Learn Hardcore Turkish: Yolda koşarken ayakkabılarım çamurlanıyor. - While running on the road, my shoes are getting muddy.

After back vowels (a, ı, o, u) → -da (e.g., yol → yolda).
After front vowels (e, i, ö, ü) → -de (e.g., ev → evde).
If the noun ends in a voiceless consonant (p, ç, t, k, f, s, ş, h), the d becomes t → -ta/-te (e.g., park → parkta, köy → köyde).

How is koşarken formed, and what does it mean?

It’s the converb “while …-ing”: koşar + iken → koşarken (the sequence -ar iken contracts to -arken).
Meaning: “while running / as (one) runs,” emphasizing simultaneity, not sequence or result.
Same pattern: yürürken (while walking), giderken (while going), okurken (while reading).

Can I say koşuyorken? How is it different from koşarken?

Yes. Koşuyorken attaches -ken to the present continuous (koşuyor + ken → koşuyorken). Nuance:

koşarken: generic “while running,” very common and neutral.
koşuyorken: focuses on a specific ongoing time slice, often used for concrete/backgrounded situations (especially in the past), e.g., “Koşuyorken ayağımı burktum.”

Who is understood to be running here? Doesn’t it sound like the shoes are running?