A parent looks at a homework page, sees a column of numbers with minus signs in the middle of it, and reasonably concludes that something has gone wrong. Nothing has. What they are looking at is partial-differences subtraction, and it produces exactly the answer that borrowing produces.
The answers are the same
Take 471 - 293. Borrowing gives 178. Partial differences gives 200 - 20 - 2, which is 178. Counting up from 293 gives jumps of 7, 100 and 71, which add to 178. Three routes, one destination. If the answers ever differ, one of them was done wrong, and that is a different conversation.
Why schools teach the unfamiliar one first
Borrowing is fast and it is opaque. A child can borrow correctly for a year without being able to say what the small crossed-out numbers mean. The newer methods are slower and much harder to fake: writing 70 - 90 = -20 requires knowing that the tens column really is short by twenty, and a child who can say that has understood place value.
Speed comes later, and for most children it comes on its own. Understanding rarely arrives the same way.
What to do at the kitchen table
- Learn their method before offering yours. A child mid-way through learning one approach who is handed a second one usually blends the two into something that works with neither.
- Ask them to talk you through it. If they can explain why a column came out negative, they are fine, whatever the page looks like.
- Compare later, deliberately. Once they are fluent, showing them your method side by side is genuinely useful. Two routes reaching the same answer is a real mathematical idea.
- Resist saying you were never any good at maths. Children take that as permission.
The pages to read
Each method has a page here with a worked example, so you can see the whole thing in one screen before the homework starts: partial-differences subtraction, trade-first subtraction and counting-up subtraction.