Let's think beyond the cliche of school house, red apple, owl, chalkboard, messaging speech bubbles, etc. unless you can make any of those into interesting and clever designs.
Think about your favorite teachers. What would appeal to them? What did their classroom look like? What made them so good? If they were anything like mine, they had bright classrooms, were serious about their jobs but also playful and engaging. They were interesting people. I hope the teem logo can represent that.
I've included sample logos below (in alphabetical order). There's a mix of text + illustration and illustration only, but I think they're all great.
The text is always very easy to read, even when the shapes have been modified as in the cases of Lyft, Strava, Dark Room, and others. With the exception of Instagram, the illustrations are all extremely simple. Just a handful of lines to draw them. Few details are lost as the illustration shrinks because there weren't many details to begin with, just clean design.
The last part is that each of them is fairly unique. I've received number of logos with four interlocking puzzle pieces or three people holding hands or other such generic elements. I'm excited to see new possibilities, just as these designers have expressed their logos in creative ways.