This is the so-called "impersonal pronoun". Si can be used to form passive-like sentences easily. Using this formula, "si" must be followed by either a third-person singular, or a third-person plural form of the verb (in this case, either "scrive" or "scrivono" and nothing else). The verb must agree with the plurality of the subject (if the subject is singular -> si scrive, but if the subject is plural -> si scrivono)
In Inghilterra, si beve il thè con del latte.
In England, tea is drunk (--> people drink it) with milk.
"Thè" is the subject, "si beve" is the predicate, and since thè is singular, the predicate has to be the third-person singular form of the verb.
In Duo's example, the subject is "cose", which is the plural form of "cosa", so the predicate "si scrivono" is a third-person plural form of the verb. (if it was "cosa", in singular, the predicate would have to be "si scrive", not "si scrivono".)
I gave quite a long answer, but I hope I could help everyone confused about this.
If Italians can talk about things being "nel piatto" (in the plate, when they mean on the plate) then we Brits can say "IN pen" One does indeed write "IN pen" or "IN pencil" or "IN crayon" or "IN biro" or even IN quill-tipped feathers from the duolingo owl, but it would be equally correct to say "One writes with a pen." :)
This brings back memories of primary school. We were required to write with pencils until our penmanship was judged good enough to "write in pen" at which time we were formally presented with a pen formed with the 'proper' grip to encourage continued excellence. All very formal. All very 1950s America.