I'm not sure if you might have misread "Ziehen" in your source text as "Zeichnen"?

In this instance, it's about taking balls/similar out of a container of some sort and putting them back in to help children learn how to count - there's a fuller explanation of this here:
Für das Urnenmodell mit zurücklegen gilt: Aus der Urne wird eine Kugel gezogen. Die Nummer wird aufgeschrieben und im Anschluss wird die Kugel wieder in die Urne geworfen. (link below)

It looks like this draws on an actual mathematical approach called the "urn problem" ("In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an urn or other container."), but honestly in your text, I'd be tempted to just call this "Urne" a "container" (an "urn" always makes me think of ashes!).