Who says learning can’t be fun? The summer is a great time for a student to take an elective that he or she doesn’t have time for during the year. Many students gladly opt to take classes in the summer.
The summer before my freshman year of high school I took a theatre class for fun. It was a great way to acclimate to a new school, meet other incoming students, and try something new.
A lot of students take academic classes during the summer so they will have more flexibility in their schedule during the school year. Taking a difficult class during the summer may give students more time to focus on that particular class when they are not taking other classes.
I personally think the summer time should a true "break" from school. Let's face it, unstructured learning (which in the homeschooling world is called "unschooling") is truly where learning really takes place. Why? Because children are allowed to explore freely what they are truly interested in. Imagine trying to pull Thomas Edison away from his inventions only to learn how to read better or study astronomy.
Kids need time to think for themselves while nobody is telling them what direction to go in all the time. Exploring new cities, traveling, museums, libraries, and more offer children time to learn from the environment based on their own curiosity (which will stick and mean more in the end).
Also, believe it or not, kids can come up with creative ideas at home. However, I do feel offering a variety in environments is crucial to well being as well as learning in general. Staying at home 24-7 does not cut the mustard. Children should be exposed to many environments but free to take in and learn what they choose.
I definitely think it's a good idea to incorporate learning into kids' summer activities, however if I tried to send my B-average daughter to summer school, she'd probably kill me. That's why I sent her to SuperCamp last summer. It's a summer camp that is part academics, like speed reading and "math mastery", and part life skills training, like communication, team building, leadership, all in an upbeat, fun, positive atmosphere. My daughter cried on the last day of camp because she didn't want to leave! She did well in school before SuperCamp, but this past year, not only did she get a 3.8, but she tried out for the cheerleading squad (and made it) and ran for class vice president (and won)! And she's going back this year to improve her leadership skills for next year. I honestly can't think of a better summer activity for kids.