### Vn100.1 Arithmetic Ripples 9/26/77-10/2&7/77

9/26 Miriam tells me today was her first day of doing math at school.
“But we did it differently there from what we [she and I] did here.”
She explained that school math was playing with cuisiniere rods. I
told her I thought that was great, and asked what she did with them.
Miriam said she used them for building. As this project comes to an
end, I will ask Miriam to build, out of cuisiniere rods, a POLYGONAL
SPIRAL. . . or perhaps ask her to describe my procedure for doing so in
the Logo language.

10/2 Robby and Miriam have lately been making home-made clay. They
mix flour, salt, and a little water, knead thoroughly, and thereby develop
a clay which they later fix by baking. Robby began counting the layers
of material he made by folding the material over and into itself. After
reaching a count of 96 (by what path I am not certain), Robby cut his
clay ply in two pieces, and superposing one on the other, declared he
had 96 plus 96 layers.
Miriam said, “That’s a hundred 92.” Robby asked me if she were
right. Miriam responded, “90 plus 90 is one eighty (looking at him for
concurrence); so it’s one eighty six, seven, eight, nine, one ninety,
one ninety one, one ninety two.” thus completing her proof.

10/7 To inquire whether Miriam’s 90 plus 90 sum might derive now from
the sum 9 plus 9, I asked this morning (after warning her I wanted her
first answer, not one thought about too much). “How much is 9 plus 9?”
After a shosrt pause, Miriam responded, “18.” “How did you get that
result?” Miriam answered, ” ‘Cause 8 plus 8 is 16; so it’s 16 plus 2.”

Relevance
These notes document Miriam’s beginning of math at school and
suggest one simple way to begin binding her experience at Logo to her
future school work. The second observation documents the ease with
which Miriam has incorporated well-known sums from turtle geometry’s
decadal arithmetic into her procedures for mental computation. This is
an indication of their permanence as members of her repertoire.