How can one know if a student is truly learning?

If I give out exercises for a child to do and she gets them all right, does that mean she has the depth of knowledge I planned to develop in her? Or could she have copied? How do I know?

If a child gets some wrong, do I know what he doesn't know? How can I help him develop the conceptual knowledge required to solve the question? Is a cross on his worksheet enough? Is teaching how to do the question one more time enough? Is asking his peer to teach him how to do enough? Is some written comments sufficient? What can I do to help him learn?

What kind of information or evidence do I need to collect to tell me whether a child is truly learning or not? How do I gather it? Through assessment, through dialogue.

What is the heart of formative assessment?