Step 1: Identify the key clue.
Children $discover$ and acquire knowledge on their own $without\ special\ guidance$. We must name this method.
Step 2: Recall the root word.
The word heuristic comes from the Greek $heuriskein$, meaning to discover. This is a strong hint.
Step 3: Check the Project Method.
It uses structured group work toward a goal, so it is guided, not free discovery. Ruled out.
Step 4: Check the Dalton Method.
It works through assignments and contracts with set targets, again guided. Ruled out.
Step 5: Check the Play-way Method.
It teaches through play and games, which is not the same as independent discovery of knowledge. Ruled out.
Step 6: Confirm the Heuristic Method.
Only the heuristic method places the child in the role of a self-reliant discoverer with minimal teacher help, matching the question exactly.
Step 7: State the answer.
So the method described is heuristic.
\[ \boxed{\text{C. Heuristic Method}} \]