For the USA, it changes all around the country. Not even in one state does school have to start at the same time as another in that state. Typically, school ends sometime in May or June and opens sometime in August or September.

It depends in which country you are and summer doesn't fall in the same months in all countries, you know basic knowledge ,the earth is round and so ;) Usually you would think of a period from June to September,it is indeed in many countries the case,but for example : In Nigeria, summer vacation begins on December 1 and ends on February 2. Students also take a winter break (June–July), and spring break (October). In Russia, summer vacation starts on May 25 (for 1st–8th and 10th grades) and usually end on September. In Singapore, depending on the school, the vacation starts in late November and ends on January 2 the next year.

In Australia schools close from Dec 19- January 31st for summer holidays

Grammatically speaking, the question should be rephrased as "Do schools close during summer all over the world?"

Are you an alien? Yes, of course they are closed.