The following refers to the school system in Germany, it may be different in other countries:
In my opinion, one really bad heuristic happens in elementary school, when children learn arithmetics with natural numbers. They learn that addition and subtraction are two entirely different things, because they are taught $a+b=b+a$ but $a-b\neq b-a$. Thus addition is commutative, and subtraction is not. At that level, numbers are solely understood as enumerations of objects.
Then they learn about numbers with units, such as lengths or prices or weights. Also they learn that numbers might have geometric meaning, e.g. as lengths of line segments. But still no concept of negative numbers.
Years later, when they finally get to know negative numbers as well, they have so much incorporated that subtraction is something different from addition that they have difficulties to grasp that $a-b=a+(-b)=(-b)+a$, i.e. that subtraction is nothing else than addition of a negative number.
I think that postponing negative numbers so long is a mistake, and that children in elementary school would very well be capable to understand them.