Why identifying what cannot be determined is sometimes the most important part of solving a problem.
By Tymur Levitin | Levitin Language School
A student reads a mathematics problem:
A rectangle has a perimeter of 40 centimetres. What is its area?
The student remembers the formula for the perimeter:
[
P=2(a+b)
]
Then the formula for the area:
[
A=ab
]
They know both formulas. They understand what a rectangle is. They can multiply and divide.
But they cannot calculate one specific area from the information provided.
And this is where something interesting happens.
Instead of saying that the problem does not contain enough information, the student may start searching for a number.
Perhaps they divide 40 by four and obtain 10.
Then they calculate:
[
10\times10=100
]
The arithmetic is correct.
A square with sides of 10 centimetres does have a perimeter of 40 centimetres and an area of 100 square centimetres.
But the question did not say the rectangle was a square.
A rectangle measuring 12 by 8 centimetres also has a perimeter of 40 centimetres.
Its area is:
[
12\times8=96
]
A rectangle measuring 15 by 5 centimetres has the same perimeter.
Its area is:
[
15\times5=75
]
The student has not necessarily made a calculation error.
They have answered a question that the available information does not uniquely determine.
This distinction matters far beyond mathematics.
Before solving a problem, we need to establish whether the information provided actually makes the requested answer possible.
1. Why students assume every school question must have an answer
Most classroom exercises are designed to be solvable.
A textbook introduces a formula, provides several examples and then presents exercises in which students are expected to apply the new method.
This is often an effective way to practise a skill.
But repeated exposure to this structure can create an expectation:
If the teacher has given me a question, there must be a number I am supposed to find.
The student may begin looking for an operation before examining the conditions.
They see two numbers and add them.
They see a percentage and multiply.
They see a distance and a time and divide.
The problem is not that these operations are inherently wrong.
The problem is that an operation is selected before the student has established what the available information represents.
A number appearing in a question does not automatically mean it should be used in a calculation.
And the presence of a familiar formula does not guarantee that the formula can produce a unique answer.
A well-designed education should therefore develop two abilities:
- Solving problems when their conditions are sufficient.
- Recognising when the conditions do not support the requested conclusion.
The second ability is often less visible in ordinary schoolwork.
Yet it is essential for independent reasoning.
2. Three different problems that students often confuse
When a student cannot obtain an answer, several fundamentally different situations may exist.
Situation A: The student lacks the necessary knowledge
Consider:
A car travels 150 kilometres in 3 hours at a constant speed. What is its speed?
The information is sufficient.
The relevant relationship is:
[
v=\frac{d}{t}
]
Therefore:
[
v=\frac{150}{3}=50\text{ km/h}
]
A student who does not know how to calculate speed may be unable to solve the problem.
But the problem itself is solvable.
The missing element is the student’s knowledge or ability to apply it.
Situation B: The question lacks necessary information
Now consider:
A car travels 150 kilometres. What is its average speed?
The distance is known.
The travel time is not.
Without additional information, the average speed cannot be uniquely determined.
A student might know the speed formula perfectly and still be unable to calculate the answer.
Here, the missing element is not the student’s knowledge.
It is information in the problem.
Situation C: The conditions contradict one another
Consider:
A car travels at a constant speed of 50 km/h for 3 hours and covers exactly 200 kilometres. What distance does it travel?
Under the ordinary relationship between constant speed, time and distance:
[
d=vt=50\times3=150\text{ km}
]
The statement also claims that the distance is exactly 200 kilometres.
These conditions cannot all be true under the stated model.
The appropriate response is not to choose whichever number looks more convenient.
It is to identify the contradiction.
These situations require different educational responses.
A student who lacks a formula needs instruction.
A problem with insufficient information needs additional conditions.
A contradictory problem needs clarification or correction.
Treating all three situations as “the student couldn’t solve it” hides the actual reason.
3. The rectangle problem: what can we determine?
Return to the rectangle with a perimeter of 40 centimetres.
We know:
[
2(a+b)=40
]
Therefore:
[
a+b=20
]
This tells us something definite.
The two side lengths must add up to 20 centimetres.
But it does not tell us what each side length is.
If:
[
a=12,\quad b=8
]
then:
[
A=96
]
If:
[
a=15,\quad b=5
]
then:
[
A=75
]
If:
[
a=10,\quad b=10
]
then:
[
A=100
]
All three rectangles satisfy the perimeter condition.
Therefore, the area is not uniquely determined.
However, this does not mean that nothing can be said about the area.
For positive side lengths:
[
A=a(20-a)
]
Rearranging:
[
A=100-(a-10)^2
]
Since a square cannot be negative:
[
A\leq100
]
So the area cannot exceed 100 square centimetres.
And because both side lengths are positive, the area must also be positive.
We can therefore establish:
[
0<A\leq100
]
This is an important distinction.
Insufficient information for one exact answer does not necessarily mean insufficient information for every meaningful conclusion.
A student may be unable to determine the precise area but still be able to identify its possible range.
That is not failure.
It is a more accurate interpretation of the problem.
4. Missing information is not always the same as missing numbers
Students often associate insufficient information with the absence of numerical values.
But a question may contain many numbers and still lack the conditions necessary for a reliable answer.
Consider:
A student studies for two hours and receives a score of 85%. Another student studies for four hours and receives 90%. How much does each additional hour of study improve exam performance?
The question provides two study durations and two scores.
It may be tempting to calculate:
[
\frac{90-85}{4-2}=2.5
]
That gives a difference of 2.5 percentage points per additional hour between the two observations.
But can we conclude that each extra hour of studying causes a 2.5-percentage-point improvement?
No.
The students may have different prior knowledge.
They may have studied different material.
They may have taken different tests.
They may have used different study methods.
Even if their scores were measured on the same assessment, two observations would not establish a general causal relationship.
The calculation describes a numerical relationship between the observations.
It does not establish a universal learning rule.
This is where students need to distinguish between:
- A calculation that can be performed.
- A conclusion that follows from the data.
- A causal claim that requires additional evidence.
These are not interchangeable.
5. When a question has several valid answers
Sometimes the information is not contradictory or useless.
It simply allows multiple solutions.
For example:
Two numbers add up to 20. What are the numbers?
Possible answers include:
[
8+12=20
]
[
5+15=20
]
[
-3+23=20
]
Without additional restrictions, there are infinitely many pairs of real numbers whose sum is 20.
The student can provide an example.
But they cannot identify one uniquely determined pair.
The wording matters.
If the question asks:
Give one possible pair of numbers whose sum is 20.
Then 8 and 12 is a complete answer.
If it asks:
Find all possible pairs of real numbers whose sum is 20.
Then a general representation is more appropriate:
[
x+y=20
]
[
y=20-x
]
If it asks:
What are the two numbers?
Without further context, the question is ambiguous if a unique pair is expected.
This demonstrates why understanding the requested output matters as much as understanding the available data.
In our earlier article, Why a Correct Answer Can Still Be Incomplete: The Hidden Requirements in School Questions, we examined why an answer can be factually correct yet fail to meet the full requirements of a task.
Here, the issue begins even earlier.
What kind of answer is the question actually capable of supporting?
6. The danger of silently inventing a condition
Suppose a student reads:
A family travels 300 kilometres by car. How much fuel do they use?
The student remembers that a car might consume 7 litres per 100 kilometres.
They calculate:
[
300\times\frac{7}{100}=21
]
The result is mathematically correct if the car consumes 7 litres per 100 kilometres over that journey.
But the problem never specified the fuel consumption rate.
The student has introduced an assumption.
Making assumptions is not always wrong.
In real-world modelling, assumptions are often necessary.
The problem arises when the assumption is presented as though it were information supplied by the question.
Compare two responses.
Response A:
“The car uses 21 litres.”
Response B:
“The fuel consumption cannot be determined from the distance alone. If we assume an average consumption of 7 litres per 100 kilometres, the estimated fuel use would be 21 litres.”
The second response is more informative.
It separates what is known from what has been assumed.
It also makes the calculation available for evaluation.
Someone can question the assumed consumption rate without rejecting the arithmetic.
This distinction is central to scientific modelling, engineering, economics and many everyday decisions.
An assumption can make a calculation possible without making its result an established fact.
7. A formula does not create information that the problem does not contain
One reason students continue calculating is that they remember a relevant formula.
But formulas describe relationships.
They do not automatically supply missing values.
Consider the density formula:
[
\rho=\frac{m}{V}
]
If a problem gives mass but not volume, the density generally cannot be calculated uniquely.
Knowing the formula does not change that.
Likewise, Ohm’s law:
[
V=IR
]
relates voltage, current and resistance in an appropriate electrical model.
If only the voltage is known, the current cannot generally be determined without additional information about resistance or the circuit.
A student may write the formula correctly and still lack enough information to obtain the requested quantity.
This is why formula memorisation and problem analysis are separate skills.
The first tells the student which relationship may be relevant.
The second tells them whether the relationship can actually be used to determine the unknown.
At Levitin Language School, this distinction is relevant to individual support in mathematics and science, including learning mathematics and science through English and learning mathematics through German.
The educational objective is not simply to produce more calculations.
It is to help students understand why a particular calculation is justified.
8. Insufficient information versus impossible conditions
These two cases deserve particular attention because they can look similar.
Consider the equation:
[
x+y=10
]
If the task is to find the exact values of both variables, one equation is insufficient to determine a unique pair.
There are infinitely many solutions.
Now consider:
[
x+y=10
]
[
x+y=15
]
No pair of values can satisfy both equations simultaneously.
The system is inconsistent.
These are different mathematical situations.
In the first case, many answers are possible.
In the second, no answer satisfies all the conditions.
Now consider:
[
x+y=10
]
[
2x+2y=20
]
At first glance, there are two equations.
But the second is simply the first multiplied by two.
It provides no independent restriction.
The system still has infinitely many solutions.
This is a useful lesson for students who have been taught that two equations are enough to find two unknowns.
That shortcut is not universally valid.
The equations must provide enough independent information to determine the unknowns uniquely.
Counting equations is not the same as analysing their informational content.
9. Why adding more information does not always solve the problem
Imagine a school administrator wants to know why students’ grades have fallen.
They collect more information:
Attendance records.
Homework completion rates.
Test results.
Class participation.
Study hours.
Teacher observations.
This additional information may be useful.
But simply collecting more data does not guarantee that the cause of the decline can be identified.
Perhaps the grading system changed.
Perhaps the assessments became more difficult.
Perhaps the students are learning through a language they are still acquiring.
Perhaps several factors are operating simultaneously.
A large quantity of information is not the same as information sufficient to support a particular conclusion.
The same applies to international education.
A student who previously received high grades may perform differently after moving to another country.
Before concluding that their academic ability has declined, we need to examine the language of instruction, curriculum expectations, assessment criteria and educational context.
Our article Your Child Was Good at School Before Moving to Switzerland. Why Are Their Grades Lower Now? examines this kind of situation.
The broader principle is simple:
Before explaining a result, establish whether the available evidence can distinguish between the possible explanations.
10. Science: a result is not always enough to identify its cause
Suppose two plants are placed in different locations.
After a month, one grows taller.
A student concludes:
“The taller plant received more sunlight, so sunlight caused the difference.”
But what if the plants also received different amounts of water?
What if they grew in different soil?
What if they were different varieties?
The observation may be accurate.
The proposed explanation may even be plausible.
But the available information does not isolate the cause.
A scientific investigation must consider alternative explanations and relevant variables.
This does not mean that students should refuse to draw any conclusion until every possible factor has been eliminated.
It means that the strength of the conclusion should match the strength of the evidence.
For example:
“The plant in location A grew taller than the plant in location B.”
This is an observational conclusion, assuming the measurements are reliable.
“Greater sunlight caused the difference.”
This is a causal conclusion requiring additional justification.
The two statements are not equivalent.
In “I Answered Correctly!” Why Knowing a Fact Is Not the Same as Proving a Conclusion, published in Russian, we explored the relationship between facts, interpretations and proof.
The present problem adds another dimension:
Do we have enough information to distinguish between competing explanations at all?
11. Language can hide missing information
Not every incomplete problem is mathematical.
Consider the sentence:
She gave him the book because he needed it.
Who needed the book?
The sentence identifies the person as “he,” but without additional context, we may not know who that person is.
Now consider:
Alex told Jordan that he was late.
Who was late?
Depending on context, the pronoun might refer to Alex or Jordan.
The grammar alone may not uniquely determine the intended meaning.
A student may choose one interpretation and continue reading as if it were certain.
But a careful reader should recognise that the sentence is ambiguous.
The appropriate response may be:
“The context is insufficient to identify the referent with certainty.”
This matters in reading comprehension, translation and communication.
Sometimes a student does not misunderstand a text because they lack vocabulary.
They misunderstand it because they turn an ambiguous statement into an unnecessarily definite interpretation.
Language learning therefore involves more than recognising words.
It also requires identifying what a sentence establishes, what it leaves open and what the reader supplies through inference.
12. The same problem appears in translation
Consider the English sentence:
They have been working together for years.
A translator may need to choose grammatical forms in a target language that require distinctions not explicitly expressed in English.
Depending on the language, the translation may require information about gender, formality or other contextual relationships.
If the source text does not supply that information, the translator has a decision to make.
They may seek clarification.
They may choose a neutral construction where possible.
Or they may make a contextual assumption and recognise its limitations.
What they should not do is treat an unsupported interpretation as a fact supplied by the original text.
The same applies to professional editing, proofreading and business communication.
A polished sentence is not necessarily an accurate sentence.
A fluent translation is not necessarily a justified translation.
This is one reason why professional translation, editing and language adaptation require attention to meaning, context and the limits of the available information.
The central issue is not whether someone can produce a plausible sentence.
It is whether that sentence expresses what the source actually supports.
13. How students confuse a possible answer with the answer
Imagine the following question:
A number is greater than 10 and less than 20. What is the number?
A student answers:
“15.”
Is that wrong?
Not necessarily.
Fifteen satisfies the conditions.
But so do 11, 12, 13 and many other numbers, depending on whether the intended domain is integers or real numbers.
The problem is not that 15 is invalid.
The problem is that the conditions do not identify 15 uniquely.
Now change the instruction:
Give one integer greater than 10 and less than 20.
Fifteen is a complete answer.
Change it again:
List all integers greater than 10 and less than 20.
Now the expected answer is:
11, 12, 13, 14, 15, 16, 17, 18 and 19.
The mathematical conditions remain closely related.
But the task requirements change what counts as a complete response.
Students need to distinguish:
One possible answer.
Every possible answer.
The only possible answer.
These are three different claims.
A student who does not recognise the difference may provide a mathematically valid example while believing they have identified a unique solution.
14. When a problem can be solved only under additional assumptions
Consider:
A person earns $20 per hour. How much will they earn in a month?
The hourly rate is known.
But monthly earnings depend on the number of paid hours.
If we assume 160 paid hours:
[
20\times160=3200
]
The result is $3,200.
But it is conditional.
If the person works 120 paid hours, the amount is $2,400.
If they work 180 paid hours, the amount is $3,600.
A student should be able to say:
“Monthly earnings cannot be determined from the hourly rate alone. We need the number of paid hours.”
Then, if the task permits assumptions, they can provide an illustrative calculation.
This distinction becomes especially important in economics and financial literacy.
A numerical estimate may be useful.
But the conditions behind the estimate must remain visible.
Otherwise, a model can produce an appearance of precision without the information necessary to justify it.
15. What if the student is expected to make an assumption?
Not every question with missing details is badly written.
Some tasks intentionally require students to estimate, model or make reasonable assumptions.
For example:
Estimate how many litres of water a household uses in a week.
There may be no single exact answer.
But the task can still be meaningful.
The student can identify relevant variables:
Number of people.
Daily water use per person.
Laundry.
Cooking.
Cleaning.
Other household activities.
They can then build an estimate and explain the assumptions.
The educational objective is different from that of a standard calculation exercise.
The student is not expected to discover a hidden exact number.
They are expected to construct a reasonable model.
The distinction should be explicit:
An exact-answer task requires sufficient information to determine the answer.
An estimation task requires justified assumptions and an appropriate method.
Confusing these task types can make students think that every approximation is a failure or that every unsupported guess is acceptable.
Neither conclusion is correct.
16. A useful classroom question: What would we need to know?
Instead of immediately asking students to solve a problem, teachers can sometimes ask:
“What additional information would make this question solvable?”
Return to the rectangle with a perimeter of 40 centimetres.
What information would allow us to determine its area uniquely?
Knowing one side length would be sufficient.
For example, if one side measures 12 centimetres:
[
a+b=20
]
[
b=8
]
[
A=12\times8=96
]
Alternatively, knowing that the rectangle is a square would also be sufficient.
Then:
[
a=b=10
]
[
A=100
]
These are different additional conditions.
They lead to different specific answers.
This exercise teaches students to analyse the relationship between information and conclusion.
Instead of asking only:
“What formula should I use?”
They learn to ask:
“What exactly must be known for this formula to determine the requested quantity?”
That is a more transferable skill.
17. Can the student identify the smallest missing piece?
A more advanced version of the exercise asks students to identify a minimal sufficient addition.
For example:
A triangle has an area of 30 square centimetres. What is its height?
The area formula is:
[
A=\frac12 bh
]
Therefore:
[
30=\frac12 bh
]
Or:
[
bh=60
]
Without knowing the base, the height is not uniquely determined.
If the base is 10 centimetres:
[
h=6\text{ cm}
]
If the base is 12 centimetres:
[
h=5\text{ cm}
]
The student should recognise that knowing the corresponding base length would be sufficient to calculate the height.
This does not mean that the base is the only possible useful additional information.
Other geometric conditions might also determine the triangle.
But asking for a sufficient missing condition helps students understand the structure of the problem rather than merely identify an absent number.
18. Why guessing sometimes receives more approval than recognising uncertainty
Imagine a classroom where every question is followed by an expectation of an immediate answer.
A student who gives a number appears active.
A student who says:
“There isn’t enough information.”
may appear hesitant or unprepared.
If the teacher has not deliberately included underdetermined problems in the learning process, the second response may be treated as avoidance.
But a justified statement of insufficiency can be the most accurate answer.
The distinction lies in the explanation.
Compare:
“I don’t know.”
with:
“The perimeter determines the sum of the two side lengths, but not their individual values. Since the area depends on their product, the area cannot be uniquely calculated.”
The second response demonstrates substantial mathematical understanding.
It identifies what is known, what remains unknown and why the missing information matters.
A teacher can evaluate that reasoning even though no single numerical answer is produced.
The educational goal should not be to reward refusal to solve problems.
It should be to reward accurate analysis of what the problem permits.
19. How to teach this without making students afraid to answer
There is a potential danger in emphasising missing information too strongly.
Students may begin responding:
“There isn’t enough information.”
to every difficult question.
That would not represent improved reasoning.
It would simply replace one automatic response with another.
The solution is to require justification.
A student claiming insufficient information should be able to demonstrate it.
For example, they can construct two different cases that satisfy all the given conditions but produce different requested answers.
For the rectangle problem:
- A 10 × 10 rectangle has a perimeter of 40 and an area of 100.
- A 12 × 8 rectangle has a perimeter of 40 and an area of 96.
Both satisfy the stated condition.
Therefore, the area is not uniquely determined.
This is a constructive demonstration.
The student is not merely expressing uncertainty.
They are showing why uniqueness fails.
In mathematics, this can be a powerful way to establish that the given conditions do not determine one answer.
20. A practical method: Four questions before calculating
Students do not need a complicated checklist for every exercise.
But four questions can help when a task appears unclear.
1. What is actually given?
Identify the explicit facts and conditions.
Do not silently add information.
2. What exactly is being requested?
Is the task asking for one example, all solutions, a unique value, an estimate or an explanation?
3. Can different situations satisfy the given conditions?
If two valid situations produce different requested answers, the information does not determine a unique answer.
4. What additional condition would resolve the uncertainty?
Identify the missing relationship, value or restriction.
These questions help students distinguish a solvable task from an incomplete one.
They also reduce the temptation to select a familiar operation merely because numbers appear in the question.
21. The role of language in mathematics and science education
For students learning academic subjects in a second language, the problem can become more complicated.
They may understand the mathematical concept but misinterpret a condition expressed in English, German or another language.
For example:
At least three students.
Exactly three students.
No more than three students.
These expressions describe different restrictions.
“At least three” means three or more.
“Exactly three” means precisely three.
“No more than three” means three or fewer.
If a student treats them as equivalent, the resulting error may appear mathematical even though its source is linguistic.
Similarly, words such as possible, necessary, sufficient, unique, approximately and assuming have important functions in academic questions.
Understanding them is not an optional addition to the subject.
It is part of understanding the conditions under which a conclusion can be drawn.
This is why language and subject knowledge should sometimes be developed together.
Levitin Language School works with this intersection through language learning combined with school subjects, including subject support in different instructional languages.
22. What parents can do when a child keeps calculating without understanding the question
A parent sees their child struggling with homework.
The child has written several formulas and crossed out multiple answers.
The parent asks:
“Why don’t you just use the formula?”
But the student may already know the formula.
What they lack is a clear understanding of whether the conditions allow it to determine the requested answer.
A more useful conversation might begin with:
“What do we know for certain?”
“What are we trying to find?”
“Could there be two different answers that both fit the question?”
“What would we need to know to choose between them?”
These questions do not require the parent to solve the entire exercise.
They help the child examine the structure of the task.
However, the goal should not be to turn every homework problem into an extended interrogation.
Sometimes a student simply needs to practise a straightforward calculation.
The deeper questions are most useful when the child repeatedly applies formulas without understanding the conditions, or when a problem genuinely permits multiple interpretations.
23. The same principle applies outside school
A company reports that sales increased after launching a new website.
Did the website cause the increase?
Perhaps.
But the increase may also be related to seasonal demand, pricing, distribution or other changes.
A person receives a higher salary than another employee.
Does that prove they work more hours?
No.
Salary may depend on many other factors.
A language learner receives a low test score.
Does that prove they cannot communicate effectively?
Not necessarily.
The assessment may measure specific skills under particular conditions.
These examples share the same reasoning problem:
A result may be known while the information needed to explain it remains incomplete.
Recognising that gap is not an obstacle to making decisions.
It is a way of making decisions more responsibly.
Sometimes the correct next step is to calculate.
Sometimes it is to investigate.
Sometimes it is to clarify the question.
And sometimes it is to acknowledge that more than one explanation remains possible.
24. The difference between a difficult problem and an impossible demand
A problem may be difficult because the student has not yet learned the necessary method.
It may be difficult because the solution requires several connected steps.
It may be difficult because the wording is unfamiliar.
But a question can also be impossible to answer uniquely from the information supplied.
These are different situations.
When teachers, parents and students fail to distinguish them, they may waste time trying to repair the wrong thing.
A student who needs a formula should learn the formula.
A student who struggles to connect several steps should practise the relationships between them.
A student who misreads the conditions needs help interpreting the language.
And a student facing an underdetermined problem should learn to identify what cannot be concluded.
In our German article, Warum Schüler alle Teilaufgaben lösen und trotzdem den Zusammenhang verlieren, we examined why completing individual steps does not always produce a coherent solution.
The present issue is different.
Even a perfectly connected sequence of calculations cannot establish a unique answer if the necessary information is absent.
25. Learning to say “We cannot determine that” — and explain why
There is an important difference between giving up and recognising a limitation.
“I can’t solve it” describes the student’s present ability.
“It cannot be uniquely determined from the given conditions” describes the structure of the problem.
The first statement may lead to more instruction or practice.
The second requires a mathematical or logical justification.
A student who can explain the second statement may understand the problem more deeply than someone who confidently invents a number.
This is especially important in a world where information is abundant and answers can be generated instantly.
Producing an answer is not always the difficult part.
Determining whether the answer is supported by the available information may be much harder.
And sometimes that is precisely the skill education needs to develop.
Conclusion: A good problem solver knows when not to calculate
The rectangle with a perimeter of 40 centimetres did not require a more complicated formula.
It required a different question:
Do the conditions determine one area?
Once that question is asked, the structure becomes clear.
The perimeter determines the sum of the side lengths.
It does not uniquely determine their product.
Therefore, the area cannot be identified as one exact value without additional information.
The student who recognises this has not failed to solve the problem.
They have identified what the problem actually allows them to know.
That distinction is fundamental to mathematics, science, language comprehension and real-world decision-making.
Learning should not train students to produce a number whenever a question contains numbers.
It should train them to understand the relationship between information, assumptions, methods and conclusions.
Because sometimes the most intelligent answer is not a calculation.
It is a precise explanation of why the calculation cannot yet be justified.
Individual Online Learning at Levitin Language School
Students may struggle with school subjects for very different reasons: missing foundational knowledge, unfamiliar academic language, difficulty selecting a method, or uncertainty about how to interpret the conditions of a problem.
These difficulties should not automatically be treated as the same learning problem.
Levitin Language School offers individual online education for children, teenagers and adults, including:
- Languages: individual foreign-language learning for practical communication, education and everyday life.
- Academic Subjects: individual support in mathematics, science and other available school subjects.
- Language + Subject: learning academic subjects through English, German or other supported instructional languages.
Teaching arrangements depend on the student’s goals, level, subject, language of instruction and the availability of a suitable teacher.
Before starting, we clarify the learning needs, schedule, teacher arrangements and price through written communication. We do not offer free trial lessons or free diagnostic consultations.
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Author: Tymur Levitin
Founder and Director, Levitin Language School
© Tymur Levitin. All rights reserved.
