!Preschool math
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agk's diary
10 March 2025 @ 03:01 UTC
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written on Evy's GPD MicroPC
after everyone's asleep, as dogs bay at the moon
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Last night daughter creamed me at Go Fish by the
campfire after dinner. We play with a poker deck
after I pull out the Jacks (only one man in the
deck) and cards denominated 6-9. That makes it
easier for her to scan, and keeps the game length
fun.
I took 6 pairs, she took 12. "Do you have any red
aces?" Aargh! I didn't pull any punches, she's just
a shark!
We gave a Boy Scout troop from Ohio a historic tour
of the big cave after our card game. They were sore
from the very muddy wild cave they'd been in all
morning, but a few still wanted to explore some of
the dusty big cave's crawly bits. Daughter ran in
those holes when it was time for them to come out,
and announced, "Boys, time to come out of there!"
After the cave tour daughter and I bedded down in
our tent under many quilts, read a story about
triangles from Shevrin & Zhitomirsky's (1978, 1985)
*Let's Play Geometry*, and slept through the 0C
night while our breakfast oatmeal slowly cooked in
a Shuttle Chef Thermos.
What's a preschooler?
Somewhere in her third year, daughter's body elong-
ated a little, her eating slowed, and her speech
and gross motor control became more effortlessly
human.
Her play became imaginative, but frequently in an
endlessly repetitive loop---putting babies to sleep
all over the house, correcting her children, making
the toy family go to school or stand in the corner,
hyperverbally narrating the antics of her baby
dinosaurs.
Anything that strongly registers in her conscious-
ness she responds to by playing it out, rehearsing
it to understand and master it. Yesterday it regis-
tered with her that the sheepskins she slept on as
a baby that we now take camping were cut from sheep
that were killed. Later, she somberly squatted and
did something inscrutable with her hands, cutting
up the dead bodies of her sheep she had killed.
She's a learning machine, building a complex
associational scaffold, hungry for whatever she can
add to it. She suddenly was able to play easily
with six-year-olds, and was no longer the peer of
not-yet-three-year-old friends who had so recently
been her peers, but were still toddlers.
She knows letters and numbers, but remains illiter-
ate. She draws tadpole people but lacks the gross
motor control to recognizably write her name.
Math games meet her desires for intimacy with me
and for stories and associations to add to her
scaffold, while giving me intimacy with her and
blessed rest from her imaginative monomanias.
If it helps to know, she's more than 3 1/2; not yet
four, like Alexander Zvonkin's son at the start of
their preschool math circle in 1980s Soviet Union.
What are our basic math games tools?
For the last couple months, we've mostly used two
books, a small group set of brightly colored wooden
Cuisenaire rods, and some drawing tools.
Notes from 20 February
We studied from about 10 til 1130. We did the third
notebook from Zhitomirsky & Shevrin's (1980, 1987)
Maths with Mummy.
Daughter recognizes the numbers, but hesitates and
needs coaching each time she encounters arithmetic
(+, -, =) notation. If I ask, "does that add or
does it take away?" she answers correctly, but when
I point at 3-2= with my pointing chopstick, she
reads out "three," then says, "I don't know" when I
tap the operator.
Today I balanced a long 10cm Cuisenaire rod (an
orange one) on a pivot (a clay sculpting tool that
looks like a dental tool). I asked her to recall
playing on the seesaw. We tipped the rod back and
forth. Then I placed two white (1cm^3) rods on one
side and one red (2 x 1 x 1cm) rod on the other.
"The equals is the pivot," I said. "It means the
seesaw is balanced. 1+1 is two. They are the same.
You can see they are equal on both sides. Neither
side of the seesaw is down."
"Is it equal when you're on one side of the seesaw
and I'm on the other? What if you were on both
sides? Would that be equal?"
I didn't know if she got any insight from that
comparison. She knew "the same" and "different"
comparisons from Anno's Math Games books, and we
kept coming back to balanced and the same as con-
ceptually interchangeable to equal in discussions
of height of people and buildings, lengths of the
sides of triangles, etc. Within a week of this
lesson she developed an easy grasp of +, -, and =.
In the book, little sister Olya, who like daughter
cannot think abstractly yet as big brother Petya
does, uses her matryoshka dolls to do sums. We used
long Cuisenaire rods as counters to do 3-2 and 3-1.
The rest of the third notebook is dedicated to
triangles, angles, and comparisons of segments of
various lengths.
I copied the first triangle using all our drafting
tools:
* I copied it to a piece of 7.4 x 10.5 cm graph
paper (5mm grid) torn from a Rhodia No. 11 pad
* I marked the vertices of the angles with a green
pencil from an 8-count pack of short Crayolas
and drew the sides with a #2 pencil snapped
down to the same length as the Crayolas
* guided by the 15 cm ruler and set-square from a
RayMay Study Mate zero-edge ruler set.
Daughter identified the angles. She picked colors
and I colored them in. We talked about how triangle
means three-angle. She showed me the three sides
and three vertices/corners. In talking about shapes
I'd not thought to distinguish the angles from the
points at their vertices!
Then I got a letter-sized sheet of copier paper for
daughter to trace the set square's right triangle,
like Petya does in the book. I held down the set
square while she drew so it didn't drift. Like
Petya's, her triangle had "whiskers" extending
beyond the green points she selected the position
of and I marked for corners.
When Petya's daddy in the book encourages him to
erase the whiskers, daughter started out with her
pencil eraser. I gave her a Pentel high-polymer
eraser I used in nursing school, about 6 x 2 x 1cm.
It was too big for her, she couldn't see what she
was erasing, so I cut off a chunk about the size of
a red Cuisenaire rod (1 x 1 x 2cm), which she liked
much better.
We compared lengths of rods, pencils, and tools,
then laughed as Lyapa the donkey confused the three
bears with the three pigs and mixed up how many
chairs were left after the wolf broke one, how many
baskets of acorns after the wolf ate one.
After our lesson, daughter found my dominoes, which
she'd never played, and I hadn't played in years.
She begged me to teach her and play with her. We
played dominoes til naptime.
