Sometimes we find a solution.

And the strange thing is:

the problem remains.

Or it disappears for a while, then comes back in another form.

That is something I have been thinking about a lot in education.

A child gets a question wrong.

We explain it.

The child understands.

They do the next question correctly.

Problem solved.

Except perhaps it isn’t.

Because tomorrow, the same mistake appears again.

Or the question changes slightly and the child is lost.

Or the method works beautifully in Mathematics class but disappears inside a word problem.

So perhaps one of the difficulties in education is that we can mistake:

a successful correction

for

a completed repair.

Those are not always the same thing.

We Like Solutions Because They Give Us Closure

There is something satisfying about solving a problem.

Wrong answer.

Explain.

Correct answer.

Done.

It fits nicely into the way we organise school.

Topic.

Lesson.

Worksheet.

Answer.

Mark.

Next topic.

But learning is not always that tidy.

Sometimes a solution only changes what we can see.

The underlying weakness remains underneath.

A student forgets to convert centimetres to metres.

We remind them.

Correct.

Later, the student forgets again.

So we create a rule:

Always check the units.

That helps.

But perhaps the real problem was never the unit conversion.

Perhaps the learner does not yet habitually inspect what a question is asking before calculating.

That is a different problem.

The rule fixes an instance.

The habit would fix a class of problems.

That distinction matters.

A Solution Can Work Locally

Suppose a child cannot answer:

3/4 + 1/8

We show them how to find a common denominator.

They follow the steps.

They get the answer.

Success.

Then we change the numbers:

5/6 + 1/4

Now they struggle again.

We might explain the same method once more.

And perhaps that is exactly what is needed.

But another possibility is that the learner has memorised a procedure without constructing the relationship underneath it.

The solution worked here:

3/4 + 1/8
↓
method supplied
↓
correct answer

But it did not travel:

new problem
↓
recognise structure
↓
select method independently
↓
solve

That is the difference between a local solution and a transferable capability.

And education needs both.

The immediate problem must often be solved.

But eventually, the learner needs something that survives beyond the original question.

Sometimes We Keep Adding Solutions

This is where things can become strange.

A student has difficulty.

So we add support.

More explanation.

More worksheets.

More tuition.

More revision.

More model answers.

More notes.

More practice papers.

More techniques.

Each one may be a perfectly reasonable solution.

But eventually we can create another problem:

too many solutions.

The learner now has five methods.

Three sets of notes.

Two tuition teachers.

A school worksheet.

An assessment book.

A parent explaining another shortcut.

And perhaps nobody knows which representation the child is actually using.

We intended to create clarity.

We created traffic.

This is why more help is not automatically better help.

Sometimes the most useful intervention is not to add another method.

It is to remove confusion.

The Solution Can Become Part of the Problem

Transport gives us a useful analogy.

A car can solve one problem: moving farther than walking easily allows.

Widespread driving can also create congestion.

Road capacity can be expanded to relieve some of that congestion.

Yet added capacity can sometimes attract more driving.

The new environment may then need traffic management.

Parking becomes another design problem.

Public transport has to fit into the same wider network.

The original solution was not necessarily wrong.

It changed the system.

And the changed system produced new problems.

Education can behave similarly.

Examinations solve a real problem.

We need some way to assess what students know.

Then examinations become important.

So students practise for examinations.

That is reasonable.

Then examination performance becomes increasingly important.

So we create more practice papers.

Repeated practice can make familiar examination structures increasingly manageable.

Now we have another question:

Can they still reason when the structure changes?

Again, the examination was not necessarily the problem.

The difficulty is that solutions alter the environment in which the next problem appears.

Tuition Can Do This Too

This is uncomfortable for someone who teaches tuition to say, but I think it is important.

Tuition is itself a solution.

A child needs more help.

We provide another teacher, another environment, more time and more feedback.

That can be extremely useful.

But tuition can also create secondary problems if we are careless.

A student may become dependent on being pre-taught everything.

The child may stop struggling productively because someone always provides the next step.

A student may begin believing school lessons are optional because tuition will explain them later.

A child may become excellent at following a tutor’s method but weak at choosing a method independently.

Or tuition simply adds more hours of work to a child who was already overloaded.

The solution is real.

So is the possibility of unintended consequences.

That means the question cannot simply be:

Does tuition help?

We also have to ask:

What kind of help is it creating?

Repair Should Reduce Dependency

I think this is one of the most useful tests of teaching.

Good repair should eventually make itself less necessary.

At the beginning, the tutor may need to provide a lot.

SHOW
↓
EXPLAIN
↓
GUIDE
↓
CORRECT

Then, gradually:

PROMPT
↓
WAIT
↓
LET THE STUDENT RECONSTRUCT

Later:

STUDENT ATTEMPTS
↓
STUDENT CHECKS
↓
STUDENT CORRECTS

And eventually:

STUDENT NAVIGATES

If the learner becomes permanently dependent on the teacher, something is wrong.

The purpose of support is not to make support permanent.

It is to build capability.

That is why I think independence matters so much.

Not independence as:

You are on your own.

But independence as:

You can now carry more of the work yourself.

Some Solutions Hide the Signal

Another difficulty is that a solution can make the immediate problem disappear so effectively that we stop seeing what caused it.

Imagine a student who struggles badly with Science explanations.

We give them a model answer.

They memorise it.

Their marks improve.

That is useful.

But now we have to be careful.

Have we improved their scientific understanding?

Their language?

Their ability to identify causal relationships?

Their ability to construct an explanation?

Or have we supplied a very good external structure that temporarily carries all four?

Those are different outcomes.

Again, there is nothing inherently wrong with model answers.

They are valuable examples.

But if the solution hides the missing capability, we may stop repairing the thing that mattered.

The score goes up.

The underlying learner may not have changed very much.

Sometimes the Correct Solution Is Temporary

This is another complication.

A temporary solution is not necessarily a bad solution.

If an examination is two weeks away and a student has serious gaps, we may need to prioritise.

There may not be time to rebuild everything from first principles.

We might create a narrower strategy.

Stabilise the most important topics.

Reduce repeated mistakes.

Teach checking routines.

Protect marks.

That can be exactly the right decision.

But then we should know what we have done.

We have solved:

the immediate examination problem.

We may not have solved:

the underlying learning problem.

Those two should not be confused.

After the examination, the repair may need to continue.

This is where time changes what counts as a good solution.

The Same Child Can Need Different Solutions at Different Times

A learner who is completely lost may need direct explanation.

A learner who understands but is unstable may need repetition.

A learner who is stable may need variation.

A learner who can solve familiar problems may need transfer.

A learner who already transfers well may need harder problems and greater independence.

So even a very good solution can become a bad one if we keep using it after the learner has changed.

This is something teaching has to keep noticing.

The question is not only:

Did this method work?

It is also:

Is this still the method this learner needs?

That is a much harder question.

Education Has Many Established Solutions

Singapore education contains many established structures intended to solve real problems.

Structured curricula.

Clear standards.

National examinations.

Teacher training.

School pathways.

Support programmes.

Technology.

Tuition.

Assessment.

Practice.

These are not foolish inventions waiting to be removed.

Many solve real problems.

But even a useful solution needs us to keep asking what it produces next.

Because once a solution becomes large enough, it becomes part of the environment.

And then new behaviour forms around it.

Students adapt.

Parents adapt.

Schools adapt.

Tuition centres adapt.

The wider ecosystem can begin adapting around the solution.

At that point, we need to look again.

Not because the original solution failed.

But because the world after the solution is different from the world before it.

This Is Why Diagnosis Cannot Stop

In the previous article, I wrote about finding where the learner actually is.

I think the same principle applies here.

We diagnose a problem.

We intervene.

Then we have to look again.

PROBLEM
↓
SOLUTION
↓
NEW STATE
↓
OBSERVE AGAIN

Not:

PROBLEM
↓
SOLUTION
↓
DONE

What happens after the intervention matters.

Did the child improve?

Did the improvement survive?

Did something else become weaker?

Did dependency increase?

Did confidence improve?

Can the student perform without the support?

Can the capability travel?

What new difficulty is now visible?

A solution changes the learner.

And after the learner changes, we need a new reading of the situation.

Perhaps Teaching Is Closer to Steering Than Repair

I sometimes use repair language because it is useful.

Something is missing.

Find it.

Fix it.

Retest.

Repair language has limits.

They continue changing while we teach them.

So perhaps another useful image is steering.

You look at where you are.

Choose a direction.

Move.

Observe what happened.

Correct.

Move again.

STATE
↓
ACTION
↓
RESULT
↓
NEW STATE
↓
NEW ACTION

You do not choose the entire route once at Primary 1 and blindly follow it until Secondary 4.

You keep navigating.

That is also why I like the word Voyage.

A voyage has a destination.

But it also has weather.

Currents.

Unexpected conditions.

Corrections.

Detours.

Different speeds.

And a traveller who is not the same person at the end as at the beginning.

So What Is a Better Solution?

I don’t think the answer is to become suspicious of every intervention.

That would be paralysing.

We need solutions.

Children need explanations.

Practice matters.

Examinations matter.

Tuition can matter.

The better question is:

What does this solution create after it succeeds?

Does it create understanding?

Dependence?

Speed?

Transfer?

Confidence?

Overload?

A stronger foundation?

A hidden weakness?

A new possibility?

The answer may be several of these at once.

Good teaching has to notice the second-order effects.

Why Tuition, Then?

For me, this becomes another reason small-group tuition can be valuable.

Not because we possess a perfect solution.

We don’t.

But a small teaching environment gives us a chance to observe what happens after a solution is applied.

Explain.

Watch.

Change the problem.

Return later.

Remove the prompt.

Ask the student to explain.

See whether the repair survived.

That feedback loop matters.

DIAGNOSE
↓
TEACH
↓
PRACTISE
↓
OBSERVE
↓
RETEST
↓
ADJUST

The solution is not the end of the loop.

It is one event inside it.

Maybe That Is the Real Problem With Solutions

Solutions feel final.

Learning rarely is.

The child who could not do fractions eventually learns fractions.

Good.

Now fractions become part of algebra.

The reader learns to decode words.

Good.

Now those words become part of arguments, inference and judgement.

The Science student learns a model.

Good.

Later, the model meets exceptions.

Every solved problem changes what the learner is capable of seeing next.

So perhaps education should not aim to produce a world with no problems.

That would be impossible.

Perhaps good education creates learners who can meet increasingly difficult problems without collapsing.

That is a very different ambition.

And it changes the question from:

Did we solve today’s problem?

to:

What did today’s solution make the learner capable of doing tomorrow?

I think that question is much closer to what teaching is really for.