My son is supposed to correct this incorrect sentence:

He performed the backward somersault more expertlier of all.
According to the rules, part of the sentence should be changed to:
most expertly of all
This sounds strange to me. Did he do it correctly? If not, would you please give me a rule to guide him?

The suffix -er is not used when you use the words more or most. The correct adverb is most because you're comparing more than two performances.

When comparing two items, use the comparative.. er as in taller or more as in more beautiful. John is taller than Henry. My dog is more beautiful than yours is.

When comparing more than two items, use the superlative. est as in tallest or most as in most beautiful.

John is the tallest boy on the team.
My dog is the most beautiful in the dog show.

Check this site.
http://www.uottawa.ca/academic/arts/writcent/hypergrammar/compsupl.html

Your son did not correct the incorrect sentence accurately. The rule to guide him in correcting the sentence is to use "most expertly" instead of "more expertlier."

Comparative adjectives, such as "more" + adjective or -er endings (like "expertlier"), are used to compare two things. On the other hand, superlative adjectives, such as "most" + adjective or -est endings, are used to compare three or more things.

In the sentence, "He performed the backward somersault more expertlier of all," the superlative form should have been used because it is comparing the backward somersault to the performance of all others. So, the correct correction would be: "He performed the backward somersault most expertly of all."

Therefore, by using "most expertly" instead of "more expertlier," you are following the rule of using the superlative form when comparing more than two things.