Retrospect | Tuition | RFE | Help
There is a very satisfying moment in tuition.
A student gets a question wrong.
We look at it.
Find the mistake.
Correct the working.
Write the right answer.
Done.
The page is clean again.
Sometimes I put a tick beside it.
And visually, everything looks repaired.
Wrong answer.
Correction.
Right answer.
Except I have become suspicious of that tick.
Because the paper may have been corrected.
I am not yet sure the student has been.
Those are different things.
A Correction Can Make the Evidence Disappear
Imagine a student writes:
3(x+2)=3x+2
Wrong.
I point it out.
The student says:
“Oh.”
They erase the 2.
Replace it with 6.
Now:
3(x+2)=3x+6
Correct.
Very good.
But what exactly happened?
Did the student understand why the 3 has to multiply both terms?
Did they remember a rule after being reminded?
Did they merely recognise from my face that something was wrong?
Did they copy the correction because I showed it?
Would the same error return five minutes later?
Tomorrow?
Inside a more complicated equation?
The corrected line cannot answer those questions.
In fact, once the correction is written, something slightly inconvenient happens.
The visible error disappears.
And the thing I most need to understand may disappear with it.
I Think We Sometimes Correct Too Quickly
Teachers need to correct work.
Tutors need to correct work.
Students need to know what is right.
I am not arguing against correction.
But perhaps there is a moment before correction that deserves more attention.
The moment when the error is still alive.
Why did you do that?
What were you expecting to happen?
Which rule were you using?
Where did this method come from?
Sometimes the student immediately sees it.
Sometimes they cannot explain it at all.
Sometimes they confidently explain a completely wrong model.
That is useful.
Because now I am not merely looking at a wrong answer.
I am looking at the machinery that produced it.
And that machinery is what I actually need to repair.
The Same Wrong Answer Can Come From Different Places
Three students can write the same wrong answer.
That does not mean they have the same problem.
Student A never learnt the rule.
Student B learnt it but forgot it.
Student C knows the rule perfectly but misread the expression.
Same red cross.
Different repair.
Student A needs teaching.
Student B may need retrieval.
Student C may need slower interpretation or a checking habit.
If I simply write the correct solution beside all three, all three pages improve.
But only one of the three learners may have received the help they actually needed.
That is the problem.
The correction belongs to the answer. The repair belongs to the cause.
I think that distinction is worth keeping.
This Happens in English Too
A student writes a sentence with a grammatical error.
I correct it.
Good.
But perhaps the student does not know why the correction is right.
They just replace one word with mine.
The composition improves.
The writer may not.
Or a comprehension answer misses the inference.
We discuss it.
The student writes the model answer.
Beautiful.
But when the next passage requires the same inferential move in a completely different context, the student misses it again.
So what did the earlier correction accomplish?
Something.
They saw a correct answer.
They may have learnt from it.
But we need another event before we can confidently call the problem repaired.
The student has to meet the idea again.
Without the answer sitting beside it.
This May Be Why Some Exercise Books Look Better Than the Student Feels
I have seen very tidy corrections.
Green pen.
Red pen.
Arrows.
Rewritten answers.
Corrections completed underneath.
Everything looks responsible.
And yet the student says:
“I still don’t understand.”
That sentence used to feel contradictory.
How can you have corrected everything and still not understand?
Now it makes more sense.
Correction is an activity.
Understanding is a state.
The first does not guarantee the second.
A student can complete the physical procedure of correction while the original representation remains unchanged.
That means the next error is already waiting.
Perhaps the Useful Question Is Not “Have You Corrected It?”
Parents ask this quite reasonably.
“Did you correct your mistakes?”
Teachers ask it.
Tutors ask it.
Students learn to answer:
“Yes.”
Perhaps there is a slightly better question.
“Can you do one like it now?”
That question changes the standard.
The goal is no longer a completed correction.
The goal is a changed capability.
If the student can solve a fresh version independently, excellent.
If they cannot, the correction gave us information but the repair is unfinished.
That is not a disaster.
It simply tells us where we still are.
A Fresh Question Is Like Asking Reality to Check Our Work
This is where I think the RFE test becomes very simple.
We believe we repaired the problem.
Fine.
Do not argue about it.
Ask reality.
Take away the old question.
Change the numbers.
Change the wording.
Perhaps change the context.
Give the student another attempt.
What happens?
If the old error returns immediately, then our repair did not survive.
Maybe the explanation was insufficient.
Maybe the student copied rather than reconstructed.
Maybe the problem was somewhere else.
Good.
Now we know.
If the error does not return, that is stronger evidence.
Not perfect proof.
But better evidence.
One Correct Retest Can Still Be Too Easy
There is another trap here.
A student gets the next question right.
Excellent.
Problem solved?
Maybe.
But perhaps the new question looked almost identical.
The student may simply have copied the surface pattern.
So sometimes I want another layer.
Can they do it when the numbers change?
When the wording changes?
When it appears later?
When it is mixed among unrelated questions?
When nobody tells them which method is needed?
This is not necessary for every tiny error.
We would never finish the syllabus.
But for errors that keep returning, the distinction matters.
A repair should survive some distance from the original correction.
Repeated Errors Are Particularly Interesting
There are mistakes I see once.
Fine.
Humans make mistakes.
Then there are mistakes that return.
Again.
And again.
And again.
Those deserve respect.
Because a recurring error is telling us something.
It may be saying:
You have been correcting the output, but the generating rule is still here.
That is different from carelessness in the casual sense.
There may be a stable wrong model underneath.
Or a missing retrieval route.
Or an overloaded procedure.
Or a decision rule that consistently chooses the wrong option.
The recurrence is evidence.
Instead of becoming annoyed that:
“I already explained this!”
perhaps the return of the error should make me curious.
Apparently the previous explanation did not change what I thought it changed.
That is useful information about my teaching too.
“I Already Taught You This” Is Not Much of a Diagnosis
I think every teacher has felt this.
We taught it.
We practised it.
The student corrected it.
Then they get it wrong again.
There is a temptation to say:
“But we did this last week.”
True.
But history does not solve the present problem.
The fact that teaching occurred is not evidence that learning survived.
It tells me an input happened.
Now I need to inspect the output.
Perhaps the student never understood it.
Perhaps they understood and forgot.
Perhaps they can perform it in isolation but cannot recognise when it applies.
These produce different next lessons.
So:
“We already covered this.”
may be administratively true.
Educationally, it does not tell us very much.
Sometimes the Correction Itself Is Too Large
Suppose a student gets a difficult problem wrong.
I show the full solution.
Eight steps.
The student copies all eight.
Now their page contains a beautiful solution.
But perhaps only Step 3 was actually broken.
The remaining seven steps were already within their capability.
By replacing the entire solution, we may hide the exact location of the failure.
This links back to something I keep returning to in tuition.
A child rarely needs help everywhere.
They need help somewhere.
Corrections should probably respect that too.
Repair the smallest thing that restores the route.
Then let the student continue.
Otherwise my correction can become another form of over-helping.
Three Students Make This Very Obvious
Imagine three students have the same wrong answer.
I could stand at the whiteboard and solve the entire question for everybody.
Efficient.
But perhaps Student A needs Step 2 explained.
Student B made a calculation slip in Step 6.
Student C used the wrong strategy from the beginning.
One model correction cannot possibly perform all three repairs equally well.
This is where small-group tuition becomes quite revealing.
I can ask one student:
“Show me why you chose this.”
Another:
“Where did your working first change from the answer key?”
Another:
“Can you redo just this line?”
The correction becomes diagnostic.
Not merely cosmetic.
There Is Also an Emotional Difference
A page full of red crosses can feel awful.
Corrections can restore order.
That matters.
Children should not be left staring at an unexplained landscape of failure.
But I think precise repair can also change the emotional meaning of mistakes.
Instead of:
“I got ten questions wrong.”
perhaps we discover:
“Seven of those came from the same rule.”
That is a much smaller problem.
Ten red crosses may not represent ten weaknesses.
They may represent one weakness appearing ten times.
That is good news disguised as bad marking.
Because one repair may remove many future errors.
This Is Why Error Counting Can Mislead Us
A child makes twelve mistakes.
Another makes five.
It is tempting to assume the first child has the bigger problem.
Not necessarily.
The twelve mistakes may all come from one narrow misconception.
The five may come from five unrelated gaps.
Again:
visible quantity is not diagnosis.
What matters is the structure underneath.
Sometimes many errors collapse into one cause.
Sometimes one wrong answer reveals something much larger.
We need enough curiosity to find out.
Parents Can Use This Without Turning the Kitchen Into a Classroom
I do not think parents need to analyse every mathematical error after dinner.
That would not improve family life.
The home version can be very small.
When a child has corrected something important, ask:
“Do you think you could do another one without looking?”
If yes, wonderful.
Try one when appropriate.
If no, the child has already told us something useful.
The correction is not finished as learning.
That is enough information to bring back to the tutor or teacher.
No lecture required.
No twenty extra questions.
Just a clearer location.
The Tutor’s Job Is Not to Produce Perfect Pages
This may sound obvious.
But tuition can accidentally reward visible completion.
Finish the worksheet.
Correct the errors.
Write the model answer.
Move on.
At the end of the lesson, everything is neat.
Parents understandably like seeing completed work.
I like completed work too.
But if I have to choose between:
a beautiful completed page with a hidden unresolved misconception
and
a messy page where we have identified and genuinely repaired one important mistake,
I think the second lesson may have done more.
The paper is not the final product.
The learner is.
So When Is a Mistake Repaired?
Perhaps not when the red cross disappears.
Not when the model answer has been copied.
Not even when the student says:
“Oh, I understand now.”
Those are useful moments.
But I want something slightly stronger.
The student encounters the same underlying demand again.
And the old failure does not return.
That is much closer.
Perhaps later it returns under pressure.
Fine.
Then we learn something else.
Maybe the capability exists but is not yet robust.
Repair can have levels.
First:
understand the correction.
Then:
reproduce it.
Then:
recognise it elsewhere.
Then:
use it reliably.
That seems more realistic than pretending a single corrected line permanently solved everything.
Mistakes Can Become Very Good Teachers If We Let Them Finish Their Job
I used to think the main purpose of correction was to remove wrongness.
Wrong answer becomes right answer.
Now I think that is only half the job.
The mistake has information inside it.
Where did the learner’s model diverge from reality?
What did they believe?
What did they overlook?
What could they do already?
What was the smallest missing thing?
If we extract that information, the error becomes useful.
If we simply overwrite it, perhaps we lose some of the lesson.
So I do not want students to worship mistakes.
Some mistakes are just mistakes.
We do not need philosophical reflection every time 7 × 8 becomes 54.
But when an error returns, or when it reveals an important misunderstanding, I think it deserves more than an eraser.
It deserves investigation.
Perhaps the Tick Should Come Later
The wrong answer is corrected.
Good.
But perhaps mentally I should hold back the final tick.
Not forever.
Just until something returns from the learner.
A fresh attempt.
A changed explanation.
A successful transfer.
Some evidence that the repair now belongs to them.
Because a corrected page tells me:
We know what the answer should have been.
A repaired mistake tells me something more valuable:
The learner is now less likely to produce the same failure again.
That is what I actually wanted.
So perhaps after the next correction, before we close the book, there is one small question worth asking:
Can you do one like it now—without looking back?
If the answer is yes, excellent.
If the answer is no, excellent too.
Not because failure is wonderful.
But because the mistake has not disappeared behind a neat correction.
It is still telling us where the learning needs to go next.
And that is much more useful than a clean page pretending the journey is finished.
eduKate Sengkang 