Trying to remember a fantasy portal book from the 1970s or early 80s

Question

I am pretty sure I read the book between 4th and 8th grade (1978 to 1982).
I remember the book was about children being transported from the "real" world to a fantasy world. Mostly, I only remember the mechanism of transportation. The character would go into a sort of secret garden area and find a colorful tile mosaic. They would manipulate the tiles in the mosaic until they formed a picture which would then begin moving and become a portal and transport them to the other world.
Not much to go on, but the description of this part of the story was really vivid for me, and I'll still remember visualizing it as I had read the book from time to time.
I also remember at least one of the times, the child was running from bullies when they found the secret garden area.
Any help you can provide would be greatly appreciated. I'm sure I would recognize the book, if I saw it.
I remembered some more details last night: Although the children were from different parts of the world, the mosaic they each found was the same. Each child completed a part of the mosaic which included a dragon. I think the dragons were from different mythical pasts, one was a Chinese dragon, one was a European dragon, et cetera.
The book, at least the first part, was more like a series of short stories about each child's completed dragon. There might have been a second half where all the stories come together, but I am not sure.

Answer 1

I'm not confident in this identification, but possibly Andre Norton's "Dragon Magic"? Not every detail matches perfectly - the kids are from the same part of the world, but have very different experiences. The portal trigger is described in summaries as a puzzle but that might be close enough to a mosaic.

There's a fairly detailed recap (and opinionated review) here that describes the four protagonists a bit and might be worth a look.