Learn French: Nous faisons les tâches ennuyeuses en écoutant un podcast. - We do the boring tasks while listening to a podcast.

To form this part of the gérondif (the present participle), we take the nous form of the verb in the present tense (nous écoutons), drop the -ons, and add -ant. This gives us écoutant.

Could I say pendant écouter to mean "while listening"?

No, this is a common trap for English speakers! To say you do something "while doing" something else, French uses en + the present participle (en écoutant). You cannot use pendant directly with an infinitive verb.

Why is the adjective ennuyeuses spelled with an "e" and an "s" at the end?

It describes les tâches (the tasks), which is a feminine plural noun. The base masculine adjective is ennuyeux. To make it feminine, we change the -x to -se (ennuyeuse), and then add an -s because there are multiple tasks.

What does the little hat (circumflex accent) on tâches do?

The circumflex over a vowel often tells us that there used to be an "s" after it in old French. Knowing this makes it easy to see that tâche shares a history with the English word "task"! Be careful to include it, because tache without the accent means "a stain".