### Vn122.1 Carrying Bugs 2/5/78

Invited to play at a friend’s house, Miriam waited for Gretchen to
drive her there. During this vacuum of activity, I asked her if she
remembered how to add with carries (cf. Home Session 23). Miriam
reacted impatiently, as though it were foregone that she did. She
agreed to solve a problem I posed on my chalk board and showed
sufficient interest that she tried to peer over my shoulder as I wrote
the sum in vertical form.

0
1000   100   10
|  4  |  7  |  3  |  4  |  5  |
+ |  2  |  2  |  8  |  5  |  7  |
_____________________________
|  7  |  0  |  1  |  9  |  2  |

After drawing the columnar division lines, Miriam first said, “5 plus 7
is 2 carry the 1.” “Carry the what?” I asked. “Ten,” she replied and
wrote her marks above the tens column (these marks of hers are hand-
written in the sum above [italics]). She then proceeded: “5 and 4 are 9 plus
10 is 19; put down the 9 and carry.” Miriam did carry a hundred but
failed to add it to her sum of 8 plus 3. Adding the carry from that
11 into the thousands column sum (7 plus 2), Miriam wrote the carry
from that 10 above the identical column with four zeroes (see above)
and added the carry of 1 into the ten thousands column sum (4 plus 2).
Satisfied with her result, Miriam asked me to indicate any columns she
should check.

When I drew an arrow under the tens column and asked whether the
4 was a 4 or a forty, Miriam crossed over the 9 with a zero. Upon my
pointing to her dropping the carry into the hundreds column, Miriam
(who knew the 3 and 8 were 3 and 8 hundreds and that a hundred had been
carried) quit and refused to do more arithmetic before going to her
friend’s.

Relevance
Even though Miriam appears to have gained a sensible way of
thinking about carries and representing them for herself, her command
is still imperfect, as these two mis-steps of hers indicate. Can she
make such errors and still be judged as understanding carrying?
I believe so. One test would be to see whether on a similar sum
she exhibits these same errors or shows confusion.