American children perform more poorly in athletic tests of speed, strength, and endurance than do their European contemporaries.
Simple rule to remember: Comparison is always between similar things. For example, in this questions American children are being compared to European contemporaries.
The pronoun "their" is correct as it unambiguously refers to plural American children.
As the subject is plural, the plural verb "perform" is correct.
The three elements speed, strength, and endurance are logically as well as grammatically parallel.
Therefore the sentence is correct as is.
A American children perform more poorly in athletic tests of speed, strength, and endurance than doB The American child performs more poorly in athletic tests of speed, strength, and endurance as
doesC American children perform more poorly in athletic tests of speed, strength, and endurance than
doesD The American child performs more poorly in athletic tests of speed, strength, and endurance as
doE The American child performs more poorly in athletic tests of speed, strength, and endurance than
doSee the choices:
The choices A, D, and E use plural verb "do" correctly as the subject is plural as discussed above. But choices D and E changed the plural verb "perform" to singular verb "performs" which is incorrect.
The choices B and C use singular verb for plural subject.