Translation:Children have a better imagination than adults.
I feel like the best option here would be "kids have better imaginations than adults" after all, the kids don't all share a single imagination. Even if we were talking about a single kid and a single adult, an article definitely sounds better here: "This kid has a better imagination than that adult" sounds better than "This kid has better imagination than that adult"
I have a very hard time understanding how 'imagination' can be plural. Even after br0d4 wrote me "I can say I have a good spatial imagination, average lexical and colour imagination, but quite poor sound/harmony imagination, so these are different imaginations.", it still is quite strange.
Anyway, my opinion doesn't matter here much as I'm not a native. I guess such an option is acceptable, added now. Also, 'a better imagination' will be the default now.
Not several different kinds of imagination but each child having their own imagination.
As in 'the children are wearing their hats.' Each child is only wearing one but there is more than one child so both children and hats are plural.
Agreed about needing an article in the singular, though. But plural is better.
You can answer without it, but our native British contributors say that "a better imagination" is better than "better imagination" on its own.
Truth be told, they also say that plural "better imaginations" would be best, but although we accept it, it's just too different to be the main answer.
Not all sayings are logical ;) It seems that plural 'głowy' may have meant the 'upper' part of the bed (I mean the side where your head usually is). Possibly using plural may be caused by the reasons of rhythm (the number of syllables), or grammatical symmetry (Genitive plural on both sides).
Is that a saying? I'd just say "Nie zapomnij podpisać swoich butów" (Don't forget to sign your shoes) or if you want your whole sentence literally, "Nie zapomnij napisać/zapisać swojego imienia/nazwiska i adresu na podeszwach... do you really mean "feet" (stóp) or rather "shoes" (butów)?