!Preschool math --- agk's diary 10 March 2025 @ 03:01 UTC --- written on Evy's GPD MicroPC after everyone's asleep, as dogs bay at the moon --- 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.