Piaget's theories are very much rooted in learning about the physical world, and are thus more popular amongst teachers in the 'STEM' disciplines. The other foundational researcher in constructivism was Lev Vygostky, who worked in the Soviet Union under Stalin, and his theories reflect the political pressures of that environment; his earlier work remains influential especially amongst humanities teachers, whereas his later work is excessively ideological.
Piaget proposed a stage-based model of development, in which children progress through four different stages of cognition. The last two stages he called the concrete operational stage and the formal operational stage. In the concrete operational stage, children become capable of one layer of abstraction or symbolic indirection; it is not until they reach the formal operational stage that they are capable of multiple layers of abstraction or symbolic indirection.
It is interesting to note that Piaget suggested that the transition between these two stages usually occurs around the age of eleven, which is when British children transition from primary to secondary school.
So, to contextualise the linked article, the studied children developed an applied understanding of mathematics that fit their concrete operational cognition: the mental operations were readily made concrete by manipulating coins and banknotes.
However, when children study mathematics in school, it is very much done as formal operations: the numbers are not intended to represent anything physical at all. Consequently, many children learn mathematics as a set of arcane rituals for manipulating symbols on paper, because they can't yet understand the abstract meanings of those symbols.
Piaget's theory on Wikipedia: https://en.wikipedia.org/wiki/Jean_Piaget#Theory
Paul Lockhart writes something parallel to this argument in A Mathematician's Lament: https://archive.org/details/AMathematiciansLament/mode/2up