Straight-facedly is the -ly form of straight-faced: it describes HOW someone does something, namely with a still, unsmiling face while saying something funny or untrue. 'He announced straight-facedly that the meeting would last nine hours.' Honestly, though, I have to tell you the truth about this word: almost nobody writes it. It exists, it is correct, and you may meet it in a book — but it is long and awkward in the mouth, and English speakers reach for other ways to say the same thing. They say with a straight face, or keeping a straight face, or they simply use the adjective: 'he was straight-faced about it'. So learn it to recognise it, not to use it. If your student wants to say this idea in their own writing, teach them 'with a straight face' — that is the natural English, it is short, and every reader knows it.

面不改色地、板著臉不笑地（做某事的樣子）。這個字其實極少人用；台灣學生要表達這個意思，用 with a straight face（一臉正經地、憋著笑地）才自然。