Changing State of Oval When User Clicks on Button on Another Slide

Based on the title of your post, the button that changes the variable is on a separate slide from where the ovals are. That's the problem. Storyline can't change something from a distance (that is, from another slide). When you go to the slide with the oval, the "when variable changes" never happens. All triggers need a "when" that occurs on the slide where the trigger is.

Variables are available from all slides. To fix your problem, edit the triggers to change the state of the oval when the timeline of that slide starts, and include a condition that checks the value of the variable. 

BTW, you only need 1 variable per term. Just use a T/F variable, set to True for correct and False for incorrect. Then the trigger to change the associated oval would look something like this: