> In my snowboarding groups, there were usually about five students, no more than ten. We would spend a full day together, and I had time to spend quite a lot o

> In my snowboarding groups, there were usually about five students, no more than ten. We would spend a full day together, and I had time to spend quite a lot of time with each student individually. In my math "exercise" classes, there were up to 25 students. I would see them 3 hours a week (they had other teachers as well). For the same hours of instruction block classes leads to poorer long term recall. Five students is the absolute upper limit of what can be considered tutoring. By the time you have ten students you’re into class teaching where the difference in learning between small and large class sizes exist but are not large enough to justify the greater expense in terms of learning. > Snowboarding students have usually quite similar level of abilities. Of course, some learn faster than others but nobody improves 10 times faster than someone else (which happens in maths). If a student is better, she/he can move to another group the following week (something impossible in my math class). We’ve known the solution to this problem since at minimum 1968 when Mastery based learning was named, and the first research on the topic dates from the 1920s. Don’t let students proceed to topic 2 until they’ve gotten 80 or 90% on a test on topic 1. > As a math teacher, I'm also the one who evaluates them, and who stands between them and their degree. As a snowboarding coach, I'm the one who helps them achieving their goal. Different dynamic. Again, this is a solved problem. AP tests exist. Math contests and the Putnam exist. The Royal Statistical Society used to set exams covering the first year, first two years and entire curriculum of a U.K. statistics degree, which latter was sufficient to get you onto a Master’s programme. They stopped due to lack of demand. Separating teaching and certification exams is not that hard. Apart from differences in native ability Mastery learning and separating certification and teaching functions solves these problems. For whatever reason they’re not widely applied. In a developing nation context with very large classes the UK’s DfID has found that the most cost efficient method of improving education is teaching children by skill level, not age, which looks awfully like mastery based learning. There may be individual university departments that do this. I’m not aware of any. The only institution I know of that does Mastery based learning is Lambda School. It’s hard and requires complete institutional alignment. The closest universities come to it are weed out classes and prerequisites. An economics professor of my acquaintance started requiring calculus for his game theory classes, not because he uses calculus, but because it assured him that all students will be solid in algebra. Looking at what institutions do instead of what they say their aims are they look much more like ranking institutions than teaching ones. Ebbinghaus’ forgetting curve research dates from 1885 and is an educational curiosity rather than a core part of instructional design. Most students forget most of what they’ve learned. If we wanted to teach instead of rank education would look enormously different from what we see in practice.