A year-on-year change in the failure rate can come from the difficulty of the test, the mix of those who entered, the scoring key and the pass mark. A test can be marked correctly and still not be comparable with last year without a further method. A disputed item can move candidates who sit near the threshold, and a low failure rate by itself says nothing about a generation’s intelligence.
1. The May conference at which six readings miss one another
Picture a May press conference. The minister reads the net failure rate and looks for whether this was an excess. The director of Cermat defends the catalogue of requirements and the common scheme. A grammar-school mathematics teacher sees items his class knows. A teacher on a vocational extension programme sees the same paper as a filter that cuts his pupils differently. A parent hears that “it was harder this year”. A candidate with 16 points hears that the next sitting is in the autumn.
The quarrel about difficulty mixes several questions. The minister watches the public effect of the result, Cermat the tie to the catalogue and the construction of the test, schools the preparation and the composition of their groups, the parent the year-on-year gap, and the candidate a concrete point threshold.
One percentage can matter for each of these views and still not prove the cause of the change. From the figure of 12.4 percent one cannot, without further analysis, infer that the year-group is less hard-working. The fairness of the exam depends at once on content, difficulty, key, threshold, the mix of those who entered, and the chance to repair a mistake.
Before we look for a culprit, we have to say whether we are comparing cohorts, whole tests, single items, scoring keys or the pass mark. These quantities can move differently from year to year, and they cannot be folded into one verdict on the year-group.
The test is not the year-group. The year-group is not the cohort. The cohort is not the scoring key. And the failure rate is not intelligence.
— Jiný Kontext
What is documented about the difference between the years
We know: in 2025 the failure rate was higher than in 2024, the expert commission judged the paper harder, and for item 25 it widened the original key by one further correct variant.[1][22] We do not know: the published papers do not split the whole year-on-year gap into the effect of item difficulty, the mix of those who entered, pupils’ preparation and other factors. One therefore cannot claim that the jump was caused only by the construction of the test, or only by a weaker cohort.
2. The result is made of six different decisions
The published percentage of those who failed is the product of the pupils’ work and of the construction of the exam. The paper, the key, the threshold and the mix of those who entered all shape it. The same catalogue therefore does not, by itself, guarantee that two spring sittings measured the same difficulty.
Six layers of one written test
- Catalogue of requirements: what the items may contain.
- The paper: the concrete items, their order, constructed-response and multiple-choice parts.
- Key and revision: which answer counts, which is accepted later.
- Pass mark: 33 percent, 17 points out of 50.
- Cohort: who chose mathematics, and from which type of school.
- Public reading: headlines about a generation, covid, or Cermat.
Cermat’s catalogue sets the knowledge and skills that may be examined in the common part. The mathematics written test in the spring 2025 paper states a maximum of 50 points, a pass mark of 33 percent, 25 items and a time limit on the answer sheet. The first part is constructed-response items 1–14, the second multiple-choice items 15–25 with options, for which the instruction says exactly one answer is correct. That is a description of a particular booklet. It is not proof that each item had a single mathematically admissible solution.[3][4]
This is where the first error of most year-on-year comparisons is born. The headline announces a contest of year-groups, but in fact it compares two papers of different difficulty, a different key and a different share of grammar schools. Or, the other way round, it merely sets raw points against the same threshold and sells the result as a verdict on knowledge. An honest comparison has to state not only the percentage, but also the population of first-time candidates, the subject, the sitting, any revision of the key, and whether the same scale was used.
A breakdown by test, key and group of those who entered helps the search for an explanation. A jump in the failure rate may go with the difficulty of the test, a change after revision with the scoring of an item, and the gap between grammar schools and vocational extension programmes with the composition of the populations. The summary sentence “the candidates failed” does not tell these possibilities apart.
Illustrative scheme: The same catalogue can, in another paper, with another key and another cohort, produce another percentage.
3. An exam error must be detectable and correctable
The state usually wants an exam with a clear threshold. That is reasonable, and incomplete. Just as important is what the error looks like, whether it can be seen, what it costs to repair, and whether the verdict can be reversed. A slip in a constructed-response item is expensive if the whole item falls with it. A pretended uniqueness in a multiple-choice item is more expensive if the key is repaired only after the press conference. Sixteen points cannot be given back in that sitting. The autumn resit is another day, not the same measurement.
Decree No. 177/2009 Coll. defines the pass mark as the lowest result a pupil must reach in order to pass the written test. The result in the common part is verbal: passed or failed, with a percentage. That is a legal construction of a certificate, not a psychometric guarantee that 17 points this year are the same as 17 points last year.[5]
| Type of failure | What it looks like | How to test it | What limits the harm |
|---|---|---|---|
| Difficulty drift | The same threshold, a different bar of items | Anchor items, IRT, an independent year-to-year audit | Do not change the cut-off and the paper together without saying so |
| A faulty key | The item has more solutions, the key has one | Review before the results are published | A revision that does not change the rules in silence |
| A binary threshold | 16 points fall, 17 pass | The share of pupils in the band ±2 points | A resit, a reasoned change of the threshold |
| A different cohort | A different share of grammar schools and vocational extension programmes | Compare school types separately | Do not read one percentage as one population |
In the reading it matters whether the system can find its own error and repair it. A subjective sense of difficulty is not the same thing as a change of key on an item that decides the result. And a pool of grammar schools and vocational extension programmes should not be sold as a homogeneous picture of “mathematics in the Czech Republic” without a split by school type.
The content of the test is therefore only one axis. The second is the observability of the key, the third the reversibility of the points, and the fourth the effect on further study. A test with a slightly weaker average item, but a published link to last year’s difficulty, can be safer for trust than a showy paper without that support.
4. The failure rate alone does not describe a year-group’s ability
The percentage of those who failed is needed, because it replaces part of the impressions. The problem starts when one number begins to stand for a whole generation. For the spring sitting of 2025 the ministry of education said that the net failure rate on the written tests was 12.3 percent, and that this matches the level of 2021 and 2022. In mathematics more than 19 percent of pupils chose the second compulsory exam, 14.9 thousand candidates sat the test, and the net failure rate of first-time candidates was 12.4 percent, which the ministry compared with 2023. In grammar schools 3.7 percent of pupils failed in mathematics, in secondary vocational schools almost a third, in vocational extension programmes 47 percent. That is the spring sitting of 2025 and the net failure rate of first-time candidates in that subject, not the autumn resits and not PISA.[1]
A year earlier, in spring 2024, the failure rate of first-time candidates in mathematics was 4.9 percent. The year-on-year jump to 12.4 percent is a jump in the share who failed on the same kind of institutional exam, not a measurement that the “average ability” of the cohort changed by the same multiple. The minister of education said of 2025 that the mathematics written test was harder than last year’s, or rather that last year’s was easier than it should have been. The independent expert commission of the ministry said that, on the analyses supplied, the 2025 test looks harder than in the previous three years, especially against 2024, and at the same time asked for more credible statistical analyses for a year-on-year comparison. That is a judgement on one sitting, not a published linking of five years onto one psychometric scale.[1][7][22]
What has to stand beside the percentage
- The sitting: spring, autumn; first-time candidates, or everyone.
- Subject and choice: mathematics versus English.
- School type: grammar school, secondary technical school, secondary vocational school, vocational extension.
- Whether a revision of the key has already taken place.
- What the number does not measure: an anchored difficulty against last year.
The national percentage is the start of a reading, not its proof. Item statistics, a split by school type and a description of how the test was built can explain more than a quarrel over whether 12.4 percent is “within the norm”.
5. Compare the construction, not the generations
The market of readings can be mapped without a false podium of winners. The map below does not say which year-group is worse in general. It shows what work each layer builds the result around, what kind of error it brings, and what the reader should look for on purpose.
| Layer | Main working position | What to check | Typical false conclusion |
|---|---|---|---|
| Catalogue | The lawful content of the items | Whether the item is in the catalogue | “This must not be asked” without support |
| Paper | The concrete difficulty of the year | Item statistics, not an impression | “The generation can do less” |
| Key | What counts as correct | Whether the item has one solution | “The pupil cannot do mathematics” |
| Cut-off | 17 out of 50 | The share in the band around the threshold | “He passed, so he can do it” |
| Cohort | Who chose the subject | School type separately | One percentage for the whole country |
| PISA/TIMSS | A different population, a different construct | Age, year, framework of items | “The maturita refutes PISA” |
The table does not judge Cermat as an institution. Each year uses a different booklet, and the result depends on the concrete construction and on the review. The point is to stop a percentage without a key and without a description of the cohort from locking a whole year-group into a label.
How to read the scheme: The height of the failure-rate column is not a measure of intelligence. It has to be read with the test, the key, the threshold and the mix of those who entered.
6. A raw point is not an anchored point
In the published marking, the Czech state maturita adds points for items and compares them with a fixed percentage threshold. That is classical test theory in an operational sense: raw score, cut-off, passed/failed. The international PISA survey, by contrast, maps performances onto a scale with item-response models and links cycles with anchor items; the PISA 2022 technical report describes this as a condition of comparison across years and countries. The purpose is different — monitoring of systems, not a certificate for one person — and so is the method. It does not follow that the maturita “has no value”. It follows that 17 points in 2024 and 17 points in 2025 are not, without further work, the same point on the same scale.[10][11][6]
Embretson and Reise, in their IRT textbook, show why a raw sum is not enough when item difficulty changes: the same number of correct answers can mean a different ability. Brennan’s Educational Measurement places standardisation and linking among the conditions of a fair comparison of forms. These are methodological books, not an audit of Cermat. They explain what a year-on-year comparison would need, and why a mere failure rate will not replace it.[13][14]
The public materials on the mathematics written tests that a reader can ordinarily reach show the booklet, the key and the summary or item results. They do not show the ordinary reader an anchor set that would join the years 2021–2025 on one IRT scale. A missing publication is not proof that no internal calibration exists. It is a reason not to read the jump from 4.9 to 12.4 as a jump in ability.
That is a reasonable reading, and incomplete if we stop there. Cermat also publishes aggregated item results, including the share of omitted answers; the expert commission nevertheless asked for more credible statistical analyses for a year-on-year comparison of difficulty. A request for further analysis is not proof that no calibration exists inside the office. It means that the papers laid before the commission were not enough for a convincing year-on-year conclusion.[7][22]
For a certificate of one person, IRT is not the only path. One can keep the same cut-off and change the paper, if it is said openly that the bar sat somewhere else this year. One can keep the paper and move the cut-off, as in 2021. One cannot do both in silence and still claim that the percentage measures the pupil.
7. The threshold of 17 out of 50 is not a small detail
The mathematics written test has a maximum of 50 points. The threshold of 33 percent corresponds to 17 points; Cermat states the same construction for the optional extended mathematics paper as well. A candidate with 16 points failed. A candidate with 17 passed. The binary break is a property of the certificate. It is not a property of mathematics as a field.[4][18]
In the band of 15–18 points, what decides is not “a systemic grasp of the secondary-school syllabus” as a whole. What decides is whether one item fell on a numerical slip, whether item 25 carried four points, whether the key accepts two paths. The ministry press release on spring 2025 does not give, as a separate figure, how many first-time candidates sit in this band in a given year. The missing figure is not a trifle. It is precisely the band in which the construction of the exam most changes a life.
8. The key is repaired. The pupil’s ability is not
In the spring sitting of 2025 the independent expert commission found that, for both parts of item 25, variant A had to be accepted as well, beyond the original key. The marking was then adjusted so that the original incompleteness of the key would not put pupils at a disadvantage; the ministry and contemporary news sources describe how the points were compensated.[1][8][9][22] That is a later repair of one item in one sitting. It shows that the original key for this item was not complete; it does not show intent, nor a general defect of the whole test.
The booklet, for multiple-choice items 15–25, says that exactly one answer is correct. When an item fails that condition, the layer of the key has failed, not necessarily the pupil. Repairing the key can save the pupil. It does not change, after the fact, what he could do on Friday morning. It changes what the state writes down about that ability.
This repair is a known procedure in testing: a disputed item is dropped, or more paths are accepted, so that no one is harmed. The problem is not that the procedure exists. It is the time and the place of the check. If the public first hears that 12.4 percent is within the norm, and only then that one item did not have a single solution, it reads the percentage before it knows the key. The order of the layers is turned around.
That does not mean every hard item is faulty. A hard item with a unique solution is a legitimate filter. An item that promises one answer in the booklet and has several in the mathematics is a different object. An honest audit will keep them apart. A headline about a generation will not join them.
What needs to be tested
The first test concerns the uniqueness of the wording before print. The second concerns items with an anomalously low success rate: is that difficulty, or a faulty key? The third concerns whether the revision came before, or after, the public reading of the number. A test that answers a day earlier need not be better if, a week later, no one can say which key was in force.
9. Choosing mathematics is not the same as difficulty
Mathematics in the common part is not compulsory for everyone. The pupil chooses between it and a foreign language. In 2025, according to the ministry, more than 19 percent chose it, interest rising for a third year; English was taken by the majority, just under 80 percent of first-time candidates, with a failure rate of 3.5 percent. Czech, compulsory for all, had a failure rate of 9 percent against 2.8 percent a year earlier. That is spring 2025 and first-time candidates. Another subject is another population.[1][7]
So 12.4 percent in mathematics cannot be added to 9 percent in Czech as “the level of the candidates”. Those who choose mathematics are not a random sample of the year-group. A grammar school with 3.7 percent failing and a vocational extension programme with 47 percent on the same test show that the paper cuts different schools differently. That may be the intent of the certificate. It must not be read as a single curve of ability.
10. PISA is not the maturita. The maturita is not PISA
PISA 2022 measured the mathematical literacy of fifteen-year-olds: 487 points in the Czech Republic, 74 percent above level 2 against 69 percent in the OECD. TIMSS 2023 measured eighth grades: 518 points against 478 internationally and 503 for the thirteen EU countries in the survey. The 2025 maturita measured a voluntarily chosen written test among 14.9 thousand candidates. These are three populations, three construct frameworks, three purposes.[11][12][15]
PISA asks whether the pupil can read a situation and use mathematics. The maturita catalogue and the booklets often rest on school procedure: rearranging expressions, equations, trigonometry, a multiple-choice option. A tension between a decent literacy of fifteen-year-olds and a swinging failure rate among maturita candidates therefore need not mean that “the international test is lying”. It can mean that the national certificate measures something else, and on top of that moves the bar between years.
Anyone who turns 487 points into the sentence that the maturita is pointless erases the purpose of the certificate. Anyone who turns 12.4 percent into the sentence that Czechs cannot do mathematics erases PISA, TIMSS and the grammar school with 3.7 percent.
The difference of constructs can be stated without a ranking. PISA does not punish a pupil for choosing mathematics or English. The maturita does: the subject is a choice, and the cohort is filtered by it. PISA does not promise that 487 points is a ticket to a faculty. The maturita promises passed or failed. When both numbers are stood in one sentence, the impression of a quarrel about the truth appears. In fact it is a quarrel about which instrument may serve which purpose.
11. What must be traceable in the booklet and the key
Before the revision the public guesses whether the item was hard. After the revision it checks whether the source — booklet, key, press release — speaks of the same rule. A citation of the catalogue is a navigation to the content. It is not proof that item 25 had one solution.
Alignment of the items with the catalogue, a likeness of the failure rate to 2023, and a change of key on one item can all hold at once. That does not mean that “nothing happened”: each claim judges a different property of the exam, and the effect of the revision on pupils at the threshold has to be judged on its own.
A four-step check of the maturita number
- Existence: the figure is from the spring sitting, first-time candidates, the given subject.
- Key: the original one was in force, or the revised one.
- Support: the percentage really carries a sentence about knowledge, or about the paper.
- Scope: grammar school, vocational extension, or the whole.
The most reliable procedure keeps the publication of the booklet, the item statistics and the reading about a generation apart. If the key cannot be traced, a claim about the “correct solution” is not promoted into a mathematical constant.
12. The price of a point is the price of the raw material, not the price of the certificate
Cermat, the school and the family use several price languages. The point is the raw material. The certificate is the result. The autumn sitting is a repair exchange. A year of waiting for university is something else. A direct comparison of “more failed this year” without the price of that wait misleads.
A cheap test with a 4.9 percent failure rate can be expensive if the bar fell below the catalogue and the certificate lost its signal. An expensive test with 12.4 percent can be cheaper if it better separates those who know the material — and more expensive if it mainly separates those who had bad luck on an item with a faulty key.
The real price of an accepted result
Paper + key + cut-off + resit + deferred study + trust in the certificate.
A result is cheap only when it can be defended by the same rule as last year, or when it is said openly that the rule is not the same.
13. What to read from the spring results
A reasonable reading does not start with the headline, but with the kind of question. The recommendations below are not a ranking of year-groups. They are a signpost to the first analysis.
| Need | First figure | The decisive test | An unacceptable shortcut |
|---|---|---|---|
| Compare the years | Failure rate of first-time candidates | Whether a linking of difficulty exists | “The generation can do half as much” |
| Compare schools | Grammar school 3.7%; vocational extension 47% | The same test, a different cohort | One number for the whole country |
| Judge an item | Booklet and key | One solution, or more | Read a multiple-choice option as the mathematics itself |
| Judge the threshold | 17 out of 50 | The band around the cut-off | 16 points as proof of illiteracy |
| Bring in PISA | 487 points, 15-year-olds, 2022 | A different population | Refute the maturita with PISA, and the reverse |
| Read 2024 | 4.9% | Whether the test was easier than it should have been | Take 4.9% as a new standard of ability |
The Czech booklet has to be judged directly. A general IRT textbook will not score the wording of item 25, a summary of all the written tests will not describe the mathematics, and the result of the grammar schools cannot be sold as the result of the vocational extension programmes.[1][13]
14. A week that says more than the year-on-year headline
The reading can be done without denying the difficulty and without a hunt for the year-group. A short audit is enough. The aim is not to prove that Cermat failed. The aim is to find the layer in which the number was made.
Seven days from headline to reading
- Day 1: Separate the subject, the sitting, the first-time candidates.
- Day 2: Add the school type and the share who chose mathematics.
- Day 3: Open the booklet and the key, not only the percentage.
- Day 4: Find out whether an item was revised.
- Day 5: Compare with last year only where the definition is the same.
- Day 6: Set PISA and TIMSS aside as another object, or describe them with age and year.
- Day 7: Write what the number measures, and what it expressly does not.
Three tests of one item
The first is the wording: does the text allow more than one path? The second is the key: does it match the sentence “exactly one answer”? The third is the effect: did the revision change only the points, or also the public story about the year-group?
Before a conclusion about the generation
A petition, teachers’ impressions and a judgement of higher difficulty can all hold at the same time as the fact that 12.4 percent is not outside the range of all previous years. The conclusion “the pupils are worse” does not follow from that concurrence. One can say that the paper was harder against 2024, and that the original key of item 25 did not contain every correct variant. From the revision it does not follow that no key existed before the exam, or that the whole test was prepared carelessly.[22]
The check should end with a rule of reading: what the percentage may be used for, which revision of the key will be published, and when the comparison of years will be repeated. Because the booklets change, every year-on-year conclusion has to state the date and the method of comparability.
15. A grammar-school 3.7 percent is not a vocational-extension 47 percent
For spring 2025 the ministry split the school types: grammar schools 3.7 percent failing in mathematics, secondary vocational schools almost a third, vocational extension programmes 47 percent. The same paper, the same maximum of 50 points, the same cut-off of 17 points. A different school. That is the net failure rate in one sitting, not proof that the vocational extension programme “cannot teach” and the grammar school “can do everything”. It shows that one national 12.4 percent is a mix of cohorts, not one curve.[1]
Anyone who turns the average into a sentence about all the candidates does what grades do: compresses four schools into one digit. The political impression of “excess, or the norm” is then run on a mixture. An audit should start with a table by type. Only then ask about the paper.
English with 3.5 percent failing among most of the year-group is another different object. Czech at 9 percent against last year’s 2.8 percent shows that the jump need not sit only in mathematics. That too is not proof about intelligence. It is a reason not to read one subject as the whole maturita.[7]
16. The year 2021 showed that the threshold is a lever
In 2021 the ministry lowered the mathematics pass mark after the fact from 33 to 27 percent. The reason given pointed to distance teaching. At the original threshold, according to the official calculation of the time, the failure rate would have reached 24.9 percent. Out of 50 points, 14 were enough. That is one extraordinary intervention, not a new standard of the catalogue.[17]
Something more precise is said here than “covid spoiled mathematics”. The cut-off is a political lever and a psychometric one. It can put out the share who fail without a single item being changed. It can also — if it stays still while the paper grows heavier — manufacture a year-on-year jump that looks like a worsening of the pupils.
Spring 2025 did not, according to the minister, reach for this lever. The revision went through the key of item 25. Those are two different tools. Both change the record about the pupil. Neither changes, after the fact, what he could do on Friday. The public has a right to know which tool was used. Otherwise it reads 12.4 percent as the character of the year-group.
An illustration, not a report. A candidate who in spring 2024 — a year with a failure rate of 4.9 percent — scores 18 points leaves with the certificate. A candidate a year later does comparable work, scores 16 points and waits for the autumn. The difference need not be in intelligence. It can be in the paper, in the key, and on which side of the threshold he landed. This pair must not be sold as two concrete scripts. It can be used as a question about the band that the state does not measure in the same headline as 12.4 percent.
17. Trust rests on a traceable key and on comparability
The first generation of the state maturita promised comparability against a school exam. The next generation added a written test and a fixed threshold. Today’s result sells something larger: a place from which the state, universities and families read who “can do mathematics”.
So the contest is not only over the items. It is over trust in the key, in the cut-off and in the year-on-year story. The more comfortable a single percentage is, the higher the price can be when it turns out that an item had two solutions, or that last year’s test was easier than it should have been.
The common exam supplies a comparison that a school grade alone does not. For that comparison to be readable, the state needs a timely review of items, a published method of comparability, statistics split by school type, and a regular check of what the 17-point threshold means.
The quality of the maturita is not set by the lowest failure rate, nor by the highest. What decides is whether a disputed item can be traced, its effect repaired, and a test error stopped from being read as the character of a generation.
At the moment when the test only closes secondary school, we are choosing a certificate. At the moment when we build a sentence about intelligence from 4.9 and 12.4 percent, we are choosing a reading of society. And then the question is no longer: “Can this year’s candidates do mathematics?”
When the result is read, what therefore decides is: Which part did we measure this year — the paper, the key, the threshold, or the pupil’s performance — and which error can we still repair?
— Jiný Kontext