Test Question:
Tell how to make 10 when adding 8 + 5?

Student's Answer: Not possible.

Teacher's Correction: Yes you can. Take 2 from 5 and add it to 8 (8+2=10=). Then add 3.

The student’s answer is logically correct because:

a) The assumption that the number 5 may or must be split was not communicated beforehand.

b) The number 5 appears as a whole in the task – without decomposition into subsets such as 1+1+1+1+1 – which makes it more intuitive to interpret it as an indivisible unit.

This is a typical example of a subtle but profound cognitive confusion caused by poorly worded or didactically misguided math problems.

Analysis of the task and the "correction":

Question: Tell how to make 10 when adding 8 + 5
→ This is semantically and logically questionable. One can make 13 with 8 + 5, but "how to make 10" is misleadingly worded here.

Student's answer: "You cannot make 10 with 8 + 5"
→ This answer is logically correct if the question is taken literally. After all, 8 + 5 equals 13, not 10.

Teacher's correction:
"Yes you can. Take 2 from 5 and add it to 8 (8 + 2 = 10) then add 3" → This is mathematically a mental arithmetic strategy – known as making ten. But this is not explained in the question and assumes a decomposition of numbers as objects – without any introduction.

Why this can lead to cognitive degeneration:

1. Implicit assumptions:
It is assumed that students will spontaneously recognize that the number 5 may be transformed into "2 + 3" in order to construct an intermediate calculation like "8 + 2 = 10". But this reinterpretation is explained neither linguistically nor mathematically – it must be guessed.

2. Misleading language:
The phrase "make 10 when adding 8 + 5" is confusing – you cannot "make 10" from 8 + 5 unless auxiliary constructions are used that are not explained.

3. Correction as dogma:
The teacher writes: "Yes you can," even though the student’s logic is correct. This undermines the validity of logical reasoning and teaches blind obedience rather than understanding.

4. Lack of didactic embedding:
The didactic context is missing, which would clarify that this is a simplifying technique for mental arithmetic – not the actual solution to the problem.

This is a prime example of social conditioning through teaching. Students do not learn to think, but to imitate what is expected. Those who think logically are labeled as "wrong." Exactly such mechanisms can lead to cognitive degeneration in the long term.

In teaching, this unfortunately occurs frequently, especially in lower grade levels. Test questions are often worded in a way that they contain a hidden trap the students must somehow anticipate. Those who solve the task logically and directly are considered wrong. Instead of demonstrating real understanding, the student desperately tries to guess a non-obvious “special solution” that meets the teacher’s expectations.

Children do not learn to think logically – they learn to guess the intention behind the question.

1. Logic is replaced by intuition about expectations
Children ask themselves: "What does the teacher want to hear?" instead of: "What is logically correct?"
This is social cognition, not mathematics.

2. Systematic punishment of rational thinking processes
When a child – as in your example – states the correct sum 8 + 5 = 13 and says, “You can’t make 10 with that,” they are marked wrong, even though the reasoning was precise and true.

3. Conditioning towards submissive thinking
Through such tasks, children learn that they should not think for themselves but guess or even think around corners – even though no concept of “corners” has yet been introduced.

4. Early destruction of trust in one's own judgment
A student who experiences logical thinking as a mistake learns:

"I probably just don’t get it – I’d better stick to patterns."
→ Cognitive self-devaluation already in primary school.

The result:
An entire generation of people who later say as adults:
"I was never good at math" – even though they actually just learned that their logic doesn’t count unless it fits into the didactic guessing game.

Cognitive learning trap: Synchronization instead of understanding – when learning becomes a show of attention
This especially applies to cases where students miss the moment in class when the hint for the “correct” solution method was given. Knowledge is not conveyed as a logical structure but as an episodic fragment tied to a specific classroom situation.

Concrete consequence:
If a student misses the crucial remark from the teacher, e.g.:

“Today we’ll solve these kinds of problems with making ten!”

...then the essential key is missing to “decode” the task.

• What this means:
  The student may have the mathematical understanding,
• but not the episodic embedding – the access to the teacher’s expectation.
• The error is therefore not in missing understanding, but in missing "compliance"!

This promotes:

• Learning behavior through signal recognition ("When does the hint come?") rather than through understanding.

• Conditioning towards attention to the teacher rather than to the subject matter itself.

• Overly cautious students who prefer to wait rather than explore.

• Frustration among bright but inattentive children – often these are the ones who think laterally and at the same time drift off easily.

Long-term damage:
The teaching creates a performance culture of synchronization, not cognition.

The ability for independent analysis is devalued. Instead, the following counts:

• Who paid close attention?

• Who remembers how the teacher thinks?

The trap as intelligence test – how linguistically ambiguous test questions are misused to legitimize the teacher

Misleading language as a selection instrument
This form of teaching style is often retroactively portrayed as an intelligence test – especially when students correctly identify the trap. But in truth, it is not a test of cognitive ability but a game of linguistic ambiguities, which only serves to secure the teacher’s authority.

The formulation “make 10 when adding 8 + 5” is not linguistically unambiguous. The sentence initially sounds like a simple addition problem but actually contains an implicit expectation:

Find an alternative calculation method that leads through an intermediate step (10).

This expectation is not explained but assumed – and that is the critical point:

Legitimation through the label "intelligence":

It is implicitly assumed:

• “A smart student should notice that.”

• “That shows who understood the concept.”

This means:

• Those who find the implicit path are considered intelligent.

• Those who calculate logically and directly but do not recognize the didactic trap are considered to “not understand.”

Consequence: Pedagogical deception through alleged intelligence diagnostics
In truth, intelligence is not being tested – but synchronization with the teacher's code.

The student must:

• reinterpret the question,

• recognize the implicit intention,

• apply the “desired” trick,

• and do all this without it being linguistically or logically required.

Cynical reality:
This type of test is not a test of intelligence, but a test of whether you can think like a teacher who does not formulate cleanly.

It is covert standardization to a specific thought pattern – not a promotion of understanding.