Now, I've heard that it takes time for children to understand the big picture. When we are very young, we see the world as it is and take things as they come... from a sensor's perspective. Our ability to make connections and extrapolate comes from our knowledge and experience. It can only increase with time. Unless you're some sort of crazy child-prodigy, of course.
I don't really know how to determine whether one is a sensor or an intuitor when one is a just a child but I can see a difference between my twin brother (ISTP) and I for example. We both were "ITP" children.
Questions I asked as a child : (more or less like that)
-Do you have many layers of thoughts ? (I pictured my brain as a spaceship with huge tanks filled with fluorescent water and people giving different layers of thoughts.)
-What if I wasn't born ? Would I be the thoughts of somebody else or would I be nothing ?
-Could I have been inside the brain of someone else with different thoughts ?
-Why do people draw the sky as a blue thing on top of a page when it's all around us and transparent when we're in it ?
-Are we controled by somebody else who makes us think we are real ?
-What's around the universe ?
--> Annoying little girl with vivid imagination.
Questions my brother asked (he was rather quiet) :
-How does it work ?
-What is this ?
--> Curious little boy who wants to know and understand.
Both : Why ? (which is apparently typical of children).
I was a leader in imaginative plays and story telling. Known to be disconected from the real world (dreamer, observer).
He learned things and experimented them (measure of angles, water boiling, etc) - a doer (builder, destroyer).
We were both into science though. I started to be into psychology and philosophy at 12, he grew out of the questionning thing and favour pratical use over theories though he needs them.
There are still things we both had decided to learn by ourselves (like most people I guess) and I assume that he was perhaps more intuitive than me in that he had understood that one could read silently and I didn't (or I was extremely dumb and annoying).
What can we tell ? That children are curious for different things and need to learn but can imagine other possibilities than what's in front of them and can be sensed.
What I do think is that everyone needs experience, whether you are a sensor or an intuitor. You can't just use one of the function, you have a dominant function but you can't live in this world being a purely sensing being or a purely intuitive being (an idea ?). This wouldn't make sense.
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I've noticed differences in the young children I work with, some may be more likely to be sensors than others, they are all rather immature (which is normal) and not really stable yet because they haven't developped their abilities but I think some might be more intuitive than other from a young age. Some are more likely to have their own world than others. Some accept everything the teacher tell them, some argue. Is it because of their functions ?
Though, honestly, it's not even easier to determine properly the I/E thing, some may be in a crowd of friends but still be secretely Introverts.
Perhaps personality is determined at birth, but it does develop over time and is influenced by what we go through, functions are just a part of our personality by the way.