It's really hard to talk in general terms about what makes something "work appropriate" which is why some places have restrictive dress codes -- or even uniforms. Otherwise it becomes a mess of interpretations.
But -- first order of business -- it has to be practical and safe for the job at hand. Different jobs = different types of clothing.
Next, you're thinking about the image you want to project. Typically, in roles of some responsibility, you want to convey a certain amount of gravitas. Teachers are in a peculiar position because they actually want to convey both authority and approachability. So it's a bit of a balance and as we've all noted above, different geographical areas will err on one side or another of the continuum.
Still, in general, beyond being neat, clean, etc. (which should be obvious!) work clothes tend to involve more structure and tailoring. This is across the board (ugh, so to speak). It could mean a full suit (for business/ lawyer types) or it could simply mean a pressed crisp shirt with denim. The tailoring and structure give an outfit its sense of being a bit more formal.
All-knit outfits that look like gym wear suggest that someone is "off duty." They are going exercising or curling up on their couch with a book. Not working. They look like home wear, not work wear.
If someone does not enjoy wearing tailored items due to comfort/ fit issues, then there are other ways of suggesting structure without actual tailoring (e.g. knit jackets, a knit skirt vs. jeans because a skirt reads as more formal, etc.)
I think as a teacher you can dress "smart casual." That means you can mix up casual pieces (like denim or like ponte pants) with a few more formal elements. You can have a lot of fun and be somewhat creative in your style.
