CHE: "The Divider" (math education)

[marshwiggle]

We don't need to optimize for teaching the most talented kids as fast as possible, because the super bright kids usually end up learning what they need eventually anyway. This is obvious in every physics course I've taught across all levels freshman-PhD and also my personal experience.

IMO segregating students based on ability has its place, but it generally leads to worse social skills, less capability for teamwork and leadership, and reinforcing negativity for the low performers. So if we want to do it, gonna need a better argument than the best students will learn slightly slower.

In my experience, lab partners work best when they are of fairly similar ability. The bigger the gap in ability, the more of the work the stronger student does, and the more passive the weaker student becomes and the less they learn.

I think the most compelling argument for offering a path to calculus in HS is that the average math students have a better chance of advancing in college engineering programs.

Yo, then please allow the talented to drop out of school early so they don't have to waste their time.

ABSO-FRIGGIN-LUTELY! One of the big reasons there's so many problems with high school outcomes is requiring that EVERYONE finish in the same amount of time. Things would work a lot better if strong students could cut off a year or two, and weak students could stay a year or two longer than at present until they learn the material.

Go for mastery, and get rid of the lockstep time progression assumptions.

Well like I said, I don't think we should be terribly concerned about what the top talented students do because they will turn out just fine. But perhaps the trend of taking college classes while a minor will accelerate (fine with me, bring on the credit hours!). Or afaict they can indeed get a GED and start uni early. But most won't because they have sports, hobbies, friends, prom, favorite teachers, etc.

I'm sorry you were bullied as a teenager but no need to take it out on all our kids.

I don't see the justification to hold more advanced students back. To me, the flexibility to advance in single subjects is literally the only benefit the US K-12 system has over the Asian and European systems. While I think the most talented students from well-to-do families will be fine, I do not feel quite as optimistic that poorly designed K-12 systems do not negatively affect talented students from poorer families who lack the social capital to opt of the stupidity of such systems.

Yes. Using the bright students as conscripts to tutor weak students is a great promotion for private schools for anyone who can afford them.

[Hegemony]

I went to a grim inner-city high school, and as I was one of the few who was literate and numerate, I was always being told to sit down with one of the lowest performers and tutor them. It was awful. The low performers resented taking instruction from some kid their own age who was supposed to "help" them. They regarded it as condescending. I had no idea how to do it. I had no idea how to keep them on task when they wanted to goof off and insult me. I had no leverage, so I actually couldn't keep them on task. And nothing was ever at my level, addressed to me. I was basically ignored except for my supposed use as a free tutor. I loathed it.

I did get revenge on one teacher. The class was Remedial Reading. Why was I assigned to Remedial Reading (I certainly did not want to be there)? So I could tutor the less literate. (I certainly did not want to tutor the less literate.) We were supposed to choose a book that we wre going to read and write a little paper about. Generally the students chose the young-adult novels in the back of the classroom and then failed to read them. I chose Voltaire (Candide) (this was not a French class), and then I read it in French, and then I wrote my paper in French, which the teacher did not know. At this point he stopped trying to make me tutor other students and just let me sit in the corner and read.

I would never advise making the more advanced students teach the less advanced ones. If they want to, fine. But not as a compulsory and fundamental part of the setup.

[marshwiggle]

I went to a grim inner-city high school, and as I was one of the few who was literate and numerate, I was always being told to sit down with one of the lowest performers and tutor them. It was awful. The low performers resented taking instruction from some kid their own age who was supposed to "help" them. They regarded it as condescending. I had no idea how to do it. I had no idea how to keep them on task when they wanted to goof off and insult me. I had no leverage, so I actually couldn't keep them on task. And nothing was ever at my level, addressed to me. I was basically ignored except for my supposed use as a free tutor. I loathed it.

I did get revenge on one teacher. The class was Remedial Reading. Why was I assigned to Remedial Reading (I certainly did not want to be there)? So I could tutor the less literate. (I certainly did not want to tutor the less literate.) We were supposed to choose a book that we wre going to read and write a little paper about. Generally the students chose the young-adult novels in the back of the classroom and then failed to read them. I chose Voltaire (Candide) (this was not a French class), and then I read it in French, and then I wrote my paper in French, which the teacher did not know. At this point he stopped trying to make me tutor other students and just let me sit in the corner and read.

Priceless! Good for you.

[fizzycist]

I'm surprised to see these opinions and makes me wonder if y'all are teaching different classes. A few experiences that shape my opinions:

My sophomore level physics classes at state Uni have students with an enormous range of abilities. I teach to the middle. The lower-ability students struggle hard, the middle do OK, and the top students end up being the ones who enjoy the class and learn the most anyway.

When I was in 10th-11th grades in HS I was "tracked" in math and put in an honors class. There was still a huge range of ability, the class went slow and tedious, and only 1 or 2 students were close enough to my pace that I enjoyed working with them. Virtually identical experience to middle school/9th grade when we weren't tracked, only now I had fewer friends in my class. Didn't mean I was an asshole and refused to help all the other kids. And the teacher still helped me learn by offering hard extra credit problems and explanations after class when I wanted them, same as the untracked class.

[Wahoo Redux]

Isn't dual enrollment supposed to let the smarter students get ahead?

Some of my best students in my last lackluster uni were h.s. students----a few duds not withstanding.

[marshwiggle]

I'm surprised to see these opinions and makes me wonder if y'all are teaching different classes. A few experiences that shape my opinions:

My sophomore level physics classes at state Uni have students with an enormous range of abilities. I teach to the middle. The lower-ability students struggle hard, the middle do OK, and the top students end up being the ones who enjoy the class and learn the most anyway.

When I was in 10th-11th grades in HS I was "tracked" in math and put in an honors class. There was still a huge range of ability, the class went slow and tedious, and only 1 or 2 students were close enough to my pace that I enjoyed working with them. Virtually identical experience to middle school/9th grade when we weren't tracked, only now I had fewer friends in my class. Didn't mean I was an asshole and refused to help all the other kids.

Even if you chose to help other people that's a lot different than designing the curriculum/pedagogy around having stronger students help weaker students. It shouldn't be imposed upon students from on high. If weaker students need more instructional time, then there should be smaller classes and/or paid tutors to give them the time they need.

[dismalist]

We don't need to optimize for teaching the most talented kids as fast as possible, because the super bright kids usually end up learning what they need eventually anyway. This is obvious in every physics course I've taught across all levels freshman-PhD and also my personal experience.

IMO segregating students based on ability has its place, but it generally leads to worse social skills, less capability for teamwork and leadership, and reinforcing negativity for the low performers. So if we want to do it, gonna need a better argument than the best students will learn slightly slower.

I think the most compelling argument for offering a path to calculus in HS is that the average math students have a better chance of advancing in college engineering programs.

Yo, then please allow the talented to drop out of school early so they don't have to waste their time.

Now me, getting streamed eventually helped me avoid getting beat up. So I didn't handily learn the social skill of beating the shit out of my opponents right away. Being mixed with others outside of my own class did allow me to learn leadership in charging to the lunchroom along an obstacle course of other pupils. Also, debating skills at the lunch table. I'd rather not go into details.

Yes, it built character. Lovely. One must not be deceived by survivorship bias.

Do you think being "streamed" is what caused you to be singled out, and dehumanized by the kids who resented having been labeled "not so smart" and, as a result, decided to beat you up because they didn't have a chance to get to know you as a person?

That misses the point. In that Junior High, everybody beat on everybody else except within classes of the better students. Streaming is a way of minimizing pollution in such environments, pollution that promotes a race to the bottom.

[Wahoo Redux]

If weaker students need more instructional time, then there should be smaller classes and/or paid tutors to give them the time they need.

We have the capability to provide excellent education in North America.

Problem is, someone has to pay for it. 

[mleok]

I'm surprised to see these opinions and makes me wonder if y'all are teaching different classes. A few experiences that shape my opinions:

My sophomore level physics classes at state Uni have students with an enormous range of abilities. I teach to the middle. The lower-ability students struggle hard, the middle do OK, and the top students end up being the ones who enjoy the class and learn the most anyway.

When I was in 10th-11th grades in HS I was "tracked" in math and put in an honors class. There was still a huge range of ability, the class went slow and tedious, and only 1 or 2 students were close enough to my pace that I enjoyed working with them. Virtually identical experience to middle school/9th grade when we weren't tracked, only now I had fewer friends in my class. Didn't mean I was an asshole and refused to help all the other kids. And the teacher still helped me learn by offering hard extra credit problems and explanations after class when I wanted them, same as the untracked class.

To me, that's an indication that your HS classes weren't sufficiently tracked, not that tracking doesn't work. To put things into perspective, middle and high schools in Singapore have competitive entry (based on a primary school leaving exam), and one does not get priority to attend good schools based on proximity to the school, but purely on perfomance on standardized examinations. As such, students within each school are much closer in ability, and on top of this, there is tracking, which results in tracked classes that contain students of uniformly high ability.

As for your physics class, your best students are succeeding in spite of the system, not because of it. It does not however mean that students of high ability would not have been more engaged if they were actually challenged. There is a clear observer bias in that situation. Shame on you, as a scientist, you should know better than to make such an ill-informed claim without a proper comparison with a tracked system at your institution.

[fizzycist]

We don't need to optimize for teaching the most talented kids as fast as possible, because the super bright kids usually end up learning what they need eventually anyway. This is obvious in every physics course I've taught across all levels freshman-PhD and also my personal experience.

IMO segregating students based on ability has its place, but it generally leads to worse social skills, less capability for teamwork and leadership, and reinforcing negativity for the low performers. So if we want to do it, gonna need a better argument than the best students will learn slightly slower.

I think the most compelling argument for offering a path to calculus in HS is that the average math students have a better chance of advancing in college engineering programs.

Yo, then please allow the talented to drop out of school early so they don't have to waste their time.

Now me, getting streamed eventually helped me avoid getting beat up. So I didn't handily learn the social skill of beating the shit out of my opponents right away. Being mixed with others outside of my own class did allow me to learn leadership in charging to the lunchroom along an obstacle course of other pupils. Also, debating skills at the lunch table. I'd rather not go into details.

Yes, it built character. Lovely. One must not be deceived by survivorship bias.

Do you think being "streamed" is what caused you to be singled out, and dehumanized by the kids who resented having been labeled "not so smart" and, as a result, decided to beat you up because they didn't have a chance to get to know you as a person?

That misses the point. In that Junior High, everybody beat on everybody else except within classes of the better students. Streaming is a way of minimizing pollution in such environments, pollution that promotes a race to the bottom.

Doesn't seem you are confining this to math instruction anymore.

If so, sad that your life experiences were so rough that they lead you to believe that society should segregate based on intellect.

[mleok]

If so, sad that your life experiences were so rough that they lead you to believe that society should segregate based on intellect.

I think you just come across as incredibly naive. That's always been the appeal of small elite private universities, not because of the quality of the professors, but because of the quality of your fellow students. It was certainly the appeal of attending Caltech as an undergraduate.

[fizzycist]

I'm surprised to see these opinions and makes me wonder if y'all are teaching different classes. A few experiences that shape my opinions:

My sophomore level physics classes at state Uni have students with an enormous range of abilities. I teach to the middle. The lower-ability students struggle hard, the middle do OK, and the top students end up being the ones who enjoy the class and learn the most anyway.

When I was in 10th-11th grades in HS I was "tracked" in math and put in an honors class. There was still a huge range of ability, the class went slow and tedious, and only 1 or 2 students were close enough to my pace that I enjoyed working with them. Virtually identical experience to middle school/9th grade when we weren't tracked, only now I had fewer friends in my class. Didn't mean I was an asshole and refused to help all the other kids.

Even if you chose to help other people that's a lot different than designing the curriculum/pedagogy around having stronger students help weaker students. It shouldn't be imposed upon students from on high. If weaker students need more instructional time, then there should be smaller classes and/or paid tutors to give them the time they need.

I'm surprised to see these opinions and makes me wonder if y'all are teaching different classes. A few experiences that shape my opinions:

My sophomore level physics classes at state Uni have students with an enormous range of abilities. I teach to the middle. The lower-ability students struggle hard, the middle do OK, and the top students end up being the ones who enjoy the class and learn the most anyway.

When I was in 10th-11th grades in HS I was "tracked" in math and put in an honors class. There was still a huge range of ability, the class went slow and tedious, and only 1 or 2 students were close enough to my pace that I enjoyed working with them. Virtually identical experience to middle school/9th grade when we weren't tracked, only now I had fewer friends in my class. Didn't mean I was an asshole and refused to help all the other kids.

Even if you chose to help other people that's a lot different than designing the curriculum/pedagogy around having stronger students help weaker students. It shouldn't be imposed upon students from on high. If weaker students need more instructional time, then there should be smaller classes and/or paid tutors to give them the time they need.

I agree. But I don't know that Boaler's agenda is accurately described as "free tutoring". At least the article in question didn't say that, and I'm not an authority in the matter.

I'm also not an authority on tracking and wouldn't say it is always bad. For example, I think it is good to have separate  University Gen Physics for majors/non-majors. But so far the arguments ITT for tracking in gradeschool math are not convincing me, as they focus too much on optimizing for the top few percent for my tastes.

[dismalist]

We don't need to optimize for teaching the most talented kids as fast as possible, because the super bright kids usually end up learning what they need eventually anyway. This is obvious in every physics course I've taught across all levels freshman-PhD and also my personal experience.

IMO segregating students based on ability has its place, but it generally leads to worse social skills, less capability for teamwork and leadership, and reinforcing negativity for the low performers. So if we want to do it, gonna need a better argument than the best students will learn slightly slower.

I think the most compelling argument for offering a path to calculus in HS is that the average math students have a better chance of advancing in college engineering programs.

Yo, then please allow the talented to drop out of school early so they don't have to waste their time.

Now me, getting streamed eventually helped me avoid getting beat up. So I didn't handily learn the social skill of beating the shit out of my opponents right away. Being mixed with others outside of my own class did allow me to learn leadership in charging to the lunchroom along an obstacle course of other pupils. Also, debating skills at the lunch table. I'd rather not go into details.

Yes, it built character. Lovely. One must not be deceived by survivorship bias.

Do you think being "streamed" is what caused you to be singled out, and dehumanized by the kids who resented having been labeled "not so smart" and, as a result, decided to beat you up because they didn't have a chance to get to know you as a person?

That misses the point. In that Junior High, everybody beat on everybody else except within classes of the better students. Streaming is a way of minimizing pollution in such environments, pollution that promotes a race to the bottom.

Doesn't seem you are confining this to math instruction anymore.

If so, sad that your life experiences were so rough that they lead you to believe that society should segregate based on intellect.

It's about all instruction, which includes math.

Don't cry for me. I got my character built. How to resist violence and such. But survivorship bias, as I said.

I'm for segregation in schools based on pollution. Mixing different intellectual speeds and capacities is one form of pollution -- in both directions! Violence is another. Differing cultural attitudes toward learning is a further source of pollution.

I repeat, too, that mixing intellectual capacities in school does no favors for the slower among us.

[fizzycist]

If so, sad that your life experiences were so rough that they lead you to believe that society should segregate based on intellect.

I think you just come across as incredibly naive. That's always been the appeal of small elite private universities, not because of the quality of the professors, but because of the quality of your fellow students. It was certainly the appeal of attending Caltech as an undergraduate.

If so, sad that your life experiences were so rough that they lead you to believe that society should segregate based on intellect.

I think you just come across as incredibly naive. That's always been the appeal of small elite private universities, not because of the quality of the professors, but because of the quality of your fellow students. It was certainly the appeal of attending Caltech as an undergraduate.

I'll take naive over snob all day. Especially if the alternative is I refuse to spend time with ppl of less intellect. (Dismalist sounds like he has even more frightening views so im gonna let that one go).

And I've never been attracted to places like CalTech, prefer more diverse and inclusive places--is that such a fringe preference?

[marshwiggle]

If so, sad that your life experiences were so rough that they lead you to believe that society should segregate based on intellect.

I think you just come across as incredibly naive. That's always been the appeal of small elite private universities, not because of the quality of the professors, but because of the quality of your fellow students. It was certainly the appeal of attending Caltech as an undergraduate.

My kids all did the IB program in high school. When other parents of younger kids asked me if I'd recommend it, I always told them the best thing about it was the culture; in IB it was OK for students to care about school and want to do well. Peer pressure was to succeed, not to appear indifferent.


Regarding segregating: In things that I'm not good at, I want to be segregated with people at my (non-expert) level of ability.  I don't want the pressure of being with people who are way above me. Why would that appeal?