You Can Know the Answer and Still Not Understand the Question

Why studying mathematics in another language is not always a mathematics problem

A student knows how to solve equations.

They understand percentages.

Functions make sense.

Geometry is familiar.

Then the family moves to Germany.

The mathematics lesson begins.

The teacher gives the student a problem.

And suddenly, the student cannot solve it.

What happened?

Did their mathematical ability disappear during the move?

Of course not.

Perhaps the real problem is much simpler.

The student knows the mathematics.

They do not yet know what the question is asking them to do.

A Formula Can Be Universal. An Assignment Is Not.

We often say that mathematics is an international language.

In one sense, this is true.

Numbers remain numbers.

A triangle remains a triangle.

An equation does not change because you crossed a border.

But mathematics at school is not made only of numbers and formulas.

It is also made of instructions.

Berechne.

Bestimme.

Begründe.

Zeige.

Vergleiche.

Erläutere.

Weise nach.

A student may understand every number on the page and still fail to understand what kind of intellectual action is expected.

Calculate?

Determine?

Explain?

Justify?

Prove?

Compare?

The mathematics may be familiar.

The task is not.

Knowing How to Solve Something Is Different From Knowing What You Have Been Asked to Solve

This distinction can easily disappear in a classroom.

A teacher sees a student sitting silently in front of an exercise.

The student does not begin.

Perhaps they write something irrelevant.

Perhaps they solve only part of the problem.

Perhaps they give the correct result but do not provide the explanation expected.

From the outside, this can look like weak mathematics.

But before concluding that the student does not understand the subject, we should ask another question:

Did the student understand the mathematical problem—or only fail to understand the language surrounding it?

These are completely different difficulties.

And they require completely different solutions.

Mathematical Vocabulary Is Only the First Layer

When people think about learning mathematics in German, they often imagine terminology.

die Gleichung — equation

die Funktion — function

die Quadratwurzel — square root

der Prozentsatz — percentage

die Wahrscheinlichkeit — probability

These words matter.

But knowing the nouns is not enough.

A student also needs to understand how mathematics is done through language.

What is the difference between:

Berechne den Wert.

and:

Bestimme den Wert.

What changes when the task says:

Begründe deine Antwort.

What must be added when the student is asked:

Erläutere deinen Lösungsweg.

A student may arrive at the same mathematical result in every case.

But the required response is not necessarily the same.

This is where language begins influencing academic performance.

The Correct Answer May Not Be the Complete Answer

Suppose a student calculates correctly.

The answer is 25%.

Mathematically, they are right.

But the assignment did not ask only for the result.

It asked them to justify it.

The student writes:

25 %.

The teacher gives partial credit.

Did the student fail at mathematics?

Perhaps not.

They may have failed to recognize the communicative requirement of the task.

This matters because school mathematics evaluates more than calculation.

Students may need to:

describe a process,

explain a relationship,

justify a conclusion,

interpret a graph,

compare two methods,

or demonstrate why an answer is correct.

The mathematical knowledge and the language used to demonstrate that knowledge become intertwined.

Migration Can Make a Strong Student Look Weak

This is one of the most dangerous effects of changing educational systems.

A child may have been strong in mathematics before moving.

Then they enter a German-speaking school.

Their grades fall.

They need more time.

They misunderstand assignments.

They stop raising their hand.

Soon, everyone begins focusing on the mathematics.

Perhaps the student even begins believing:

I am no longer good at math.

But the mathematics may never have been the main problem.

The student has lost immediate access to the language through which their mathematical ability must now become visible.

That can create an artificial academic weakness.

The knowledge is still there.

The route to demonstrating it has changed.

Translating Every Word Does Not Always Solve the Problem

There is another complication.

A student can translate an assignment and still misunderstand what is expected.

Why?

Because educational language is not simply ordinary language with difficult words.

Certain verbs function as instructions.

They tell the student what kind of answer counts as successful.

If the learner translates:

begründen

simply as:

explain

they may miss the expectation that a claim must be supported with reasons.

If several instruction verbs are translated into approximately the same word in another language, the student may understand the general topic while missing the exact task.

This is why bilingual support can help—but literal translation alone may not be enough.

The student needs to learn the logic of the instruction.

There Are Actually Two Problems on the Page

When a student solves mathematics in another language, they may be solving two problems simultaneously.

The visible problem is mathematical.

The invisible problem is linguistic.

First:

What does this instruction require?

Then:

How do I solve the mathematical problem?

Then perhaps a third:

How do I express my solution in the form expected here?

For a native-speaking student, much of the linguistic layer may happen automatically.

For a newcomer, it consumes attention.

This means the same exercise can require significantly more cognitive effort from two students with identical mathematical ability.

One is solving the mathematics.

The other is solving the language and the mathematics at the same time.

The Student May Need German Support, Not Easier Mathematics

This distinction has practical consequences.

Suppose a teenager already understands algebra well but struggles with German assignments.

One possible response is to simplify the mathematics.

But perhaps that is exactly the wrong intervention.

The student does not need easier equations.

They need access to the equations they are already capable of solving.

That may mean learning:

mathematical terminology,

instruction verbs,

the language of explanation,

the structure of written solutions,

the vocabulary of graphs and functions,

and the phrases used in German-speaking classrooms.

The subject level can remain intellectually appropriate.

The linguistic barrier can be addressed separately.

Sometimes Mathematics Can Become the Place Where German Starts Making Sense

There is also another side to this.

The same subject that creates difficulty can become a bridge.

A student may feel uncertain in ordinary German conversation but completely understand the mathematical logic in front of them.

That familiarity gives the language context.

die Gleichung lösen

is easier to remember when you are actually solving an equation.

durch drei teilen

becomes meaningful while dividing by three.

die Funktion steigt

is no longer an isolated vocabulary phrase when you can see the graph.

The mathematical concept anchors the German.

The student does not need to imagine what the language means.

They already know.

This is why learning mathematics through German can work in both directions.

German gives the student access to mathematics in the new educational environment.

Mathematics gives the student a familiar structure through which German can develop.

We Should Be Careful What We Measure

When a student performs poorly in a subject taught through a new language, the result may reflect several things at once.

Subject knowledge.

Language proficiency.

Understanding of instructions.

Familiarity with the educational system.

Ability to explain reasoning.

Speed of reading.

Confidence.

These factors interact.

A grade may look like one number.

The problem behind it may not be one problem.

That is why the first question should not always be:

Why doesn't this student understand mathematics?

Sometimes the better question is:

At what exact point does their understanding stop becoming visible?

Perhaps they do not understand the concept.

Then we teach the concept.

Perhaps they understand the concept but not the terminology.

Then we teach the terminology.

Perhaps they understand both but misread the instruction.

Then we teach the language of tasks.

Perhaps they can solve the problem but cannot explain the solution.

Then we build the language needed to demonstrate mathematical thinking.

Different obstacles require different teaching.

Mathematics Does Not Disappear When the Language Changes

A student who knew mathematics yesterday does not become mathematically empty because today's textbook is written in German.

Their knowledge travels with them.

But access to that knowledge can become temporarily blocked.

The task of education should be to identify the blockage.

Not automatically lower expectations.

Not assume that silence means ignorance.

Not confuse unfamiliar language with unfamiliar mathematics.

Sometimes the student already knows the answer.

The first thing they need is simply to understand the question.

And once that door opens, we may discover that the mathematics was there all along.

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About the Author

Tymur Levitin
Founder & Director, Levitin Language School
Language educator, teacher and author writing about language, thinking, learning and human communication.

© Tymur Levitin. All rights reserved.

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