI metric and its evaluation procedures, now automated.
And here problems arise.
- Who decides which gaps are considered acceptable, how and with what degree of legitimacy and publicity, given that the tests are not accessible and there are no standards of minimum learning provided for in our school system?
- Who establishes the measurement methods, the probabilistic models that synthesize into numerical scores the answers provided digitally by students and that would qualify their “degree of competence”?
- What simplifications, what level of accuracy and error, what reproducibility?
- Finally, how to verify and control the data, given that today INVALSI provides for the use of machine learning techniques for test correction?
Not by chance, a complaint to the Data Protection Authority is awaiting feedback, presented by some parents with the support of FLC CGIL, after INVALSI denied them access to the data of the tests taken by their children.
“Implicit dispersion” is a numerical indicator without scientific basis. Its use by ISTAT, Save the Children, Fondazione Agnelli or the Ministry of Merit does not give it validity.
Based on unverifiable assumptions, it serves more to legitimize an ideology: it presupposes that teachers are not able to assess correctly and gives normative and now also predictive value to the results of standardized tests. The “fragile” student in the INVALSI tests would potentially be at risk of social and cultural marginalization. Do we really believe that the answers given by a boy or girl from 7 to 18 years old in a handful of minutes can tell us what their destiny will be?
Standardized tests are “unequal by design” (Unequal by design, 2022) that is, designed to produce a certain percentage of failures: so defines them the international critical literature, which in our country finds no voice in the public debate. We prefer not to discuss the validity of the tool, but only the need to continuously reform what that tool claims to measure.
This article was taken from il Manifesto of 16.9.25.
