Continuously vs. discontinuously
In this issue, the main question, which is important for the observation is: "How does the development creature proceed?"
When we talk about discontinuously development, we talk about a qualitative change in the bahavior. To illustrate this more efficiently we can think about the logic of a child. When a child is at the age of 5 it would give different answers to questions than it would in it's teenage years. A child would identify peace as to not hurt a friend, which is in this case a non abstract answers. But laterly this same child can tell us that for example peace is harmony or a world without war etc. when it grew up to a teenager. This would be a logical and abstract answer.
The development here is qualitative and discontinuously, because the child has an step to step development, where the change of it's logic takes time and becomes completely different in contrast to how it was before.
On the other hand, there is the continuously development. This kind of development is quantative and has a straight linear change (incrementally).
In this case, we can think about the idea, that children learn continuously new abilities and skills, which gives them a quantitative rise of the things they know, which affects on their development.