Shortcut or Skipped Step?

Before You Tell Your Child to Show More Steps

A mother recently told me something about her son that caught my attention.

He is bright. His IQ is above average. Teachers say that once he gets into his “focus zone”, he grasps things very quickly.

But getting him there can be difficult.

He may focus for only about twenty minutes. He needs coaxing to begin academic work. And when solving mathematics problems, he does not like writing down all his steps.

His mother added something else.

He often tries to shorten the solution.

That was the part that interested me.

Not because shortening a solution is necessarily clever.

And not because refusing to show working should automatically be accepted.

But because whenever a child removes steps from a solution, I want to know one thing before deciding whether to stop him:

What did he see that made those steps unnecessary to him?

A shortcut and a skipped step can look exactly the same on paper

Suppose the teacher expects five lines of working.

Your child writes two.

There are at least two very different possibilities.

In the first, the child does not really understand the missing three steps. He is rushing, guessing, or jumping from one thing to another without sufficient reasoning.

That is a problem.

But there is another possibility.

The child has mentally compressed several steps because he has noticed a relationship that makes them unnecessary.

That is thinking.

Unfortunately, when we look only at the amount of working on the page, both children can look identical.

Three missing lines.

That is why I hesitate whenever a parent tells me:

“He always wants to take shortcuts.”

My next question is not:

“Why doesn't he follow instructions?”

It is:

“When he takes the shortcut, is his reasoning sound?”

In this case, I would want to observe more

When I asked the mother whether her son's shortened methods were logically correct, she could not give me an affirmative answer.

And that matters.

There are already several things here that make me pay attention: he appears capable, he learns quickly once engaged, he dislikes writing down all his steps, and he prefers a shorter route.

These are behaviours I have seen in many Round Peg learners.

But the shortened working itself is not enough for me to conclude that he is seeing something deeper.

I would want to know:

When he removes those steps, has he genuinely seen a relationship that makes them unnecessary?

Or:

Has he simply skipped the reasoning because he does not want to write it?

That distinction matters.

If his reasoning is sound, the shortcut may reveal something very interesting about how he sees the problem.

If it is not, then this is an area where he needs support.

So I would not rush to either praise or correct the shortcut.

I would observe first.

Because before deciding what this behaviour means, I want to understand the thinking behind it.

Why some capable children dislike showing every step

Adults often see written workings as evidence of thinking.

Children do not necessarily experience them that way.

For some children, writing the steps helps them organise their thinking.

For others, the thinking has already happened.

They see:

A → B → C → D → E.

But mentally, they may experience:

A → E.

Ask them to write B, C and D and they genuinely wonder:

“Why?”

This does not mean we should tell them:

“You're clever, so you never need to show your working.”

Quite the opposite.

If a child can see something others cannot, there is an additional ability I want that child to develop:

What is obvious to you may be invisible to everyone else. Learn to show them what you saw.

That is a very different conversation from:

“Do it this way because the teacher said so.”

One suppresses thinking.

The other extends it.

What this can look like in real life

Let me give a concrete example of what I mean.

Suppose the child is given this question:

31 × 26 − ? × 13 = 19 × 26

A conventional approach would be to calculate:

31 × 26 = 806

19 × 26 = 494

806 − 494 = 312

312 ÷ 13 = 24

So the answer is:

24

This is a perfectly valid method.

And because it is clear, sequential and easy to verify, it is also the kind of method a teacher may naturally expect to see.

But now imagine another child looks at exactly the same question and says:

“24.”

You ask:

“How did you get 24?”

He replies:

“I just know.”

That answer can be frustrating.

To an adult, it can sound like guessing.

To a teacher, especially in a busy classroom, it may seem to confirm why the child needs to stop taking shortcuts and use the conventional method.

And if the child himself cannot explain what he has done, it is understandable that the teacher may not be able to see his route either.

But this is precisely the moment when I would want to probe a little further.

“I just know” may not be the end of the thinking

Suppose you continue asking.

Not:

“Do it again properly.”

But:

“What did you see?”

The child still struggles.

You ask again.

Eventually, the best he can tell you is:

“62 − 24 = 38.”

Now something interesting has appeared.

Where did 62 come from?

Where did 38 come from?

The original question was:

31 × 26 − ? × 13 = 19 × 26

Yet somewhere in the child's thinking, 31 has become 62 and 19 has become 38.

The child may not be able to tell you why.

He may not be able to explain that:

26 is twice 13.

He may not be able to articulate that:

31 × 26 can therefore be seen as 62 × 13

and

19 × 26 can be seen as 38 × 13.

So the original question can be re-seen as:

62 × 13 − ? × 13 = 38 × 13

and once the common 13 is recognised, the structure reduces to:

62 − ? = 38

which gives:

? = 24

The child may have seen some or all of this.

But he may not yet have the language, sequencing or self-awareness to retrace it for us.

That is a very different situation from simply guessing 24.

Sometimes the child can see further than he can explain

This is where I think we need to be careful.

We should not immediately conclude:

“He found 24 quickly, therefore he must have brilliant structural thinking.”

Perhaps not.

But neither should we conclude:

“He cannot explain it, therefore there was no thinking.”

His statement:

“62 − 24 = 38”

is a clue.

It tells us there may be something underneath the answer worth uncovering.

Perhaps he has seen the structure but cannot yet reconstruct the path.

Perhaps he has grasped only part of it.

Perhaps his intuition is ahead of his ability to communicate.

That is what needs further observation.

And this is why I think:

“I just know” should sometimes be the beginning of our questioning, not the end of our judgement.

Why a teacher may still insist on the conventional method

There is another side to this that I think parents should understand.

Imagine being the teacher.

The child gives you the answer 24.

You ask for his working.

He cannot explain how he moved from:

31 × 26 − ? × 13 = 19 × 26

to:

62 − 24 = 38.

From the teacher's perspective, the reasoning is invisible.

The conventional method, on the other hand, can be followed line by line and checked.

So it is quite natural for the teacher to say:

“Use the method I taught you.”

The problem is not necessarily that the teacher refuses to accept another way.

The teacher may simply have no access to what the child saw, especially when the child himself cannot make it visible.

And that creates a gap.

The child may feel:

“But I already know why.”

The teacher may feel:

“But you haven't shown me why.”

Both may be right from where they are standing.

That is why the missing skill is not simply “show more working.”

It is helping the child learn how to unpack what was already visible in his own mind so that another person can follow it too.

We should preserve the ability to see.

And build the ability to explain.

A good shortcut should eventually survive questioning

This is where probing becomes useful.

Instead of immediately saying:

“Show all your steps.”

I might ask:

“Where did the 62 come from?”

“Why did 19 become 38?”

“What did you notice about 26 and 13?”

“Can you show me how your 62 − 24 = 38 connects back to the original question?”

Or:

“If I changed the numbers, would your idea still work?”

Those questions help us distinguish between a shortcut based on understanding and a shortcut based on avoidance.

Because genuine understanding tends to survive change.

A memorised trick often doesn't.

And even when the child cannot yet give us the whole explanation, each answer gives us another glimpse of what is happening inside his thinking.

There is another issue hidden inside this child's story

The mother also described a child who takes considerable effort to start but learns quickly once he is engaged.

That interests me too.

Parents sometimes combine all of these behaviours into one conclusion:

“He is lazy.”

Or:

“He has no discipline.”

Or:

“He just doesn't want to study.”

Maybe.

But I would want to separate three questions.

Can he do it?

Can he start doing it?

Can he sustain doing it?

Those are not the same ability.

A child can have very high capacity for understanding and still struggle with initiation.

Another can begin easily but lose attention.

Another can stay at a desk for an hour without deeply thinking for ten minutes.

So when a parent tells me:

“Once he focuses, he learns very fast.”

I don't immediately hear a contradiction.

I hear something worth investigating.

The difficulty may not be in learning.

The difficulty may be in entering the state in which learning happens.

And if we mistake one for the other, we may spend years trying to fix the wrong problem.

Before correcting, try watching

The next time your child produces an unexpectedly short solution, resist the urge to immediately say:

“Show your steps.”

Try something different first.

Ask:

“I can see what you wrote. Show me what happened inside your head.”

If they say:

“I just know.”

Don't stop there.

Try:

“What did you notice?”

Or:

“Which part made you think of that?”

Or:

“If I changed this number, would your way still work?”

You are not testing your child.

You are trying to see their thinking before you interfere with it.

Of course, a child still needs to learn how to explain and verify their reasoning.

The aim is not to excuse missing workings.

It is to find out whether there is thinking worth uncovering before we decide what needs correcting.

So what should we do with the shortcut?

Don't praise it simply because it looks clever.

Don't reject it simply because it is unconventional.

Uncover it.

Find out what the child saw.

Find out how much of it they truly understand.

Find out where their ability to explain begins to break down.

If the reasoning is incomplete, build it.

If the explanation is weak, develop it.

If there is genuine insight, preserve it.

Because there is an important difference between telling a child:

“You need to learn how to communicate your thinking.”

and telling the child:

“You need to stop thinking that way.”

The first helps the child develop.

The second risks teaching the child that the way he sees things is something he should no longer trust.

Sometimes the workings really are missing.

Sometimes they are compressed.

And sometimes the child has reached a structure that he does not yet know how to retrace for someone else.

Those are three very different situations.

So before calling the child lazy, ask what is stopping him from starting.

Before calling him careless, look at what he actually noticed.

Before calling him stubborn, find out whether he has constructed another logic.

And before insisting on more steps, make sure we understand why he thought fewer were enough.

Sometimes a missing step is simply a missing step.

But sometimes, hidden inside that missing step, is the very thinking we should be helping the child learn to explain rather than teaching him to abandon.

That is why I believe the first job of a Round Peg Parent is not to defend the child.

It is not to excuse the child.

It is to understand the child well enough to know what is worth protecting—and what still needs to be built.

Preserve the seeing. Build the explaining.