Probably "Infinity Jinx" (2005) by Margaret Peterson Haddix, which was collected in Unexpected: 11 Mysterious Stories. Does the cover ring a bell?
I found it by searching this site for [story-identification] learn read children which returned Story ID: Boy who is stuck at 5 years old with robot nanny which matches your description quite well.
A scientist introduces a vaccine to stop children from aging so that parents never have to suffer the loss of watching them grow up and leave home.
From the question above:
The injection/serum used to halt the aging process was developed by a scientist, who when he first shared his findings had a 5 year old son and injected him, then told the onlookers/potential buyers/other parents to come back in 20(?) years. When they did, their children were adults and no longer needed them or were ungrateful layabouts, and the scientist's son was still 5 years old, cute, needy, etc.
And
When a child whose aging process has been stopped learns how to read, they begin aging normally again, so the parents don't want them to learn to read.
The main character is a mother who lives in an apartment complex and does almost the same thing everyday with her ageless child.
Perhaps you mistook the nanny for the mother? From the review linked in the previous answer:
When mommy and daddy are at work, the robot-nanny is there to care for him by cooking, cleaning and guarding the door when the doorbell rings until the person leaves.
A rebellious kid in the complex introduces this child to books.
Also from the review:
It’s a boy, taller than him and a face he hadn’t seen before. Curious he opens the door just a tiny bit and alarms burst into sound and the robot-nanny races over to close the door and place him back to the safe security of the couch. Only she didn't. The strange boy rushed in and to her back and she stopped moving. This is the start of Timmy’s adventure as he learns about learning, reading, writing, counting and many other things we find so commonplace and bring. He learns how to read the clock on the wall and basic books. He also learns he is hungry for more knowledge. Timmy wishes to grow.
