Unnecessary shift in tense
Unless you have a good reason to do otherwise, stick to a tense:
As the roller coaster stopped, the child became frantic, then starts to laugh and shout, "Again, again!"
Problem and cure: The sentence begins in the past tense, i.e., "stopped" and "became," but shifts to present tense with "starts." One would simply change "starts" to "started" or, if the writer prefers the present tense, one might change "stopped" to "stops" and "became" to "becomes."
This rule applies not only to phrases and sentences, but also to paragraphs and whole papers. Some fiction writers, Faulkner for one, shift tenses for artistic reasons, but most of the papers students write for their classes require a consistent tense.
FYI: Generally, when writing about or referring to a specific text (an essay, a poem, the transcript of a TV show, a web page, a billboard, etc.), one should stick to the present tense, even if it is a very old one. This is sometimes called "historical present":
In his essay "Walking," Thoreau writes that "in Wildness is the preservation of the world."