If you say or smile something patronizingly, you do it in that looking-down way — slowly, sweetly, or with a little laugh — as if the other person could not possibly keep up. It is the same idea as patronizing, but this word is an adverb: it tells you how they spoke or acted, not what kind of person they are named as. “He was patronizing” describes him. “He explained it patronizingly” describes the explaining. Students often have the feeling already (“她用那種把人當小孩的口氣”) and only need the English handle for the how. Same spelling fork as the adjective: American English usually keeps the z (patronizingly); British English often writes patronisingly.