The basic capability for formal operations sets in much earlier.
I think it depends. The wikipedia page says that the onset is between 11 and 20 years or so.
My aptitude in mathematics was a bit above average when I was 11 years old. Maybe I had already met the criterion for the formal operation stage, despite not doing well in math the first couple years of high school. But something significant happened when I was 17, and it seemed to be a qualitative change in the way I understood mathematics. I also seemed to be developed the ability to excel in Algebra (with motivated effort) later than my peers. Perhaps it wasn’t a specific stage identified by Piaget, but it felt physical/neurological.
I do think Piaget is considered outdated. He might have gotten some of the details wrong or its not the whole story. (For example, I’m skeptical that babies ever lack object permanence.) Nevertheless, Piaget is likely correct that certain concepts develop in stages that are timed with physical development.
I think it depends. The wikipedia page says that the onset is between 11 and 20 years or so.
My aptitude in mathematics was a bit above average when I was 11 years old. Maybe I had already met the criterion for the formal operation stage, despite not doing well in math the first couple years of high school. But something significant happened when I was 17, and it seemed to be a qualitative change in the way I understood mathematics. I also seemed to be developed the ability to excel in Algebra (with motivated effort) later than my peers. Perhaps it wasn’t a specific stage identified by Piaget, but it felt physical/neurological.
I do think Piaget is considered outdated. He might have gotten some of the details wrong or its not the whole story. (For example, I’m skeptical that babies ever lack object permanence.) Nevertheless, Piaget is likely correct that certain concepts develop in stages that are timed with physical development.