ASL-speaking Kinder learning basic math

One day at dinner, the bilingual kindergarten Aslian (age 5;0) and I chatted and accidentally came across a topic of basic math, specifically addition equations. Juli quickly acquired the concept of addition equations. Note that all conversations between her and everyone in these posts here take in American Sign Language (ASL). Any quotations in English are the translation from ASL.

Realizing that she was ready to learn basic additions, we experimented with various addition equations, using a zero, simple numbers below 10 and a bit over 10, and 100. E.g. 5+0=5, 100+0=100, 1+1=2, and so on.

Over the first couple of months from her 5th birthday, she played with addition equations sometimes. One day, she played, pretending to be a school student at home with her grandparents. She wrote a series of the math equations herself (image below).

Image: the kindergarten child's own math equations in addition. Age 5;1.

A few numbers, especially the number 3, were sometimes reversed. The upper, right section of the image above in lighter black contains the reversed numbers "two" and "three", even though when I reminded her, she was aware of them.

Why did she reverse these two numbers? By looking at the patterns in the section (which was the first of the series), it appeared that her logic was that these numbers 2 and 3 would be in the same direction as numbers 5 and 6. A peer into the world of a child's logical mind. That's only my speculation.

One day in mid-February, I gave Juli a math test. It was part of a pretend play that she role-played as a student sitting at the mock desk. It was opportune that we played school. I gave her a test in a relaxing environment. As I handed her the paper, she was surprised by the first equation. I knew very well that it was the "toughest" but also an easy one.

Image: the kindergarten child's own math equations in addition. Age 5;1.

She looked up at me, telling me that she wasn't sure of the first equation. I hinted her, ZERO. She hesitatnly replied "50?" I replied, "Right on". She completed the rest of it all by herself; then she handed me back.

The summer passed by. Then Juli was in her first month of grade one. One dinner, Juli (age 5;8) completed the fill-in squares counting up to 100 by herself. I never knew she could count up to 100. The last time I asked her to count as far as she could was that, motivated by the chocolate mould which had 20s, she counted them all. As soon she reached 20s, I looked around to see if there's more chocolate mould. No luck. Now I asked her if she could count the number up to 100 in ASL. As she counted toward about 20, she stopped, saying "It's too long and boring."

When I asked Juli to count the numbers from 10 just to see how she handled the ASL numbers 20-29, I captured her early phonological acquisition in number between 20 and 29 before the child learned to pronounce the ASL numbers 20-29 correctly. It's interesting to watch the early concept or how it works inside a child's brain.

Note: this child signed 20+1, 20+2, etc. but at that time in the video, she used the "21" handshape without thinking right.

Video: showing math equations. Age 6;3.

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