Explanation
Correct answer: A.
Choice A is the best answer. The convention being tested is punctuation use between sentences. This choice correctly uses a period to mark the boundary between one sentence ("The pedagogy...tenets") and another ("Developed...‘March in G’"). The participial phrase "developed by Japanese violinist Shinichi Suzuki" modifies the subject of the next sentence, "the method."
Why the other choices are wrong
Choice B
Choice B is incorrect because it results in a run-on sentence. The sentences ("The pedagogy...tenets" and "Developed...‘March in G’") are fused without punctuation and/or a conjunction.
Choice C
Choice C is incorrect because it creates a confusing and illogical sentence structure. The relative pronoun "that" followed by a comma can’t be used in this way to mark the boundary between sentences.
Choice D
Choice D is incorrect because it results in a comma splice. A comma can’t be used in this way to mark the boundary between sentences.