You've drilled the facts. You've watched the YouTube videos together. You've bought the flashcards. And yet, every time a subtraction problem shows up on the page, your child stares at it like it's written in a foreign language — or worse, just writes down any number to make the discomfort stop.
Here's the thing most well-meaning adults don't realize: your child is not broken, and this is not a laziness problem. It's a sequencing problem. Somewhere along the way, a crucial step got skipped.
The Step Nobody Talks About
Math learning moves through three stages: concrete, pictorial, and abstract. That's not just educational jargon — it describes the actual way the brain builds real understanding.
- Concrete means physically touching and moving objects. Blocks, counters, fingers.
- Pictorial means drawing or seeing a picture of that same idea.
- Abstract means the bare number sentence: 13 − 7 = ?
The problem? Most classrooms — and most well-intentioned home practice — rushes children from concrete straight to abstract. A few manipulatives on day one, and then worksheets for the rest of the year. But the pictorial bridge never got built. So when the blocks go away, the understanding goes with them.
When a child hits a problem like 32 − 17 with no visual model in their head, they're not being stubborn. They're genuinely lost. They're trying to balance invisible numbers in working memory that hasn't been trained to hold them yet.
What "Not Getting It" Actually Looks Like
There are a few telltale signs that a child is stuck at the abstract stage without a solid foundation underneath:
- They subtract the smaller digit from the larger one regardless of position (writing 32 − 17 = 25 because 7 − 2 feels wrong, so they flip it).
- They guess, then immediately ask "is that right?" — they're hoping for confirmation rather than checking their own reasoning.
- They can do easy problems quickly but completely shut down when regrouping enters the picture.
- They get it right one day and wrong the next, with no apparent pattern.
That inconsistency is the real giveaway. True understanding is consistent. Fragile memorization is not.
A Simple Concrete Method You Can Try Right Now
You don't need special equipment. Grab 32 small objects — pennies, dried beans, cereal pieces, whatever you have. Arrange them as three groups of ten and two singles.
Now ask your child: "Can we take away 17?"
Let them try. They'll quickly see that they can't take 7 from the group of 2. This is the moment. Don't explain it yet — let them feel the problem. Then ask: "What if we broke one of those groups of ten apart?"
Watch their face when they realize they now have 12 single pieces and can take 7 away easily. That "oh!" moment — the physical, tactile discovery — is the foundation that makes written subtraction make sense later. They've just invented regrouping for themselves. That's far more powerful than being told how it works.
Do this a few times across different days with different numbers. Draw pictures of it. Then, and only then, connect it to the written method.
Why the Written Method Falls Apart Without This
The written subtraction algorithm — the one with the crossing out and the little borrowed numbers above the column — is actually a beautiful shortcut. But it's a shortcut that only makes sense if you understand what it's shortcutting.
When children are taught the notation before the concept, they memorize a sequence of steps with no meaning attached. Steps without meaning are fragile. They get muddled, reversed, or forgotten under pressure. That's why your child can do it perfectly in a calm practice session and then completely fall apart on a test.
Meaning, on the other hand, is sticky. When a child genuinely understands that "borrowing" is really just breaking a ten into ten ones — because they've held it in their hands — the written method becomes a way to record something they already know, not a mysterious ritual to be performed correctly.
Where to Go From Here
If your child is in that gap right now — past the concrete stage at school but clearly not solid on the abstract — the most helpful thing you can do is gently back up. Not as a punishment, not with frustration, but with curiosity. "Let's figure this out together."
Start with the beans and the pennies. Draw it. Talk about it. Make the problems tiny and manageable before making them bigger. Confidence is built one genuinely understood problem at a time — not one drilled problem at a time.
If you want a structured, step-by-step path that does exactly this — concrete to pictorial to abstract, at a child-friendly pace — Subtract With Ease and Subtract With Confidence are both built around this exact philosophy. One starts at the very beginning with no-regrouping problems; the other takes on regrouping directly, with visual methods that actually stick.
Because the goal was never getting to the right answer by any means necessary. The goal is a child who knows why the answer is right.
