If you are near a large academic library (preferably at a university), you can get on-site access to many commercial databases. Ebsco's Education Research Complete gets 18 hits for the search: (Flipping or Inverting) and classroom*. Their default search is author, title, journal name, abstract, and subjects; and you can also limit to "scholarly/peer reviewed" either before OR after you do a search. You can also put the entire search string all into one box, even if you use the advanced search that has several boxes. You can also "Select a field" TX all text, and use "proximity search" to find words/phrases close together (at least in one place in each full text article). For example, the TX search: (Flipping or Inverting) n20 classroom* gets 47 hits in peer reviewed. Proximity search is tricky, and varies greatly among databases so I often don't risk trying to group the words into a set. But it seems to work in Ebsco; flipping n20 classroom* gets 29 peer reviewed and inverting n20 classroom* gets 19.
Some smaller universities, and many colleges will NOT have Education Research Complete, but most will at least have Academic Search Premier (also Ebsco), which gets 14 hits (6 peer reviewed) for the default search: (Flipping or Inverting) and classroom*. TX (Flipping or Inverting) n30 classroom* gets 37 peer reviewed.
