How did math and science education grow out of math and science departments?

In the 18th and 19th centuries, mathematics became part of the core curriculum, and in the early 20th century, mathematics education started being taken seriously.  The first Chair of mathematics education was created in 1893 — in a mathematics department.

I don’t know how science education research came to be seen as a standalone field.  I know that the earliest Physics Education Researchers (like Lillian McDermott) started (and in Lillian’s case, remain) in Physics.

If you look at most Schools/Colleges/Departments of Education today, there are programs in science education, mathematics education, and sometimes even history or reading education.  At what point did these fields break away from their original domain departments become established in Education?  What was the development path?  Clearly, becoming part of the core curriculum is key.  Then it’s important to teach teachers about it.

I honestly don’t know the answer, and I’m hoping that readers here might be able to lend some light.  What is the developmental path such that computing education is becomes entrenched, part of what we teach teachers about, and something that grows beyond computer science departments?