Ellis showed a subtraction problem, performed both using the traditional regrouping, or borrow-and-carry, algorithm and using an example from the common core. Here’s a screenshot of the two methods.

What do you notice? The split isn’t tens and ones. This time it has been split into 30 and 13. If you add 30 and 13 together it makes 43. Why split 43 in this way? The 8 ones in 18 is bigger ...

Journal for Research in Mathematics Education, Vol. 23, No. 2 (Mar., 1992), pp. 98-122 (25 pages) Conceptually based instruction on place value and two-digit addition and subtraction without ...