Philip was a boy-wonder, a genius of sorts. At age 8, he masterminded several projects, at home and in the family van. One of these projects was a system that alerted Philip when visitors arrived at the front door. He devised a simple wiring configuration connecting the welcome mat to a red light bulb in his room that flashed a warning. Amazing!
Philip was one of my second grade charter homeschool students, and we had reached an impasse with regrouping in addition. Though he was able to come up with and engineer wonderfully creative and inventive projects, he was unable to grasp the concept of “carrying” numbers.
We tried something new on one of my home visits: I laid three large, felt color-coded columns side by side on the floor, and told Philip that each one of them represented 1’s, 10’s, and 100’s. Then I wrote an addition problem on a large piece of paper and supplied Philip with large numbered cards. This was the problem:
2 4 7
3 6 3
2 3 2
+________
Philip “copied” the numbers by placing each one on its appropriate column, so we had a duplicate of the problem on the columns on the floor. I also gave him smaller cards with number 1’s written on them, and then asked him to add up the 1’s column.
When he said “12” I told him to place the 2 at the bottom and asked him (as I indicated the smaller cards with the number 1) where he thought the 1 should go. The lights went on! Philip J-U-M-P-E-D to the top of the 10’s column and placed the “carrying” number there. He did the same with the 10’s and 100’s column, got the concept, was able to translate it to pencil and paper, and had no further problems with regrouping.
The kinesthetic approach works best for some, but it always helps to use large, colorful, and interactive materials when introducing new concepts. Concepts can be taught very concretely at first before translating them to their more abstract forms. 
