Step 1: Read the question.
We must find the method that gives the maximum participation of students.
Step 2: The learning principle.
Modern teaching favours active learning, where students learn by doing rather than by only listening.
Step 3: What activity based method is.
In the activity based method, students take part directly through experiments, projects, group work, role plays, and problem solving.
Step 4: Why participation is highest.
Here students are active doers, not passive listeners. Every student gets to take part, so involvement is the greatest.
Step 5: Check the other methods.
The historical, lecture, and deductive methods are mostly teacher led, so students stay more passive.
Step 6: Final answer.
Maximum participation comes through the activity based method.
\[ \boxed{\text{Activity based method.}} \]