CHE: "The Divider" (math education)

[mleok]

So what is the debate over?  Methods of math instruction?  Diversity and inclusion in math?

The article is really sketchy on details, but ti seems to be that her focus is on lots of group work, with students of all ability levels, and she claims it reduces math anxiety and makes weaker students do better at math. Her critics (reading between the lines) suggest that the better students are being held back by it. (Anyone who knows more feel free to correct me.) If improving the performance of the bottom 30% (arbitrarily chosen number) is at the expense of the top 10% (arbitrarily chosen number), is that an improvement or not?
Again, if that's kind of what's going on, there is lots of history of using good students to essentially tutor weak students, which may benefit the system, but may not be best for the good students.

Actually, tutoring weaker students helps the stronger students by making them learn the material more deeply in order to explain it to others, and in different ways.

It's not a zero-sum game.

That's been my anecdotal experience teaching formal logic. The strong students develop more fluency and facility with the material, which makes them better able to apply it to novel problems.

So yeah, marshwiggle, they don't learn more brute content. But there's a limit to how much new content they will get in any class, and they'll get there by the end of the course. If there was no cap to how much they'd get, then sure, it's be holding the ones who get it back somewhat. But that's not the case.

But it also benefits the students who aren't getting it to have them explain it to me/one another (with supervision). It helps them to identify and understand where their gaps are, and it is easier to fix the problem that way. If they don't understand where they're struggling, it just seems impossible to them.

Except that the proposed California framework would literally prevent more advanced students from taking more advanced mathematics classes. Mind you, calculus isn't the pinnacle of mathematics, it is literally an introductory language class for STEM majors, and there is absolutely no reason it needs to be delayed until college. Students in Asia and Europe most certainly are introduced to it in high school.

[marshwiggle]

So what is the debate over?  Methods of math instruction?  Diversity and inclusion in math?

The article is really sketchy on details, but ti seems to be that her focus is on lots of group work, with students of all ability levels, and she claims it reduces math anxiety and makes weaker students do better at math. Her critics (reading between the lines) suggest that the better students are being held back by it. (Anyone who knows more feel free to correct me.) If improving the performance of the bottom 30% (arbitrarily chosen number) is at the expense of the top 10% (arbitrarily chosen number), is that an improvement or not?
Again, if that's kind of what's going on, there is lots of history of using good students to essentially tutor weak students, which may benefit the system, but may not be best for the good students.

Actually, tutoring weaker students helps the stronger students by making them learn the material more deeply in order to explain it to others, and in different ways.

It's not a zero-sum game.

That's been my anecdotal experience teaching formal logic. The strong students develop more fluency and facility with the material, which makes them better able to apply it to novel problems.

So yeah, marshwiggle, they don't learn more brute content. But there's a limit to how much new content they will get in any class, and they'll get there by the end of the course. If there was no cap to how much they'd get, then sure, it's be holding the ones who get it back somewhat. But that's not the case.

But it also benefits the students who aren't getting it to have them explain it to me/one another (with supervision). It helps them to identify and understand where their gaps are, and it is easier to fix the problem that way. If they don't understand where they're struggling, it just seems impossible to them.

The problem is it provides a perverse incentive.

In a high school, suppose you have 40 students in Grade 9. You can offer two classes of Algebra; you could offer one "remedial" and one "advanced" , or two "remedial". The perverse incentive is to go with two "remedial", because using the good students as tutors will improve the average grades in both sections. The primary benefit of this is to the school and its average. Putting the students first would require having the two different classes so that each class could focus on one group of students. (But, of course, it would show that a single teacher without unpaid tutors would have limits. This is a system problem, that shouldn't be "*solved" on the backs of the good students.)

*Hidden is more like it.

[dismalist]

So what is the debate over?  Methods of math instruction?  Diversity and inclusion in math?

The article is really sketchy on details, but ti seems to be that her focus is on lots of group work, with students of all ability levels, and she claims it reduces math anxiety and makes weaker students do better at math. Her critics (reading between the lines) suggest that the better students are being held back by it. (Anyone who knows more feel free to correct me.) If improving the performance of the bottom 30% (arbitrarily chosen number) is at the expense of the top 10% (arbitrarily chosen number), is that an improvement or not?
Again, if that's kind of what's going on, there is lots of history of using good students to essentially tutor weak students, which may benefit the system, but may not be best for the good students.

Actually, tutoring weaker students helps the stronger students by making them learn the material more deeply in order to explain it to others, and in different ways.

It's not a zero-sum game.

That's been my anecdotal experience teaching formal logic. The strong students develop more fluency and facility with the material, which makes them better able to apply it to novel problems.

So yeah, marshwiggle, they don't learn more brute content. But there's a limit to how much new content they will get in any class, and they'll get there by the end of the course. If there was no cap to how much they'd get, then sure, it's be holding the ones who get it back somewhat. But that's not the case.

But it also benefits the students who aren't getting it to have them explain it to me/one another (with supervision). It helps them to identify and understand where their gaps are, and it is easier to fix the problem that way. If they don't understand where they're struggling, it just seems impossible to them.

Tutoring works in college, both informally within classes and formally from higher level classes to lower level classes. The better students are not held back in any way. Indeed, they are promoted in their understanding and in the formal systems they are paid.

What is going on in K-12 is quite different. The bright kids will learn less than they could by the time they graduate. It's clearly a wedge to equalize outcomes without it being clear that the less bright kids will benefit.

Now, if parents could choose what math pedagogy they want their kids subjected to, we'd have a big experiment and we could see results, or not.

[ciao_yall]

So what is the debate over?  Methods of math instruction?  Diversity and inclusion in math?

The article is really sketchy on details, but ti seems to be that her focus is on lots of group work, with students of all ability levels, and she claims it reduces math anxiety and makes weaker students do better at math. Her critics (reading between the lines) suggest that the better students are being held back by it. (Anyone who knows more feel free to correct me.) If improving the performance of the bottom 30% (arbitrarily chosen number) is at the expense of the top 10% (arbitrarily chosen number), is that an improvement or not?
Again, if that's kind of what's going on, there is lots of history of using good students to essentially tutor weak students, which may benefit the system, but may not be best for the good students.

Actually, tutoring weaker students helps the stronger students by making them learn the material more deeply in order to explain it to others, and in different ways.

It's not a zero-sum game.

That's been my anecdotal experience teaching formal logic. The strong students develop more fluency and facility with the material, which makes them better able to apply it to novel problems.

So yeah, marshwiggle, they don't learn more brute content. But there's a limit to how much new content they will get in any class, and they'll get there by the end of the course. If there was no cap to how much they'd get, then sure, it's be holding the ones who get it back somewhat. But that's not the case.

But it also benefits the students who aren't getting it to have them explain it to me/one another (with supervision). It helps them to identify and understand where their gaps are, and it is easier to fix the problem that way. If they don't understand where they're struggling, it just seems impossible to them.

The problem is it provides a perverse incentive.

In a high school, suppose you have 40 students in Grade 9. You can offer two classes of Algebra; you could offer one "remedial" and one "advanced" , or two "remedial". The perverse incentive is to go with two "remedial", because using the good students as tutors will improve the average grades in both sections. The primary benefit of this is to the school and its average. Putting the students first would require having the two different classes so that each class could focus on one group of students. (But, of course, it would show that a single teacher without unpaid tutors would have limits. This is a system problem, that shouldn't be "*solved" on the backs of the good students.)

*Hidden is more like it.

I can assure you that the students whose parents have the most political juice will push for at least one advanced algebra section. There will not be two remedial sections.

The best alternative might be two advanced sections with mixed students and group work, which helps the stronger students with their own learning and helps the weaker students build math skills and strategies by learning from their peers.

[dismalist]

...
I can assure you that the students whose parents have the most political juice will push for at least one advanced algebra section. There will not be two remedial sections.

The best alternative might be two advanced sections with mixed students and group work, which helps the stronger students with their own learning and helps the weaker students build math skills and strategies by learning from their peers.

How help the stronger students? They are held back by the weaker students, and the weaker students are overwhelmed by speed and quantity of material. Both groups learn less than if they were streamed by ability. If tutoring is considered valuable, one can still organize it.

[marshwiggle]

...
I can assure you that the students whose parents have the most political juice will push for at least one advanced algebra section. There will not be two remedial sections.

The best alternative might be two advanced sections with mixed students and group work, which helps the stronger students with their own learning and helps the weaker students build math skills and strategies by learning from their peers.

How help the stronger students? They are held back by the weaker students, and the weaker students are overwhelmed by speed and quantity of material. Both groups learn less than if they were streamed by ability. If tutoring is considered valuable, one can still organize it.

I'm always baffled by academics who enjoy the bright students in their own classes, but are dismissive or downright contemptuous of bright students in other disciplines. If I had an English student taking a STEM course as an elective, I certainly wouldn't want to saddle them with having to help STEM students write better lab reports, just because they were more capable.

[Wahoo Redux]

...
I can assure you that the students whose parents have the most political juice will push for at least one advanced algebra section. There will not be two remedial sections.

The best alternative might be two advanced sections with mixed students and group work, which helps the stronger students with their own learning and helps the weaker students build math skills and strategies by learning from their peers.

How help the stronger students? They are held back by the weaker students, and the weaker students are overwhelmed by speed and quantity of material. Both groups learn less than if they were streamed by ability. If tutoring is considered valuable, one can still organize it.

I'm always baffled by academics who enjoy the bright students in their own classes, but are dismissive or downright contemptuous of bright students in other disciplines. If I had an English student taking a STEM course as an elective, I certainly wouldn't want to saddle them with having to help STEM students write better lab reports, just because they were more capable.

Tutoring English essays was one of the best things I've ever done to learn to write other than the writing itself, however.

[dismalist]

In my yute, there was streaming of various kinds from fourth grade through high school. For whatever reason, I got streamed into fourth grade incorrectly. Or maybe somebody needed to make up a quota, or perhaps somebody merely hated me. While instruction was going on I typically read books surreptitiously at my desk spot. Teacher, who was lovely, knew what was going on, so everything was fine. [She was also very kind to a boy who clearly had grave learning difficulties of some sort.] One day a substitute teacher, who did not, punished me for reading while she was babbling!

Now, mix abilities in greater equality of numbers, not just a small number by mistake, and mass mayhem will break out.

[kaysixteen]

The discussion here seems to be focusing on the question of whether the parents of the math high achievers should be able to prevent their children from being tutors in math class.  But even if High Achiever Parent X has no problem with that, we gotsta ask the question, does the actual High Achiever himself want to be a tutor?  Many such kids would very much *not* want to do this, for a variety of reasons.   They may not like tutoring and/or be very good at it, and they may well be resented and picked on by the low achievers for acting in this role.   I can only imagine what I might have had to endure in my working class town jr hs, had I been made to do this, for students who not only did not care much about school themselves, but also often had parents who did not much care either...

[dismalist]

The discussion here seems to be focusing on the question of whether the parents of the math high achievers should be able to prevent their children from being tutors in math class.  But even if High Achiever Parent X has no problem with that, we gotsta ask the question, does the actual High Achiever himself want to be a tutor?  Many such kids would very much *not* want to do this, for a variety of reasons.   They may not like tutoring and/or be very good at it, and they may well be resented and picked on by the low achievers for acting in this role.   I can only imagine what I might have had to endure in my working class town jr hs, had I been made to do this, for students who not only did not care much about school themselves, but also often had parents who did not much care either...

Nay, the discussion is about cross pollution among students. Tutoring is independent of all of this.

'Ya want tutors, pay them! :-)

[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.

[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.

[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.

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.

[mleok]

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.

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.

[ciao_yall]

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?