I discovered a couple of days ago that I had managed to reach the age of nearly 76 without finding out, not only the Welsh for ladder, but that it is the same word as school - ysgol! (Diolch to Duolingo for telling me!) My question, quest, journey of discovery is to chase up the derivation! I can see obvious connections. We scale mountains or cliffs or heights. We have escalators in shops and in the London underground. We talk about education as a ladder sometimes, even in English. I presume ‘ladder’ comes from Germanic routes. If I had paid attention in school, oh irony, I might have come across scaling ladders in Caesar’s Gallic Wars, which I ended up learning chunks of by heart to fake translation to scrape my O-level! As it is, all I have found is that school comes from the Greek. which is no surprise as teaching seems to have started there in terms of formal learning from a teacher, rather than being shown a trade or skill by a parent, relation or merely an expert wanting to pass on that skill.
If any of you experts in linguistics can tell me where Cymraeg got ysgol from in both sences and English got ladder from, I will be very grateful for the solving of the puzzle!
The etymology for ladder is from the Old English hlǣd(d)er, of West Germanic origin; related to Dutch leer and German Leiter .
The etymology of ysgol (school) is from the Latin schola, from Ancient Greek σχολή (skholḗ).
The etymology of ysgol (ladder) is from the Middle Welsh yscawl, from Latin scāla.
Why they both ended up as ysgol though, I’m afraid I haven’t found out! 
Oh diolch yn fawr iawn iawn, @siaronjames! I think it makes sense! I suspect scala has the same root as scola and is older here because teaching is a very ancient concept in Britain, with Druids and/or Bards and Storiwr teaching verbally and passing on legends and stories/verses about important people. Oh, OK maybe the ladder meaning came as an accident because there was very little writing in Welsh and yscawl sounds a bit like ysgol?
Ystol is also used for ladder. More dialect than general use. GPC also says it comes from scala