Maybe the problem here is just the word “declare.” As you say, since WWII that declaration has evolved into a formalism and the real power to actually engage in a war is the President’s under the constitutional commander-in-chief power. (Putting aside what ought to be the rule and just being descriptive here.)

So it’s a good thing you added “according to the constitution” to the text of your question. If you hadn’t, maybe those students would be correct, or at least deserve credit for the answer…