Students learn mathematics best when they construct their own mathematical understanding.
Learning mathematics requires special ability, which most student do not have. In other countries, students, parents, and teachers all expect that most students can master mathematics if only they work hard enough. All students must have the opportunity to learn mathematics. Years of teachers' and students' time were spend trying to remediate children who lacked this ability. But research shows that repeating the same uninteresting tasks in the same unimaginative way is not effective.