A closer possible, at least partial, match than "Robbie" is "R.U.R. "Rossum's Universal Robots" by Karel Čapek (1920).
It has been a long time since I read it; there are numerous summaries and synopses and study guides online.
There are more or possibly better summaries than on Wikipedia; Britannica has one, and here is another summary.
It is also on Gutenberg.
A firm invents androids (which have some biological matter), but Capek coined the term "robot".
There is eventually a war between humans and "robots" intelligent enough to desire freedom. Eventually all humans are killed except one of the sympathetic humans. The robots manufacture everything, including other androids/robots.
(1) Story plot match: The "robots' manufacture everything eventually, including other andoids/robots.
(2) Time-period match: Although I couldn't find a textbook containing it on ISFDB, even the translation into English is old enough to have been in textbooks even before the 1950s or the 1930s.
(3) Possible similar-anthology match: It is also in anthologies such as the 1954 anthology about robots and androids, "Science-Fiction Thinking Machines: Robots, Androids, Computers" edited by Groff Conklin.
(I do not know how often it was used in schools, although I would have read it enthusiastically in my grade school or high school.)
(4) Possible phrase-match: A decades-old memory could misremember "Rossum's Universal Robots" somewhat differently as "Robbie's Robots".
(Asimov's "Robbie" was also famous, which would make misremembering or conflating the names even easier.)