What is independent processing?
After the explanation and the shared check, the class has to use the material: explain it to someone else, apply it to a new case, compare, solve a problem. Only here does it show whether a pupil can do it without your help.
On their own does not mean alone. A structure gives groups roles and steps, so that one pupil does not do the work while three watch. The structure takes the place of the support you gave at first.
Which structure for which kind of processing?
For material that falls into parts, Jigsaw is strongest: every pupil becomes the expert on one part and explains it to the others. In 1 goes, 3 stay one group member visits another group as the messenger, and in Gallery Walk the work hangs on the wall and the class walks past with a few fixed questions.
For a text or a problem, Read and Ask and Which approach? fit, and Predict, Observe, Explain has pupils predict an outcome first and explain it afterwards. For designing and finding causes there are Design thinking in miniature, The worst plan and Five Whys; World Café and Conversation Café are for a conversation with the whole class.
What to watch for
Only start processing when the check went well. A processing task on material that has not landed becomes copying from whoever understood it. The order is the work: together first, then on their own.
Walk round and listen instead of helping. Every question you answer takes away a pupil's chance to find it; point to the role or the step on the board. What you hear is your best material for the closing.