what does riding in sth mean?

The phrase is not riding in, but "riding on the recent popularity of various constructivist theories". "In particular" was the phrase inserted between "riding" and "on".

Idiom: (one thing) makes inroads into something, meaning that the first thing has a noticeable effect on the second, especially by reducing the importance of it.

Idiom: riding on something, depending on something

riding in particular on the recent popularity of various constructivist theories
特別是靠著近來建構主義理論的盛行