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I used to teach maths (undergraduate level) and I was also a snowboarding coach. These two roles aren't really comparable. - In my snowboarding groups, there w

I used to teach maths (undergraduate level) and I was also a snowboarding coach. These two roles aren't really comparable. - 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). - Unlike math students, snowboarding students were all very motivated. Nobody forced them to be there. - 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). - 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. - I'm confident that anyone without disability can learn to be a decent snowboarder after a few weeks of training. But I think that a lot of students don't have what it takes to learn the mathematics curriculum they signed up for, no matter how you teach them.

Alex3917 7y ago
Not sure if you saw the book I linked to in my other comment, but that's the premise: "This book compares how traditional schools can, metaphorically, act like a ski school, which temporarily organizes its students into classes where each student shares a specific and common instructional need but has previously mastered the critical prerequisites that will enable new learning to take place." https://www.amazon.com/General-Systems-Unique-Learning-Schools/dp/1683196309 https://www.amazon.com/General-Systems-Unique-Learning-Schoo...
jacobolus 7y ago
> nobody improves 10 times faster than someone else (which happens in maths). This does not happen in math either. What does happen is some students have significantly more preparation than others (including, for example, introspecting more while doing their homework for several years, playing board games, solving logic puzzles, building with construction toys, ...) and do more or better focused practice during a course. Better-prepared students already know a significant part of the material being presented in a course, have extensively thought about ideas which are similar, or have improved their generic problem-solving skills. They end up stuck behind fewer blocking misconceptions.
- varjag 7y ago
  And the effect is they improve 10 times faster than others who don't do all that.
  - jacobolus 7y ago
    Solving problems faster or comprehending a concept similar to one you already know is not the same as “improving 10 times faster”. Most of the “improvement” is already in the past. In the same way a concert pianist doesn’t “improve 100x faster” than me if he can learn a new song in 6 minutes that takes me 10 hours to learn. In the same way Bill Gates’s savings account doesn’t “improve 1 million times faster” than mine when we both earn interest. The analogy for snowboarding might be taking an experienced snowboarder and a novice, and introducing some new type of obstacle on the slope. The experienced snowboarder will learn how to deal with it much faster than the novice.
    - pdpi 7y ago
      > Solving problems faster or comprehending a concept similar to one you already know is not the same as “improving 10 times faster”. Most of the “improvement” is already in the past. Continuing with the original example — these would be the newbie snowboarders who have prior experience with other board sports.
  - smokeyj 7y ago
    But it’s not “times faster”, it’s a linear function of time..
- gameswithgo 7y ago
  are you suggesting talents does not exist or only that it accounts for much less than factor of ten differences? what expertise or what evidence do you have supporting this belief?
  - jacobolus 7y ago
    There are definitely differences between people (e.g. differences in personality, interests, working memory, focus, emotional control, ...) But my impression is that differences in (a) preparation/trained skills and (b) other context like diet, exercise, amount of sleep, family/relationship stress, illness, .... are more significant. At the least, nearly everyone is capable of successfully handling the standard school curriculum, given a few hours per week of 1:1 tutoring by an expert.
MathematicalArt 7y ago
But I think that a lot of students don't have what it takes to learn the mathematics curriculum they signed up for, no matter how you teach them. This part is simply untrue. The problem with math education is largely one of poor communication between student and teacher. The biggest being that the teacher tends to be unable to sufficiently vary the way they instruct to adapt to the way a particular group of students in a class need to hear it. This is amplified by the fact that most math teachers tend to be frightened by the subject [1]. That fear tends to be passed on from generation to generation despite its irrationality. Thus it persists memetically. Add to this the fact that education has been trending towards standardized testing, and most incentives to create engaging ways of expressing these concepts are actively discouraged if not futile (within the system). Mathematics isn’t something to be “signed up for” in the sense that it is pervasive in every single aspect of our lives. With this being stated, there is an important aside that must be made. People tend to focus on the relationship between the student and the teacher and the failure of communication there. However, there is an equally important chasm that remains hidden in plain sight—the relationship between educators and the academy itself. Mathematicians tend to take pride in performing their research for its own sake without concern for pragmatic applications. While there is merit to performing research without having to immediately justify its utility, that lack of justification should stop at practical applications to feed whatever social machinery is en vogue for the time period. It absolutely is not an excuse to put no effort into communicating what is being worked on in terms that others can understand. Thus we see a lack of empathy and communication from the genesis of mathematical ideas to the ones who find/create[2] those ideas to the ones who must pass that knowledge along to the ones who must absorb and apply this knowledge as students in order to expand their horizons or to simply find food, shelter, and partners for procreation. [1] Calling Mathematics a subject is actually disingenuous since it encompasses so many different ways of thinking, conceptualizing, and expressing. [2] Depending on your point of view, either concepts are “discovered” by the mathematician or they are “created” and did not exist before the creation.
- Mirioron 7y ago
  >The problem with math education is largely one of poor communication between student and teacher. The biggest being that the teacher tends to be unable to sufficiently vary the way they instruct to adapt to the way a particular group of students in a class need to hear it. I'm sure if you spend enough resources on teaching a student to do something then almost every student will eventually get it, but at what point does the amount of resources spent become too much? Just the fact that math classes have 25-40 students each already means the resources we spend are limited and within those constraints it might very well be likely that those kids can't be taught this. It's not like we're suddenly going to get a massive surge in math teachers. >Mathematics isn’t something to be “signed up for” in the sense that it is pervasive in every single aspect of our lives. It might be pervasive, but most people could go through their life without learning half the mathematics that they do in school. I think studying mathematics is important to learn ways of thinking, but I also recognize that, in practice, most people have little need for most mathematics they learn.
joe_the_user 7y ago
As a PE student, I have only taken large classes where the teachers barely gave any attention. I did, however, take an undergraduate honors seminar where there were seven self-selected students all of whom were there voluntarily and who got individual attention from the professor. So I think both sorts of dynamics exist in the university (though formal HS probably does little to no "coaching" type activity and math stars coach each other in high school math teams). I don't think very many folks who were herded into the PE classes I've taken learned that much and everyone in the honors undergraduate seminar learned a lot. I can't prove that anyone who wants to can learn strong math but I don't think the results of a typical mass-level math class proves much about this either way. (I too, have taught your typical average crappy undergraduate math class).
mac01021 7y ago
I've always thought it would be better if teaching and evaluation were done by separate people.
- pbhjpbhj 7y ago
  In what respect. During teaching you constantly have to evaluate your students to establish feedback so you can adjust your teaching. Evaluation is an inherent part of teaching. IME high-school teachers (my parents, wifes parents, and all my parents friends are teachers) could always predict the grade a student would get -- though sometimes public predictions were given differently as a motivator "you need to put a bit more effort in to get a C [minimum pass many employers used to look for]". Maybe if you're seeking objectivity?
- closeparen 7y ago
  That's what standardized testing is. It has a bad failure mode where the curriculum starts to cater to the evaluator instead of the teacher's pedagogical needs.
icegreentea2 7y ago
I think these types of reflection (both in the original opinion piece and your response) are useful because they highlight two very different perspectives to the situation. Urschel's opinion piece points out how the two different systems treated him as an individual differently. He wonders (rightfully) what a world where the type of individual attention and energy that he was able to receive in football could be also received in mathematics. This is a very microscale discussion. Your response (and many others) point out that on the macroscale, the two systems are incredibly different. But I feel that a lot of the macroscale differences aren't nessecary inherent. Like, they might be super baked in through path dependence, but they aren't intrinsic to the "platonic ideal" of producing football players and mathematicians.
- ghaff 7y ago
  >macroscale differences aren't [necessarily] inherent. That's true up to a point. In general, phys ed classes/requirements in high school and university aside, if you're a thoroughly so-so team athlete in general, society is mostly perfectly fine with programs that strongly prioritize attention on the gifted. To some degree this happens with academics at the university level. But in high school there's an, if not zero sum something close to, tradeoff between focusing on the students who are more motivated and/or have seemingly more aptitude for certain subjects vs. focusing resources on mainstream or even struggling students.
- closeparen 7y ago
  Whatever K12 math education is aimed at, I don't think it can possibly be "producing mathematicians." Producing human computers, maybe.
  - wcarey 7y ago
    I've long suspected that K-12 math was designed as vocational training for the job "computer", which was a common job in the defense industry prior to its replacement by electromechanical and digital computers. For example, the computation of the firing tape measures for US artillery in WW2 would require enormous, precise calculations of just the sort that one practices in K-12 mathematics.
chrisseaton 7y ago
> Unlike math students, snowboarding students were all very motivated. Nobody forced them to be there. Who's forcing anyone to do an undergraduate maths degree? And who does a degree in maths without being extremely motivated?
- DanBC 7y ago
  > Who's forcing anyone to do an undergraduate maths degree? People are forced to do maths classes as part of other degree courses.
alexashka 7y ago
The entire point of the article is to make them more comparable. Learning the basics of snowboarding is the equivalent of learning how to count or do basic arithmetic. Most everyone is capable of counting and finds it immediately useful, as soon as they have money and see prices of things. You're comparing snowboarding 101 to advanced math, of course they're different. Most people will not be able to do advanced snowboarding either, nor will they be motivated to do it.
bsder 7y ago
In addition, coaches "cut" those who don't make the grade. This allows them to focus attention on those who already have some aptitude. And we're not even talking about the fact that they feed steroids to those at the top (220 pounds in high school--not bloody likely without some major chemical enhancement).
svat 7y ago
This comment seems a reply to the headline more than to the article. And given that headlines are almost never chosen by the authors of articles, it may be worth coming up with an alternative headline to the article. As I read it, the article is the author mentioning that as a student he had a poor idea of what professional mathematicians did, that he received a lot of encouragement from his athletic coaches but not math teachers, and finally wishing that as a kid he knew what excitement was possible from mathematics. So if I were picking a title for the article I might choose “I wish math students got the kind of motivation [from their teachers] that athletic students get [from their coaches]”. (This is wordy and poor as a headline of course, but it's probably a better reflection of the article.) How much of the differences you mention affect these points, do you think? That might be more illuminating.
learnstats2 7y ago
> I'm also the one who evaluates them... different dynamic. This is major difference from my experience. My math students are examined externally so I'm the one helping them achieve their goal. My experience of teaching math is more similar to your experience of teaching snowboarding. Your last point drives this home - in my experience, anyone around average intelligence can ace school math if they have a coach who helps them approach it in the right way.
barry-cotter 7y ago
> 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.
staticvoidmaine 7y ago
It feels to me that you are really just bringing a fixed mindset to the equation. I think the world could stand to adopt more of a growth mindset, especially when it comes to learning math as I think football coaches focus more on improvement and growth as an individual and a team whereas many math teachers such as yourself seem to focus on whether you can or you can't learn math.
de_watcher 7y ago
We had a school where math was the focus. So half of the whole time was dedicated to the math classes. And students were motivated because they've come there for exactly that.

Alex3917 7y ago

Not sure if you saw the book I linked to in my other comment, but that's the premise: "This book compares how traditional schools can, metaphorically, act like a ski school, which temporarily organizes its students into classes where each student shares a specific and common instructional need but has previously mastered the critical prerequisites that will enable new learning to take place." https://www.amazon.com/General-Systems-Unique-Learning-Schools/dp/1683196309 https://www.amazon.com/General-Systems-Unique-Learning-Schoo...

jacobolus 7y ago

> nobody improves 10 times faster than someone else (which happens in maths). This does not happen in math either. What does happen is some students have significantly more preparation than others (including, for example, introspecting more while doing their homework for several years, playing board games, solving logic puzzles, building with construction toys, ...) and do more or better focused practice during a course. Better-prepared students already know a significant part of the material being presented in a course, have extensively thought about ideas which are similar, or have improved their generic problem-solving skills. They end up stuck behind fewer blocking misconceptions.

varjag 7y ago
And the effect is they improve 10 times faster than others who don't do all that.
- jacobolus 7y ago
  Solving problems faster or comprehending a concept similar to one you already know is not the same as “improving 10 times faster”. Most of the “improvement” is already in the past. In the same way a concert pianist doesn’t “improve 100x faster” than me if he can learn a new song in 6 minutes that takes me 10 hours to learn. In the same way Bill Gates’s savings account doesn’t “improve 1 million times faster” than mine when we both earn interest. The analogy for snowboarding might be taking an experienced snowboarder and a novice, and introducing some new type of obstacle on the slope. The experienced snowboarder will learn how to deal with it much faster than the novice.
  - pdpi 7y ago
    > Solving problems faster or comprehending a concept similar to one you already know is not the same as “improving 10 times faster”. Most of the “improvement” is already in the past. Continuing with the original example — these would be the newbie snowboarders who have prior experience with other board sports.
- smokeyj 7y ago
  But it’s not “times faster”, it’s a linear function of time..
gameswithgo 7y ago
are you suggesting talents does not exist or only that it accounts for much less than factor of ten differences? what expertise or what evidence do you have supporting this belief?
- jacobolus 7y ago
  There are definitely differences between people (e.g. differences in personality, interests, working memory, focus, emotional control, ...) But my impression is that differences in (a) preparation/trained skills and (b) other context like diet, exercise, amount of sleep, family/relationship stress, illness, .... are more significant. At the least, nearly everyone is capable of successfully handling the standard school curriculum, given a few hours per week of 1:1 tutoring by an expert.

MathematicalArt 7y ago

But I think that a lot of students don't have what it takes to learn the mathematics curriculum they signed up for, no matter how you teach them. This part is simply untrue. The problem with math education is largely one of poor communication between student and teacher. The biggest being that the teacher tends to be unable to sufficiently vary the way they instruct to adapt to the way a particular group of students in a class need to hear it. This is amplified by the fact that most math teachers tend to be frightened by the subject [1]. That fear tends to be passed on from generation to generation despite its irrationality. Thus it persists memetically. Add to this the fact that education has been trending towards standardized testing, and most incentives to create engaging ways of expressing these concepts are actively discouraged if not futile (within the system). Mathematics isn’t something to be “signed up for” in the sense that it is pervasive in every single aspect of our lives. With this being stated, there is an important aside that must be made. People tend to focus on the relationship between the student and the teacher and the failure of communication there. However, there is an equally important chasm that remains hidden in plain sight—the relationship between educators and the academy itself. Mathematicians tend to take pride in performing their research for its own sake without concern for pragmatic applications. While there is merit to performing research without having to immediately justify its utility, that lack of justification should stop at practical applications to feed whatever social machinery is en vogue for the time period. It absolutely is not an excuse to put no effort into communicating what is being worked on in terms that others can understand. Thus we see a lack of empathy and communication from the genesis of mathematical ideas to the ones who find/create[2] those ideas to the ones who must pass that knowledge along to the ones who must absorb and apply this knowledge as students in order to expand their horizons or to simply find food, shelter, and partners for procreation. [1] Calling Mathematics a subject is actually disingenuous since it encompasses so many different ways of thinking, conceptualizing, and expressing. [2] Depending on your point of view, either concepts are “discovered” by the mathematician or they are “created” and did not exist before the creation.

Mirioron 7y ago
>The problem with math education is largely one of poor communication between student and teacher. The biggest being that the teacher tends to be unable to sufficiently vary the way they instruct to adapt to the way a particular group of students in a class need to hear it. I'm sure if you spend enough resources on teaching a student to do something then almost every student will eventually get it, but at what point does the amount of resources spent become too much? Just the fact that math classes have 25-40 students each already means the resources we spend are limited and within those constraints it might very well be likely that those kids can't be taught this. It's not like we're suddenly going to get a massive surge in math teachers. >Mathematics isn’t something to be “signed up for” in the sense that it is pervasive in every single aspect of our lives. It might be pervasive, but most people could go through their life without learning half the mathematics that they do in school. I think studying mathematics is important to learn ways of thinking, but I also recognize that, in practice, most people have little need for most mathematics they learn.

joe_the_user 7y ago

As a PE student, I have only taken large classes where the teachers barely gave any attention. I did, however, take an undergraduate honors seminar where there were seven self-selected students all of whom were there voluntarily and who got individual attention from the professor. So I think both sorts of dynamics exist in the university (though formal HS probably does little to no "coaching" type activity and math stars coach each other in high school math teams). I don't think very many folks who were herded into the PE classes I've taken learned that much and everyone in the honors undergraduate seminar learned a lot. I can't prove that anyone who wants to can learn strong math but I don't think the results of a typical mass-level math class proves much about this either way. (I too, have taught your typical average crappy undergraduate math class).

mac01021 7y ago

I've always thought it would be better if teaching and evaluation were done by separate people.

pbhjpbhj 7y ago
In what respect. During teaching you constantly have to evaluate your students to establish feedback so you can adjust your teaching. Evaluation is an inherent part of teaching. IME high-school teachers (my parents, wifes parents, and all my parents friends are teachers) could always predict the grade a student would get -- though sometimes public predictions were given differently as a motivator "you need to put a bit more effort in to get a C [minimum pass many employers used to look for]". Maybe if you're seeking objectivity?
closeparen 7y ago
That's what standardized testing is. It has a bad failure mode where the curriculum starts to cater to the evaluator instead of the teacher's pedagogical needs.

icegreentea2 7y ago

I think these types of reflection (both in the original opinion piece and your response) are useful because they highlight two very different perspectives to the situation. Urschel's opinion piece points out how the two different systems treated him as an individual differently. He wonders (rightfully) what a world where the type of individual attention and energy that he was able to receive in football could be also received in mathematics. This is a very microscale discussion. Your response (and many others) point out that on the macroscale, the two systems are incredibly different. But I feel that a lot of the macroscale differences aren't nessecary inherent. Like, they might be super baked in through path dependence, but they aren't intrinsic to the "platonic ideal" of producing football players and mathematicians.

ghaff 7y ago
>macroscale differences aren't [necessarily] inherent. That's true up to a point. In general, phys ed classes/requirements in high school and university aside, if you're a thoroughly so-so team athlete in general, society is mostly perfectly fine with programs that strongly prioritize attention on the gifted. To some degree this happens with academics at the university level. But in high school there's an, if not zero sum something close to, tradeoff between focusing on the students who are more motivated and/or have seemingly more aptitude for certain subjects vs. focusing resources on mainstream or even struggling students.
closeparen 7y ago
Whatever K12 math education is aimed at, I don't think it can possibly be "producing mathematicians." Producing human computers, maybe.
- wcarey 7y ago
  I've long suspected that K-12 math was designed as vocational training for the job "computer", which was a common job in the defense industry prior to its replacement by electromechanical and digital computers. For example, the computation of the firing tape measures for US artillery in WW2 would require enormous, precise calculations of just the sort that one practices in K-12 mathematics.

chrisseaton 7y ago

> Unlike math students, snowboarding students were all very motivated. Nobody forced them to be there. Who's forcing anyone to do an undergraduate maths degree? And who does a degree in maths without being extremely motivated?

DanBC 7y ago
> Who's forcing anyone to do an undergraduate maths degree? People are forced to do maths classes as part of other degree courses.

alexashka 7y ago

The entire point of the article is to make them more comparable. Learning the basics of snowboarding is the equivalent of learning how to count or do basic arithmetic. Most everyone is capable of counting and finds it immediately useful, as soon as they have money and see prices of things. You're comparing snowboarding 101 to advanced math, of course they're different. Most people will not be able to do advanced snowboarding either, nor will they be motivated to do it.

bsder 7y ago

In addition, coaches "cut" those who don't make the grade. This allows them to focus attention on those who already have some aptitude. And we're not even talking about the fact that they feed steroids to those at the top (220 pounds in high school--not bloody likely without some major chemical enhancement).

svat 7y ago

This comment seems a reply to the headline more than to the article. And given that headlines are almost never chosen by the authors of articles, it may be worth coming up with an alternative headline to the article. As I read it, the article is the author mentioning that as a student he had a poor idea of what professional mathematicians did, that he received a lot of encouragement from his athletic coaches but not math teachers, and finally wishing that as a kid he knew what excitement was possible from mathematics. So if I were picking a title for the article I might choose “I wish math students got the kind of motivation [from their teachers] that athletic students get [from their coaches]”. (This is wordy and poor as a headline of course, but it's probably a better reflection of the article.) How much of the differences you mention affect these points, do you think? That might be more illuminating.

learnstats2 7y ago

> I'm also the one who evaluates them... different dynamic. This is major difference from my experience. My math students are examined externally so I'm the one helping them achieve their goal. My experience of teaching math is more similar to your experience of teaching snowboarding. Your last point drives this home - in my experience, anyone around average intelligence can ace school math if they have a coach who helps them approach it in the right way.

barry-cotter 7y ago

> 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.

staticvoidmaine 7y ago

It feels to me that you are really just bringing a fixed mindset to the equation. I think the world could stand to adopt more of a growth mindset, especially when it comes to learning math as I think football coaches focus more on improvement and growth as an individual and a team whereas many math teachers such as yourself seem to focus on whether you can or you can't learn math.

de_watcher 7y ago

We had a school where math was the focus. So half of the whole time was dedicated to the math classes. And students were motivated because they've come there for exactly that.