Personally, I think the quality of teachers, school reputation, and facilities should be the deciding factor for parents in choosing which schools their children should be educated in.

deciding 是动词 decide 的现在分词形式，decide 意思是"决定、判定"。在这里 deciding 作为形容词使用，表示"决定性的、关键的"。 factor 是名词，意思是"因素、要素"，指影响结果或决策的各种条件或变量。 deciding factor 指在多个因素中起决定性作用的关键因素，也就是最终影响决策的最重要因素。