It seems likely that no one taught those students how to think about math.
I.e. teaching students the steps to solve a math problem is not teaching them how to think about the problem.
I instantly knew 12/13 + 7/8 was ~2 because I visualize two pie charts in my head, both of which are mostly full. This is in contrast to the other way to solve the problem, converting the fractions to a common denominator and then dividing by the denominator. It would take me some time to do the latter, whereas I can instantly do the former.
I don't think the students who got that wrong (nor some who got it right) do any kind of visualization in their heads.
Teachers need to realize that it's the operations in the head that count the most, not rote memorization of steps to solve a problem.
I.e. teaching students the steps to solve a math problem is not teaching them how to think about the problem.
I instantly knew 12/13 + 7/8 was ~2 because I visualize two pie charts in my head, both of which are mostly full. This is in contrast to the other way to solve the problem, converting the fractions to a common denominator and then dividing by the denominator. It would take me some time to do the latter, whereas I can instantly do the former.
I don't think the students who got that wrong (nor some who got it right) do any kind of visualization in their heads.
Teachers need to realize that it's the operations in the head that count the most, not rote memorization of steps to solve a problem.