Step 1 - Remembering systems
a) open system: may exchange both energy and matter with its surroundings
b) closed system: may exchange only energy with its surroundings
c) isolated system: may exchange none. The universe taken as a whole is an example of an isolate system.
Step 2 - A glowstick is thus...?
If we heat a glowstick, its temperature will be raised. If we freeze it, its temperature will decrease. These are examples of heat exchange and, therefore, of energy exchange.
On the other hand, there's no way we can add matter to it, unless we break the glowstick (then it becomes a completely different system).
Therefore, a system that can exchange energy but not matter is a closed system.
Answer: glowsticks are closed systems