だんだん

だんだん means "gradually": a change happens bit by bit over time, not all at once. It goes before the verb that describes the change, most often なるafter an adjective.

With ～てくる and ～ていく

だんだん often comes with 〜～てくる, for a change that has been building up to now, or 〜～ていく, for one that continues from now on.

だんだん, 少しずつ and どんどん

だんだん describes a change of state. すこしずつ少しずつ also works with an action done a bit at a time, so only 少しずつ fits a verb like 食べる. どんどん is a change or a series that goes fast and keeps going.

• × だんだん食べてください → 少しずつ食べてください