Teachers in this country have generally been trained either to approach mathematics like a creative activity or that they should force students to memorize rules and principles without truly understanding how to apply them.
The original sentence incorrectly pairs an infinitive ("to approach") with a clause ("that they should...") in the construction "either X or Y." Moreover, the use of "like" in the phrase "to approach mathematics like a creative activity" is incorrect. “Like” is used to compare the similarities between things, while “as” is used in comparisons that show equality. In this case, mathematics is a creative activity; thus, “as” is necessary.
(A) This choice is incorrect as it repeats the original sentence.
(B) While this choice does contain proper parallel structure, it incorrectly uses "like" instead of "as" in the phrase "to approach mathematics like a creative activity".
(C) CORRECT. The construction "either X or Y" requires parallelism between X and Y. In choice C, X and Y are parallel infinitive phrases ("to approach . . ." and "to force . . .").
(D) While this choice does create a parallel construction, it awkwardly begins the parallel elements with the words "that they" instead of the infinitive "to." Moreover, this choice incorrectly uses "like" instead of "as" in the phrase "to approach mathematics like a creative activity".