"They write while I sleep."
Translation:Zij schrijven terwijl ik slaap.
"Tijdens" is preposition (usually translated as 'during'), while "terwijl" is a conjunction. So after "tijdens", you must have a noun, not a subordinate clause. For example:
- Ik zing tijdens het lopen - I sing while walking
Here "lopen" is used as a gerund, something that you'll encounter much later in the tree.
In this sentence you need to use a subordinate clause, because the person writing and the person sleeping are not the same. So it must be "terwijl".