### Vn133.1 4/28/78-5/8 & 31/78

4/28 The calorie counting continues for me, and the adding for

Miriam. The sum of Addendum 133 – 1 is interesting because of its error:

the left justification of 3 and 4 digit addends in the same vertical grid.

Despite this mal-arrangement, with its implication that the place-value

basis of column alignment has not been mastered, Miriam’s carrying

procedure was standard.

5/8 When the children started squabbling over whose turn it was to

add up my daily calorie count, I refused either the privilege. But today

Miriam took up the task with no complaint from Robby so I let her proceed.

She wrote the addends and result thus:

Most interesting was her procedure. Beginning at the left, Miriam cal-

culated 14 for the column and carried a 10 to the next right column. I

intervened, “Miriam, don’t you remember your good trick for when you

have carries?” She restarted on the right and reached a standard result.

5/31 After staying up late last night at a dinner with Mimi Sinclair

and Marvin and Gloria (whereat Miriam showed off a little by working with

the soma cubes and the 7-piece pythagorean puzzle), Miriam stayed home

from school today. During the course of the day, I posed the following

problem, designed to contrast for her results of mental addition and

vertical form addition to point up the question of place value in the

vertical form.

When Miriam saw the horizontal sum, a sheet of paper covered the question

and sums below the dotted line. She knew the result was 20 and after she

had written down the answer I took away the covering sheet. Miriam read

the question, then mused, “For both, the numbers are eleven.” Puzzled,

I asked what she meant, but Miriam continued without responding to add the

left sum from the left to 65. She stepped back, then with a “No. That’s

not it.” returned to the chalk board to erase her result. I stopped her

erasure and directed her to the second sum, which she added to 20 (from

the right, with only mental marking of the carry), then encircled. When

I asked how she knew the right sum was correct, Miriam argued that the

answer was 20.

**Relevance**

These three incidents all focus on the imperfections of

Miriam’s place value comprehension. The last I expect to be seminal,

leading Miriam to recognize that the results of addition, in whatever

form, should be consonant, and that she can herself judge the correctness

of small vertical sums by checking through mental computation.

**Addendum 133-1**

**Column Alignment Error**