I was taught "numeral" in the New Math era, and if you had asked me in my youth what it meant, I would have probably replied, "What? You mean like zero through nine?" In my mind, I would have been thinking of the graphemes for zero through nine rather than the words or numbers, although I would not have had the pedantic precision to express that thought.
"Number" meant to me any quantity, whether numbers with units (signifying length, area, weight, money, etc.) or not. The fact that you could equate different numbers — eight quarters are two dollars — was just a cool game you could play with numbers.
Thus, "numeral" meant for me (and still does) the tokens used to express numbers (in the decimal system at first, and later in other bases). "Numeral" did not mean, nor does it now, "a word that describes a numerical quantity." If pressed, I would say that such a word is called the name of the number, but that's me searching for the nearest word I could quickly come up with. But I would not say that "zero point nine repeating," which describes the number 1 in the real-number decimal system, is the name of 1. The name of 1 is "one." The "digits of a number," which phrase I also learned in school, meant the (sequence of) numerals used to express the number. "A decimal point followed by infinitely many nines," for example.
Later, study in mathematics, computer science, and linguistics challenged some aspects of these conceptualizations for me. They allowed me to talk about numbers with enough pedantic precision (1) to wonder whether I'm speaking the same language as the rest of English-speaking Americans and (2) to be wrong instead of sort-of-right, esp. with regard to linguistics. Back to Feynman's execration of pedantic precision, excessively precise language does not sound like ordinary English to most teenagers in the U.S. It makes them doubt what you are saying, which is the opposite of what you're hoping to achieve.
In mathematics, there are (it seems to me, if I'm not making a linguistics gaffe) different language-games for talking about "numbers." A discussion sometimes begins switching between them until the speakers find a common language-game. For instance, speaking with a student beginning calculus versus talking with someone who has had real analysis.
Finally, with respect to an implicit question in the OP's statement, "I believe that for this lack of terminology children are very likely to believe that a number is nothing more than a scribble on a piece of paper." Coincidentally, yesterday I was talking with a neuroscientist about mathematical concept development. It's not their area, and I was just looking for pointers on how to find out what is known. They made the point that there is evidence that the concepts that are learned early, even if not mastered, form a framework on which future knowledge will be built. Early learning informs their later learning. And those who are taught mathematical concepts underlying arithmetic do better later than those who are taught only how to do arithmetic, even if the ones taught concepts are not as proficient at calculating. So the question of whether a certain term could help lay a good foundation for understanding the concept of number seems important. I don't know that such a question has been investigated, so I can't give a scientific answer to it.
