Around age 11 or 12, thinking crosses into Piaget's formal-operational stage — the mind can now juggle abstract, hypothetical “what if” ideas and test them systematically. Here is Inhelder & Piaget's classic proof: what makes a pendulum swing faster? Set up the two pendulums, then release them — but to actually prove anything, you must run a fair test.
Two pendulums
The blue and coral counters tick up once per full swing. If they drift apart, the change you made mattered; if they stay locked together, it didn't.
The pendulum problemwhich variable sets the swing rate?