Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Americans pronounce schoolwork as SKOOL-wurk (/ˈskulˌwɜrk/). The L in "schoolwork" is a dark L — the back of the tongue rises toward the soft palate, adding a small "uh" quality before the L. This is called the Dark L vs Light L, and it's one of the defining features of casual American English. It comes out as SKOOL·WURK. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "She put her full attention into her schoolwork".
Record yourself saying "schoolwork" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 7 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Round your lips into a tight circle. Let your tongue rest in the middle of your mouth, slightly raised.
Keep the tongue tip down and pull the back of the tongue up toward the throat. The 'dark' sound comes from the back.

Round your lips into a tight circle. Lift the back of your tongue toward the soft palate and add voice.

Flare your lips and push them away from the face. Lift the middle of your tongue toward the roof of the mouth.

Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

The textbook way isn't wrong — it's just not how anyone actually says it.
The L in "schoolwork" is a dark L — the back of the tongue rises toward the soft palate, adding a small "uh" quality before the L. Dark L adds a small schwa-like "uh" before the L. The back of the tongue lifts toward the soft palate.
In "schoolwork", the "k" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.
Stress falls on the first syllable, not the others. Stretch SKOOL — keep everything else short and quick.
Americans use a relaxed retroflex R — the tongue curls back rather than rolling. The R is one continuous sound with the vowel before it, not two separate sounds.