Learn Turkish: Sendeleyen işçi şarampole düşeyazdı. - The worker who staggered almost fell into the ditch.

This uses the approximative compound verb structure. It is formed by the verb root (düş-), the connecting vowel -e-, and the helper verb yazmak (which entirely loses its normal meaning of 'to write' here), followed by the past tense -dı. It indicates that an action came dangerously close to happening, but ultimately did not. You will almost always see this structure used for sudden, negative accidents like falling (düşeyazmak) or fainting (bayılayazmak).

The English translation says 'The worker who staggered', which is in the past tense. Why do we use the present participle sendeleyen (-en/-an) instead of a past form?

In Turkish, the -(y)An participle is used when the modified noun (the worker) is the subject doing the action. Even though the staggering happened in the past, sendeleyen acts as an adjective describing the worker's state at the exact moment the main action (düşeyazdı) occurred. It translates smoothly as 'The staggering worker almost fell.' If you used a past participle like sendelemiş olan, it would sound like the staggering had completely finished before the near-fall happened.

I haven't seen the word şarampole before. What is the root, and why is it in the dative case?