I. INTRODUCTION

We start from Gaudêncio Frigotto's category—"productivity of the unproductive school" (1984; 2018)—to test, using recent Adequate Learning data, whether the Brazilian school still produces the very failure it claims to fight. In his first text (1989), Frigotto examines the relationship between education and the capitalist socio-economic structure, arguing that school does not serve "society"—especially the most vulnerable—but rather the productive system. In the second (2018), nearly thirty years later, he revisits the issue and recognizes a scenario of "social regression and reverse hegemony." This is a frontal critique of a school system acknowledged as inept—or designed not to work.

Such criticism has long been on the minds of major thinkers: Paulo Freire, in a striking 1993 interview, states indignantly that education policy does not take public education seriously - Escola Viva - Interview with Paulo Freire, 1993 (TV Cultura, 1993); Darcy Ribeiro used to say that Brazilian schooling "is not a crisis; it is a project" (Roitman, 2022); Anisio Teixeira, involved in public policy, repeatedly voiced a resounding critique of such an inept school (1936; 1957; 1967). Although Frigotto's expression sounds blunt, any focused diagnosis reveals an unbelievable average for public schooling. At times, in the name of defending public schools (which enroll about $80\mathrm{\%}$ of students), some authors avoid criticism—a pernicious stance, since we only change what we diagnose, as medicine suggests (Zhao, 2018). Diagnosis is always ambiguous: it can be used to classify only—or to care. Every diagnosis classifies, but its pedagogical rationale is to ensure student learning.

Nor is it only public schooling that faces endemic problems: private schools do too. In this text we show, based on IDEB (run by INEP), to what extent the productivity of the unproductive school can be indicated. In the 1990s, John Taylor Gatto (1992) spoke of "programmed stupidity" in schools aimed at the functional docilization of students. Which country was he talking about? The United States.

II. A SCHOOL FAR FROM LEARNING

What is public school for? We would say: to learn. Learning is not its sole purpose, but it is its core, most recognized one. In the context of instructionism (education reduced to reproductive instruction), schools take care of the curriculum, striving to cover it in full during the school year. At the same time, state and municipal departments only check whether classes were held; if so, the year is considered "complete." It is now clear that attending classes and taking tests does not produce the expected effect—provided we diagnose student learning, as IDEB intends.

A conspicuous example of this ineptitude appears in ENEM (the national exam offered annually).

In 2024, only 12 candidates out of 3.2 million earned a perfect score in writing. Even if one questions the "canned" essay format (partly designed to ease textual assessment), writing is crucial to learning, especially in a view that conceives learning as authorship (Dehaene, 2020; Demo, 2015; 2018). Why has writing vanished from school practice? In part because teachers do not write; nor is this skill cultivated in pedagogy degrees and teacher education. We lack basic education teachers who are authors, scientists, researchers, digitally literate—we train classroom performers of teaching and content, whereas we need, beyond that, professionals of learning.

Any theorization of learning, especially when anchored in neuroscience (Dehaene, 2020), insists that learning requires active participation (a passive organism does not learn), engagement, and protagonist—so learning is, crucially, authorship. This resonates with our autopoietic evolutionary structure (Maturana & Varela, 1997): pressed by the environment, we are capable—albeit relatively—of producing authorship. This direct involvement of students appears in so-called constructivist views, now somewhat out of fashion for overstating authorship (learning is more aptly a reconstruction, not a construction), as Barthes suggested in the "death of the author," albeit via a different argument (he emphasized innate mental structure: we reconstruct texts as this structure enables, without determinism) (Barthes, 1977). Magolda, in the late 1990s, tackled the challenge of self-authorship (still constructivist, arguably pleonastic) (1999; Magolda et al., 2010).

Given that we likely will not have a consensual theory of learning—it is exceedingly complex and contested—we limit ourselves here to highlighting the challenge of authorship in learning. It does not depend on class or test; it depends on learning activities (reading, studying, researching, drafting, grounding...), things largely absent from school. It is not the result of "active methodologies" (Bacich & Moran, 2018) or "flipped classrooms," because such proposals ultimately seek to save the lesson (teaching), not learning.

Learning does not happen in class; it happens in the student's mind, provided they engage and reconstruct curricular content. What comes from outside is mediation—important, to be sure. But nothing replaces student effort, motivation, and authorship. We generally overestimate teaching, as teachers tend to see themselves as the artisans of student performance—a stance that is, in itself, colonizing. The more eloquent fact is that school is not up to students; on average they waste time in it. By itself, school should not fail (if a student does what they can, failing makes no sense), nor pass without learning (that is fraud). In practice, crowds advance without learning, as the data show. Hence the "years of schooling" indicator has lost meaning (still used, e.g., in the HDI): those who complete upper secondary would have 12 years of study which, if scrutinized, would be worth no more than three or four. Massive public funds are squandered to maintain a school largely useless to students.

We remain in the age of content-ism, of which private schools often boast—yet it does not work, as we shall see. It is also clear that school is not yet an institution of the student, made for the student. It is the teacher's institution, keeping the teacher on a pedestal and staging empty performances without caring whether students learned—or alleging that the teacher's task is to teach and the student's is to learn; if learning does not occur, it is not the teacher's problem.

Of course, learning does not depend solely on pedagogy. There are many other impactful factors, such as student poverty. Since most students are poor, this introduces major obstacles—even though poverty does not necessarily prevent learning. In this respect, there is a stark difference between public and private schools: the latter serves the wealthiest $20\mathrm{\%}$. It does not achieve the bragged-about performance either, especially as the best basic schooling in Brazil is public—a specific federal model with very low coverage ( $\sim 1\mathrm{\%}$ ). Teacher issues strongly influence performance: weak initial training in universities that maintain an outdated format; continuing education that merely reheats undergraduate training; low pay (teachers' socioeconomic condition is "proof" that education "isn't worth it"); precarious hiring; devaluation of the profession (BID, 2018). Moreover, a prevailing neoliberal context slashes public budgets, threatens privatization as if private schooling were exemplary, and precarizes teaching. In the end, the country is stuck with obsolete, stagnant, inert provision—in both public and private sectors, on average.

To grasp the extreme difficulty of learning in school, we use the concept of the "unlearning effect" (Demo & Silva, 2021) to designate the striking tendency to learn less and less as one moves up the stages. Typically, the starting point in the Early Years (national average) is very insufficient, and even more so in Mathematics (a worrying gap: if Mathematics starts out inferior, it never catches up)—yet that is our best stage. Early Years are the pedagogue's stage, which shows the best performance (although with avoidable math gaps). In the Final Years, when the subject specialist enters, the drop is shocking, especially in Mathematics, with highly deteriorated figures—even with the presence of a "specialist." In Upper Secondary, Mathematics becomes residual, drifting away from Portuguese and leaving an unsettling question: why are language teachers, though still insufficient, so far above mathematics teachers, who seem to have given up?

III. ON IDEB

This index has sparked many controversies, including resistance among teachers to its application—partly because the results are alarming. To this day, IDEB does not include science (PISA always has), because we still have not awakened to the importance of science education (Linn & Eylon, 2011; Slotta & Linn, 2009; Demo, 2010). In the BNCC (2018), science education appears mainly in Biology, as usual, although it is a typically interdisciplinary strand. Teachers are not authors, scientists, researchers, or digitally literate, hence not up to students' needs—especially the most vulnerable.

IDEB is part of assessments linked to Item Response Theory (IRT), but it has shown constant weaknesses in the application of Prova Brasil: many schools focus only on Portuguese and Mathematics; many drill the IDEB test weekly to ensure some performance; some bring only the best-performing students on test day. Organizing such a test is indeed difficult in a continental country with vast disparities. The series dates back to 1995.

A deeper problem is that the IDEB-Proficiency version lacks statistical consistency—surprisingly so. It is a number from 0 to 10, obtained by averaging scores in Portuguese and Mathematics on Prova Brasil and multiplying by the pass rate. First, averaging LP and M makes no sense—they are different magnitudes; both must be learned fully, not averaged. This is a bizarre idea, aggravated by using a pass rate outside IRT coverage (it is provided by teachers). For instance, in the Early Years, the "average" in LP and M was 5.91, which, multiplied by the pass rate 0.97, yields 5.7. States and municipalities quickly realized that passing everyone raises IDEB: if 1.0 were used, IDEB would be rounded to 6. This masks the misery of mathematics performance: in Upper Secondary, for example, LP was $32\mathrm{\%}$ and M $5\mathrm{\%}$, resulting in a nonsensical "average" of

18.5. The suspicion lingers that this most-used IDEB version was designed to cloak the worst learning difficulties at school.

In this text, we use only IDEB – Adequate Learning (a percentage), which separates LP and M and follows them across three stages (Early Years, Final Years, Upper Secondary). This version also has problems (e.g., what counts as "adequate learning," easily reduced to content-ism—memorization—because it is more measurable). If we wanted to assess authorship-based learning, it would certainly be a very pale measure.

It is important to stress that the aim of evaluation is to take care of student learning, which is what matters most in school. Evaluation is not done merely to classify—much less to oppress—but to preserve the opportunity to learn. Within natural parsimony and without forcing ethereal national means, IDEB – Adequate Learning can be used.

IV. THE PROFILE OF ADEQUATE LEARNING IN PUBLIC SCHOOLS

In Table 1 we see the profile of Adequate Learning in LP and M in Early Years, Final Years, and Upper Secondary for 2023 in Brazil and four states (as examples). These are large national averages, very abstract given the country's dimensions. Adequate Learning in Portuguese in the

Early Years was $55\mathrm{\%}$, a very insufficient figure; in Mathematics it was $44\mathrm{\%}$, even more insufficient, with an 11-pp gap—an early inferiorization that will not be recovered. In the Final Years, Portuguese drops from $55\mathrm{\%}$ to $36\mathrm{\%}$ ( $-19$ pp); Mathematics from $44\mathrm{\%}$ to $16\mathrm{\%}$ ( $-28$ pp), an enormity. In Upper Secondary, Portuguese shows $32\mathrm{\%}$, while Mathematics is a mere $5\mathrm{\%}$ —residual. The unlearning effect is far stronger in Mathematics ( $44\mathrm{\%}\to 16\mathrm{\%}\to 5\mathrm{\%}$ ). In Portuguese it is smaller ( $55\mathrm{\%}\to 36\mathrm{\%}\to 32\mathrm{\%}$ ).

Focusing São Paulo, figures stand above national averages—except in Upper Secondary: Portuguese is only 5 pp higher; Mathematics is the same (5%). In the Federal District, the picture is similar, despite being the nation's capital; there, Adequate Learning in Mathematics in the Final Years is already only $14\mathrm{\%}$. In two other (poorer) states the figures are well below national averages, with residual Mathematics even in the Final Years and $2\mathrm{\%}$ in Upper Secondary. This suggests that, despite regional differences, the profile is insufficient everywhere, especially in Mathematics— and even more so in Upper Secondary, a state- run provision and the nation's most precarious school level.

The Early Years, typically municipal and tied to pedagogues, have been the country's best performing stage, though still very insufficient. The Mathematics gap is worrying: there is no reason to inferiorize Mathematics—even if many pedagogues do not favor it. The greater concern is that, once Math is inferiorized in the Early Years, it never recovers, even when the licensed subject specialist enters. The Final Years are delivered by specialists yet show huge declines. One tends to assume that specialists would have better training, but the data do not bear this out.

The Final Years showed precarious performance, but the most catastrophic results were in Upper Secondary (Table 2). In mathematics, in 2023, the state averages for Adequate Learning ranged from $2\mathrm{\%}$ to $9\mathrm{\%}$, with $5\mathrm{\%}$ as the national average (Brazil). The data suggest an exasperated disinclination toward mathematics, as if it were impossible to learn. In every state the figures were residual (below $10\mathrm{\%}$ ). Only two states reached $9\mathrm{\%}$ —Espírito Santo and Goiás—and they are not among the country's leading states. Note the very poor performance of São Paulo, the country's richest state ( $5\mathrm{\%}$ ).

In Portuguese language, the figures were much higher—though still very insufficient—indicating a marked divergence between the performance of language teachers (who still seemed to believe in recovery) and mathematics teachers (who seemed to have capitulated). The range was $19\mathrm{\%}$ to $43\mathrm{\%}$; none of it satisfactory, although well above mathematics, with an average of $32\mathrm{\%}$.

The data suggest that schools maintain a perfectly inept teaching practice, particularly in mathematics, because it fails in its chief function: to ensure the student's authorial learning. The raison d'etre of teaching is learning. Mathematics classes are offered systematically, as always—many basic-education teachers deliver them "religiously," yet to no avail. We tend to see the class as the founding event of school and university, when it is merely mediation. Learning does not reside in the class; it resides in the student's mind. What comes from outside is mediation, as Vygotsky famously said (1989; 1989a). Learning is not something that can be caused from the outside, from above; it is student protagonist, which can be mediated—and therein lies the teacher's indispensable relevance.

Just as a woman, when she conceives, carries, and brings forth a child, does so as a mediator (Hrdy, 1999)—and is therefore the most exuberant instance of mediation in nature—not as a "causer." The child does not belong to her, although she typically cares for the child with utmost devotion. The teacher's fundamental role is to care for the student's authorship, just as a mother cares that her child becomes the author of their own life. One day the child must "free themselves" from the mother—and we call that emancipation. In Rosa's hard critique (2010; 2019) of eurocentric self-determination, emancipation is unilateral, colonizing, privatizing: it always implies preventing the other's emancipation, because in eurocentric (Euro-American) civilization the other is a rival to be eliminated, not an "authentic other" (Maturana, 2002).

One of the most forceful critiques of this useless teaching appears in Barthes (1996), following Foucault (1977; 2004): referring to the May 1968 student uprising in Paris, he challenges the libido dominandi, the power ambushed within teaching, the "fascist" language. What is the point of a class that yields $2\mathrm{\%}$ adequate learning in mathematics? Is it not perfectly useless?

Carraher et al. (1995) produced a very illuminating study—"Ten in life, zero at school"—showing that while in everyday life it is hard to find anyone who cannot shop at the market, understand prices and change, or gauge a child's weight and size, at school this "mathematics" becomes a torment, leaving the impression that school goes out of its way to make it difficult. We only learn mathematics if we understand it. Understanding is not a product of the lesson; it is a capacity of the student. The role of the mathematics teacher is not to hand over content, but to enable the student to understand mathematics. Until that happens, the class is useless. There was a time when a supposed mark of quality for a math teacher was to flunk everyone. We no longer accept that. But the scenario has not changed: mathematics remains a deep marker of exclusion.

Yet this is not only a Brazilian problem. In the United States, PISA 2022 performance (PISA-2022, 2023) was very insufficient—an embarrassment for MAGA (Table 3)—with the country in 34th place in the mathematics ranking (Table 3). Clearly, mathematics is a serious problem in American schooling, standing more than 100 points below Singapore's performance. In practice, high performance in mathematics is an Asian phenomenon (concentrated in Singapore and China, plus Japan and South Korea), even though it is common to criticize the methods used as "draconian," causing absurd stress among students (Zhao, 2018; Ripley, 2013; Sahlberg, 2017). Canada ranked 9th, far above the United States. Mathematics is—today even more than before—a gatekeeping criterion for the most advantageous jobs globally, especially in the digital and AI world. Quite likely, in digital technologies China may overtake the United States (Lee, 2018; Jin, 2023).

Brazil appears in 62nd place, no surprises. It performed poorly in all three domains, especially in mathematics. It was a certificate of backwardness (backwardness as a project, in Darcy Ribeiro's critique), but, "comparatively," it is not so different from the American position in "moral" terms (Lubienski & Lubienski, 2013; Ravitch, 2020). The United States once had the best high school system in the world, in the postwar period, when nearly all school-age students attended high school and from there an exuberant middle class emerged (Piketty, 2022), but it was destroyed (McMahon, 2023)—as was the middle class (Piketty & Sandel, 2025).

V. PRIVATE SCHOOL BOASTING

As we can see in Table 4, the private sector is well ahead of the public sector—an expected result, since private schools serve the wealthiest $20\mathrm{\%}$ (the elite). While Adequate Learning in Portuguese (LP) and Mathematics in the Early Years (Al) was $55\mathrm{\%}$ and $44\mathrm{\%}$ in public schools, in private schools the figures were $83\mathrm{\%}$ and $73\mathrm{\%}$, respectively. In the Final Years (AF), they were $36\mathrm{\%}$ and $16\mathrm{\%}$ versus $68\mathrm{\%}$ and $49\mathrm{\%}$. And in Upper Secondary (EM), $32\mathrm{\%}$ and $5\mathrm{\%}$ versus $64\mathrm{\%}$ and $31\mathrm{\%}$. It is clear that in private schools the "unlearning effect" operates dramatically, as does the math gap, because, in the end, the teachers are the same. In mathematics, above all, the drop is astonishing: $73\mathrm{\%}$ in the Early Years; $49\mathrm{\%}$ in the Final Years; $31\mathrm{\%}$ in Upper Secondary, on the national average. Even the Early Years figures are not satisfactory; they should be above $90\mathrm{\%}$. And the $31\mathrm{\%}$ Adequate Learning in mathematics in Upper Secondary is not essentially "different" from the $5\mathrm{\%}$ in public schools (on average).

What stands out, however, is that the best basic schooling is the federal system (we do not have data for 2023 except for Upper Secondary – EM), yet the table makes it clear that its performance is much better. The federal system has very small coverage (around $1\mathrm{\%}$ ) (School Census... 2024:15), but its results have drawn attention, as they suggest that quality public schooling is possible and need not be as elitist as the private sector. This federal system exhibits ailments common to Brazilian education—such as the unlearning effect, the mathematics gap, and the steep decline in math performance—but it is "consoling" that it is the best basic school option, perhaps in the same vein as Lubienski & Lubienski (2013).

The private sector generally claims to be staunchly content-driven and, for that reason, to place students in the top entrance examinations, including the most competitive slots at the best public universities. In practice, this occurs due to the weakness of public schooling, as the data amply attest, not because of private virtue. In Table 5 one can see that private-sector performance in Mathematics in 2023 was blatantly insufficient: $15\mathrm{\%}$ to $49\mathrm{\%}$ across states, with a national mean of $31\mathrm{\%}$. Considering that it serves the national elite and charges tuition, this amounts to a counterfeit product. Major states such as Rio de Janeiro and Rio Grande do Sul posted $21\mathrm{\%}$ and $28\mathrm{\%}$ (respectively), and the best state, Minas Gerais, did not reach $50\mathrm{\%}$. One may say that there, too—overall and on average—the mathematics lesson is perfectly useless... and paid for.

In Portuguese Language (LP) the performance was significantly better, as is common here (LP is learned far better than Mathematics), ranging from $48\mathrm{\%}$ to $77\mathrm{\%}$, with a mean of $67\mathrm{\%}$, yet it is still not satisfactory. This is a very inept school system that, to a large extent, defrauds its students and, ironically, charges them dearly.

Table 6 shows the historical series since 1995 in mathematics, indicating that, after 28 years, we have only moved backward in Upper Secondary (EM). There was progress in the Early Years (AI)—the stage typically taught by pedagogues—but stagnation in the Final Years (AF). And in Upper Secondary, a systemic cataclysm. The most striking example is the Federal District (DF): it started in 1995 with $31.5\mathrm{\%}$ adequate learning in mathematics (a figure that seems suspicious; we have never had another like it), and by 2023 we had reached $5\mathrm{\%}$! Pará, which began at $4.3\mathrm{\%}$, was at $2\mathrm{\%}$ in 2023.

Tabel 6: Aprendido adequado de matemática, AI, AF, EM, 1995-2023, Brasil, São Paulo, DF, Pará.

São Paulo, the richest state in the federation, started at $14.4\mathrm{\%}$ and fell to $5\mathrm{\%}$ (the same as the national average), indicating a school system designed not to work. Although one might highlight the rise in adequate learning in mathematics from $19\mathrm{\%}$ (1995, national average) to $44\mathrm{\%}$ (2023), this figure is still, frankly, miserable.

VI. CONCLUSION

The data do not say that we are inept ad aeternum, with no way out; they say that the current school, yes, has no way out. In large part, we avoid diagnosis because it is too painful. The best way not to have cancer is not to see a doctor. This ostrich policy is at the heart of Brazilian educational policy—and of private schooling. In this instructionism, left and right are cheerful partners. They deliver the same useless lesson. A lesson can be useful—there are emblematic lessons—but they are delivered by authors, not parrots. Since the project is to train parrots, the school must be a parrot aviary. That is what Darcy Ribeiro, Paulo Freire, and Anísio Teixeira criticized head-on, and to this day we have not changed it. It is what Frigotto has been castigating for 36 years. In this landscape, the federal school system appears as a consolation, because—even if still elitist—it offers something far higher in quality; yet, when scrutinized from within, the provision remains instructionist, because we have not even minimally grasped the insanity of this view. Millions of Brazilian students show up at school every day to be defrauded, in broad daylight or in the penumbra of night. In the Federal District, adequate learning in mathematics was $50\mathrm{\%}$ in the Early Years (AI), $14\mathrm{\%}$ in the Final Years (AF), and $5\mathrm{\%}$ in Upper Secondary (EM). How can there be a 36-percentage-point drop from AI to AF, precisely when the licensed subject specialist enters—one from whom better performance would be expected? This ineptitude seems endemic, "painstakingly crafted." No wonder privileged states such as São Paulo and the Federal District have $5\mathrm{\%}$ adequate learning in mathematics in Upper Secondary. Is this not a school made not to work?

Modus in rebus, as the sensible Romans said! First, it is not a matter of "blaming" teachers, as is customary in the United States, to the point of firing teachers whose students perform poorly (Goldstein, 2014). We are responsible for what we do, but guilty. Second, the teaching task can be greatly hindered by countless other reasons, starting with student poverty, extreme in many parts of the country; insecurity in and around schools; devaluation/precarization of the teaching profession; utterly outdated university programs; continuing education reduced to reheating already inept undergraduate training; and so on. Problems this complex do not have a single cause, but a bundle of causes that is likewise indiscernible. The data certainly indict the lesson being delivered, because it is blatantly useless—even though a lesson need not be an obstacle. However, if a lesson only works when it is delivered by an author, researcher, scientist, then the school lesson does not work, because it is a copy to be copied. Just look at ENEM: if no one writes well, it is because everything is copied, amen.

At the same time, it is possible to make a diagnosis, certainly preliminary like the one I have attempted here, but it is avoided or anathematized, because it hurts too much to see oneself laid bare. Yet we assess in order to care, not to flog, massacre, exclude. What is done in schools today is, in many senses, a massacre—carried out by those who often imagine they are redeeming the world. School remains colonizing (or docilizing, in Foucault's language) (1977; 2004), or stultifying in Gatto's (1992), at least in part because it is not an institution devoted to the student's right to learn; it is a teacher-centered institution. The great school event is not student learning, but the teacher's performance.