Let's take a simple addition question like 34 + 17. We line them up vertically and then say 7 + 4 is 11, so 'carry' the 1 and put is over the 3. Ahhhh, carry the one. It isn't really a 1, it is a group of ten, so it's somewhat misleading. We have really regrouped the 1's into a group of 10 and we put a 1 in the 10's column, the 1 represents a group of ten.
Let's take the same question 34 - 17 and line the numbers up vertically. We then say, you can't take 7 away from 4 so let's borrow 1 and make it 14. Again, we are actually taking a group of 10. The term borrowing also suggests that we pay it back. So, once again we regroup by taking 1 ten from the tens column and our 4 becomes 14.
The very best way to support young learners with this concept is to use counters, preferably base 10 manipulatives. Another good way to support these concepts are to use money and let dimes and pennies become the counters.
See also:Addition and Subtraction Worksheets