Just wondering what the mathematicians (or anyone) would think about this profile of Stanford math-education innovator and provocateur Jo Boaler. It's a bit lengthy but very well written and an interesting profile of a contradictory character.
CHE: Meet the Stanford Professor at the Center of the Knock-Down, Drag-Out Math Wars (https://www.chronicle.com/article/the-divider)
Is there a non-paywalled version? I'd be interested to read it.
If you give them your email (I used gmail) so CHE can annoy you with their newsletter, ads for their special issues, and the news feed you should be able to read anything on their site for free.
I read it a couple days ago.
Boaler comes across as someone who thinks they got learning all figured out. The rest of us chumps who struggle and think hard about learning are inclined to call BS.
I've never met an academic who was passionate about reducing their work to practice who didn't exaggerate and play fast and loose with the literature. Nothing really special about this case. I can't stand an overconfident pitch about a fundamentally uncertain topic, but i bet there is some misogyny in how she gets challenged.
I thought the article was pretty fair on presenting the state of CA math wars.
Overall the article is a good read, at least for a relative novice to the topic like me.
So what is the debate over? Methods of math instruction? Diversity and inclusion in math?
Quote from: fizzycist on March 26, 2023, 08:49:20 PM
I read it a couple days ago.
Boaler comes across as someone who thinks they got learning all figured out. The rest of us chumps who struggle and think hard about learning are inclined to call BS.
I've never met an academic who was passionate about reducing their work to practice who didn't exaggerate and play fast and loose with the literature. Nothing really special about this case. I can't stand an overconfident pitch about a fundamentally uncertain topic, but i bet there is some misogyny in how she gets challenged.
That's quite possibly true, although she doesn't help herself by claiming that rather than addressing the actual issues that are raised.
But the desire of educational policy makers to treat every new policy as The Second Coming is well-known (and frustrating, since it's often based on pretty sketchy "research").
Quote from: apl68 on March 27, 2023, 07:39:22 AM
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.
I googled around a bit and found a document explicating California's math framework, based in part on her work. https://www.cde.ca.gov/ci/ma/cf/ (https://www.cde.ca.gov/ci/ma/cf/)
I read the FAQ's.
Incomprehensible bureaubabble. There is one comprehensible thing, though. The so-called "rush to calculus" is criticized
QuoteThe Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) issued a joint statement that included the premise: "Although calculus can play an important role in secondary school, the ultimate goal of the K–12 mathematics curriculum should not be to get students into and through a course in calculus by twelfth grade but to have established the mathematical foundation that will enable students to pursue whatever course of study interests them when they get to college."
I infer that bright students will indeed be slowed down.
As a mathematician, I have not generally been impressed by the methodology employed by professors of mathematics education.
Quote from: mleok on March 28, 2023, 12:06:33 AM
As a mathematician, I have not generally been impressed by the methodology employed by professors of mathematics education.
It has always bugged me that dislike of math has been accepted (or even lionized) whereas something such as dislike of
*essays (which is quite common in techies) is dismissed as something people just have to get over. (It probably has to do with the fact that most of the people who write, such as journalists, are
by definition people who probably think essays are cool and math is gross.)
As someone who's spent a career running labs for majors and non-majors, I have no problem working with people who are only taking this because they have to, and I can tailor labs for them, but
the goals for those are very different from the goals for the majors who have to know this stuff and are prepared to learn it.One-size-fits-all is a bad way to do education, for
everyone.
*and subjective grading. Don't even get me started on that one....
Quote from: marshwiggle on March 27, 2023, 08:51:43 AM
Quote from: apl68 on March 27, 2023, 07:39:22 AM
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.
If it works, though--an awfully big if--then it might have the effect of reducing math illiteracy among the weaker students. Which would be very desirable for society in all sorts of ways, and in the long run might go some way toward addressing that "math is gross" stigma you complain about in another post on the thread.
I'm kind of interested in this issue, since I know little about math pedagogy. I know that in some societies most educated people reportedly grow up with strong math skills. But I also know that these societies tend not to have particularly sophisticated pedagogy--they owe their high levels of student achievement to a powerful tradition of brute-force rote learning and a cultural expectation that one simply has to suck it up and do what one must.
Are there methods of learning math that genuinely have been shown to produce better outcomes, or is math achievement pretty much all a matter of motivation and persistence, which are both strongly lacking in most of our students?
Quote from: marshwiggle on March 27, 2023, 08:51:43 AM
Quote from: apl68 on March 27, 2023, 07:39:22 AM
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.
Quote from: ciao_yall on March 28, 2023, 08:13:05 AM
Quote from: marshwiggle on March 27, 2023, 08:51:43 AM
Quote from: apl68 on March 27, 2023, 07:39:22 AM
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.
But it's not the same as them learning
more material. And the incremental benefit of learning that more deeply will decrease rapidly the longer they stay on one specific topic.
The fact that the class will do better if it gets a bunch of (unpaid) tutors added is no big surprise. But if parents don't get to choose how much of their kids' time is spent as (unpaid) tutors rather than learning more themselves, they're entitled to be unimpressed.
Quote from: ciao_yall on March 28, 2023, 08:13:05 AM
Quote from: marshwiggle on March 27, 2023, 08:51:43 AM
Quote from: apl68 on March 27, 2023, 07:39:22 AM
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.
Quote from: apl68 on March 28, 2023, 07:39:13 AM
Quote from: marshwiggle on March 27, 2023, 08:51:43 AM
Quote from: apl68 on March 27, 2023, 07:39:22 AM
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.
If it works, though--an awfully big if--then it might have the effect of reducing math illiteracy among the weaker students. Which would be very desirable for society in all sorts of ways, and in the long run might go some way toward addressing that "math is gross" stigma you complain about in another post on the thread.
I'm kind of interested in this issue, since I know little about math pedagogy. I know that in some societies most educated people reportedly grow up with strong math skills. But I also know that these societies tend not to have particularly sophisticated pedagogy--they owe their high levels of student achievement to a powerful tradition of brute-force rote learning and a cultural expectation that one simply has to suck it up and do what one must. Are there methods of learning math that genuinely have been shown to produce better outcomes, or is math achievement pretty much all a matter of motivation and persistence, which are both strongly lacking in most of our students?
As a person who was educated in Singapore, a big part of the quality of K-12 education in mathematics there is that there is a set rigid sequence of mathematics courses, and there are never gaps in which a student is not taking mathematics of some sorts, so it is possible to build up mathematical skills in a scaffolded fashion. In addition, as a society, we did not accept the premise that some students were "bad" at mathematics, only that they did not apply themselves sufficiently. In contrast, I literally have distinguished colleagues in chemistry who think that requiring all undergraduates to take calculus is cruel and unusual.
Quote from: Parasaurolophus on March 28, 2023, 09:21:29 AM
Quote from: ciao_yall on March 28, 2023, 08:13:05 AM
Quote from: marshwiggle on March 27, 2023, 08:51:43 AM
Quote from: apl68 on March 27, 2023, 07:39:22 AM
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.
Quote from: Parasaurolophus on March 28, 2023, 09:21:29 AM
Quote from: ciao_yall on March 28, 2023, 08:13:05 AM
Quote from: marshwiggle on March 27, 2023, 08:51:43 AM
Quote from: apl68 on March 27, 2023, 07:39:22 AM
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.
Quote from: Parasaurolophus on March 28, 2023, 09:21:29 AM
Quote from: ciao_yall on March 28, 2023, 08:13:05 AM
Quote from: marshwiggle on March 27, 2023, 08:51:43 AM
Quote from: apl68 on March 27, 2023, 07:39:22 AM
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.
Quote from: marshwiggle on March 28, 2023, 09:28:59 AM
Quote from: Parasaurolophus on March 28, 2023, 09:21:29 AM
Quote from: ciao_yall on March 28, 2023, 08:13:05 AM
Quote from: marshwiggle on March 27, 2023, 08:51:43 AM
Quote from: apl68 on March 27, 2023, 07:39:22 AM
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.
Quote from: ciao_yall on March 28, 2023, 10:18:56 AM
...
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.
Quote from: dismalist on March 28, 2023, 10:31:02 AM
Quote from: ciao_yall on March 28, 2023, 10:18:56 AM
...
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.
Quote from: marshwiggle on March 28, 2023, 10:59:02 AM
Quote from: dismalist on March 28, 2023, 10:31:02 AM
Quote from: ciao_yall on March 28, 2023, 10:18:56 AM
...
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.
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.
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...
Quote from: kaysixteen on March 28, 2023, 06:40:27 PM
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! :-)
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.
Quote from: fizzycist on March 28, 2023, 07:35:45 PM
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.
Quote from: dismalist on March 28, 2023, 07:57:18 PM
Quote from: fizzycist on March 28, 2023, 07:35:45 PM
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.
Quote from: fizzycist on March 28, 2023, 10:16:33 PM
Quote from: dismalist on March 28, 2023, 07:57:18 PM
Quote from: fizzycist on March 28, 2023, 07:35:45 PM
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.
Quote from: dismalist on March 28, 2023, 07:57:18 PM
Quote from: fizzycist on March 28, 2023, 07:35:45 PM
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?
Quote from: fizzycist on March 28, 2023, 07:35:45 PM
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.
Quote from: dismalist on March 28, 2023, 07:57:18 PM
Quote from: fizzycist on March 28, 2023, 07:35:45 PM
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.
Quote from: mleok on March 28, 2023, 10:40:56 PM
Quote from: fizzycist on March 28, 2023, 10:16:33 PM
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.
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.
Quote from: Hegemony on March 29, 2023, 05:58:37 AM
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.
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.
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.
Quote from: fizzycist on March 29, 2023, 06:14:50 AM
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.
Quote from: ciao_yall on March 29, 2023, 01:57:32 AM
Quote from: dismalist on March 28, 2023, 07:57:18 PM
Quote from: fizzycist on March 28, 2023, 07:35:45 PM
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.
Quote from: marshwiggle on March 29, 2023, 09:23:59 AM
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.
Quote from: fizzycist on March 29, 2023, 06:14:50 AM
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.
Quote from: dismalist on March 29, 2023, 09:48:09 AM
Quote from: ciao_yall on March 29, 2023, 01:57:32 AM
Quote from: dismalist on March 28, 2023, 07:57:18 PM
Quote from: fizzycist on March 28, 2023, 07:35:45 PM
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.
Quote from: fizzycist on March 29, 2023, 11:10:09 AMIf 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.
Quote from: marshwiggle on March 29, 2023, 09:23:59 AM
Quote from: fizzycist on March 29, 2023, 06:14:50 AM
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.
Quote from: marshwiggle on March 29, 2023, 09:23:59 AM
Quote from: fizzycist on March 29, 2023, 06:14:50 AM
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.
Quote from: fizzycist on March 29, 2023, 11:10:09 AM
Quote from: dismalist on March 29, 2023, 09:48:09 AM
Quote from: ciao_yall on March 29, 2023, 01:57:32 AM
Quote from: dismalist on March 28, 2023, 07:57:18 PM
Quote from: fizzycist on March 28, 2023, 07:35:45 PM
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.
Quote from: mleok on March 29, 2023, 11:12:40 AM
Quote from: fizzycist on March 29, 2023, 11:10:09 AMIf 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.
Quote from: mleok on March 29, 2023, 11:12:40 AM
Quote from: fizzycist on March 29, 2023, 11:10:09 AMIf 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?
Quote from: mleok on March 29, 2023, 11:12:40 AM
Quote from: fizzycist on March 29, 2023, 11:10:09 AMIf 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?
Jo Boaler is very good, and much of what has been discussed on this thread has little to do with her. There is a in fact a rich literature on small group learning in physics and math, and it is highly underutilized in the US. That literature applies in both tracked and untracked settings.
mleok, much of what mathematicians claim about math educators in fact has little to do with what they study and write about. I'm confining my remarks here to those who study cognitive aspects of the field, and classroom efforts at effecting change. The cognitive work to me is compelling to the point of being settled.
Anyone who really wants to learn about this should utilize the resources of the Dana Center at the University of Texas. Headed by Uri Treisman (a mathematician), you can learn wonders about the available research om math education in school settings. For the cognitive side, I'd recommend the work of Alan Schoenfeld at Berkeley.
Everything discussed on this thread has to do with Jo Boaler. From the Wikipedia entry under her name:
QuoteBoaler is the primary author of the California Department of Education's controversial mathematics draft framework.[46][47][48] The draft framework seeks to refocus mathematics education towards equity.[49][50] The draft framework recommends that all students take the same fixed set of math courses until their junior year of high school, which critics, including some leading mathematicians, say will hold back students.[51][52][53] Berkeley Professor Jelani Nelson found the framework worrying, saying it removed rigor and created a lower track of study, which would negatively impact diversity in STEM careers.[54]
Googling the Dana Center leads to invitations to buy stuff. Zero information. The Wikipedia link for Uri Treisman is criticized by Wikipedia itself.The Wikipedia entry for Alan Schoenfeld
https://gsi.berkeley.edu/programs-services/hsl-project/hsl-speakers/schoenfeld/ (https://gsi.berkeley.edu/programs-services/hsl-project/hsl-speakers/schoenfeld/)
is, well, a tad weird.
Quote from: dismalist on March 29, 2023, 02:07:12 PM
Everything discussed on this thread has to do with Jo Boaler.
Sorry, no. Boaler was tasked with the California Framework (along with others). She has written about far more nuanced aspects of learning. I was a primary member of a state task force. Saying that is what I am is inaccurate; I researched far more than that.
If you pm me I can send you a couple of Shoenfeld's accessible articles. Don't buy anything from the Dana Center; try to find links to the research compendiums and databases.
I'm also confused as to what you find weird about the link you sent? That describes one of his talks; the Wikipedia link about how is below that one in a Google search.
No eighth grade algebra. No rush to calculus.
That's what I need to know.
Quote from: dismalist on March 29, 2023, 02:36:51 PM
No eighth grade algebra. No rush to calculus.
That's what I need to know.
That's about the framework, right? Not Schoenfeld. FWIW, I helped create algebra courses for 6th graders in several districts. I'm a firm believer in advancing students who have learned material, and want to move on.
Quote from: jimbogumbo on March 29, 2023, 02:22:53 PM
Quote from: dismalist on March 29, 2023, 02:07:12 PM
Everything discussed on this thread has to do with Jo Boaler.
Sorry, no. Boaler was tasked with the California Framework (along with others). She has written about far more nuanced aspects of learning. I was a primary member of a state task force. Saying that is what I am is inaccurate; I researched far more than that.
If you pm me I can send you a couple of Shoenfeld's accessible articles. Don't buy anything from the Dana Center; try to find links to the research compendiums and databases.
I'm also confused as to what you find weird about the link you sent? That describes one of his talks; the Wikipedia link about how is below that one in a Google search.
Fair enough, but to what extent, if any, is the California Framework backed up by rigorous research, and what are the metrics for which it is optimized for? In particular, to what extent does the Framework deemphasize the learning outcomes of the most advanced students in favor of more "egalitarian" outcomes. I have a hard time with any approach that favors holding back the best students with a view towards creating a more uniform outcome.
Quote from: mleok on March 29, 2023, 03:01:48 PM
Fair enough, but to what extent, if any, is the California Framework backed up by rigorous research, and what are the metrics for which it is optimized for? In particular, to what extent does the Framework deemphasize the learning outcomes of the most advanced students in favor of more "egalitarian" outcomes. I have a hard time with any approach that favors holding back the best students with a view towards creating a more uniform outcome.
I'll depart after this one.
Our posts crossed, so I lust modified this to include the above. I clearly agree with mleok's last sentence, and don't have enough deep familiarity with California to answer the questions re research and metrics.
Boaler did a longitudinal study (three years) comparing a r
eform middle school curriculum with no algebra versus a
traditional one which did. I think her best work is on mindsets in a discipline (math) and helping students develop them.
Here are statements regarding the latest Framework (which is the 2nd revision of the 2005 framework) and what it says about "acceleration" ( a very mild version of acceleration fr those of us who have have worked with students learning Calc I-III in hs):
What does the draft Mathematics Framework say about middle school mathematics acceleration programs?The IQC discussions from the May 2021 meeting underscored that the decision about acceleration/honors and AP courses is a local one and requested that the updated draft include specific guidance on acceleration (including middle school acceleration) and serving high achievers and gifted students. Those changes are reflected in the draft that is posted for the second 60-day public comment period.
Chapter 8 of the draft Mathematics Framework notes that: "Some students will be ready to accelerate into Algebra I or Integrated Mathematics I in eighth grade, and, where they are ready to do so successfully, this can support greater access a broader range of advanced courses for them."
The framework also notes that successful acceleration requires a strong mathematical foundation, and that earlier requirements that all students take eighth grade Algebra I were not optimal for all students.
What does the draft Mathematics Framework say about access to calculus in high school? The draft Mathematics Framework includes calculus in the possible high school pathways, and also suggests ways to enable more students to get access to calculus. It notes that many high schools currently organize their coursework in a manner that requires eighth grade acceleration in order to reach calculus or other advanced mathematics courses by senior year. While some students succeed with this approach, acceleration has proved a problematic option for other students who could reach higher level math courses but would benefit from a stronger foundation in middle school mathematics.
In chapter 8, the draft framework notes: "Since achieving a solid foundation in mathematics is more important for long-term success than rushing through courses with a superficial understanding, it would be desirable to consider how students who do not accelerate in eighth grade can reach higher level courses, potentially including Calculus, by twelfth grade. One possibility could involve reducing the repetition of content in high school, so that students do not need four courses before Calculus. Algebra 2 repeats a significant amount of the content of Algebra 1 and Pre-calculus repeats content from Algebra 2. While recognizing that some repetition of content has value, further analysis should be conducted to evaluate how high school course pathways may be redesigned to create a more streamlined three-year pathway to pre-calculus / calculus or statistics or data science, allowing students to take three years of middle school foundations and still reach advanced mathematics courses."
While encouraging greater access to calculus, the framework also presents research that the "rush to calculus" without depth of understanding is not helpful to students' long-term mathematics preparation. Data shows that about one-half of all high school students who take calculus repeat the course in college or take pre-calculus in college.
The Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) issued a joint statement that included the premise: "Although calculus can play an important role in secondary school, the ultimate goal of the K–12 mathematics curriculum should not be to get students into and through a course in calculus by twelfth grade but to have established the mathematical foundation that will enable students to pursue whatever course of study interests them when they get to college." (See MAA and NCTM Joint Statement ).
Similarly, the University of California's board of admissions "strongly urges students not to race to calculus at the cost of full mastery of the earlier math curriculum. A strong grasp of these ideas is crucial for college coursework in many fields, and students should be sure to take enough time to master the material. Choosing an individually appropriate course of study is far more important than rushing into advanced classes without first solidifying conceptual knowledge."
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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.
Yikes. What a word.
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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.
Yikes.
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I repeat, too, that mixing intellectual capacities in school does no favors for the slower among us.
You are acting as though capacity and learning is fixed and only relies on a few dimensions. People are smart in many different ways.
I have been the fast learner in class and enjoyed taking leadership among my peers when that happened. I have been the slow learner in class and learned to take advice and help from others, learned to think about problems in different ways, and developed appreciation and admiration for people in unexpected ways.
Quote from: jimbogumbo on March 29, 2023, 03:05:46 PM
Here are statements regarding the latest Framework (which is the 2nd revision of the 2005 framework) and what it says about "acceleration" ( a very mild version of acceleration fr those of us who have have worked with students learning Calc I-III in hs):
What does the draft Mathematics Framework say about middle school mathematics acceleration programs?
The IQC discussions from the May 2021 meeting underscored that the decision about acceleration/honors and AP courses is a local one and requested that the updated draft include specific guidance on acceleration (including middle school acceleration) and serving high achievers and gifted students. Those changes are reflected in the draft that is posted for the second 60-day public comment period.
Chapter 8 of the draft Mathematics Framework notes that: "Some students will be ready to accelerate into Algebra I or Integrated Mathematics I in eighth grade, and, where they are ready to do so successfully, this can support greater access a broader range of advanced courses for them."
The framework also notes that successful acceleration requires a strong mathematical foundation, and that earlier requirements that all students take eighth grade Algebra I were not optimal for all students.
This sounds incredibly weasely to me; without being clear on
how they determine when a student is "ready" for acceleration it's quite possible the practical result may be to assume virtually
no-one is.
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What does the draft Mathematics Framework say about access to calculus in high school?
The draft Mathematics Framework includes calculus in the possible high school pathways, and also suggests ways to enable more students to get access to calculus. It notes that many high schools currently organize their coursework in a manner that requires eighth grade acceleration in order to reach calculus or other advanced mathematics courses by senior year. While some students succeed with this approach, acceleration has proved a problematic option for other students who could reach higher level math courses but would benefit from a stronger foundation in middle school mathematics.
It's stating the obvious to point out that some (actually
many) students struggle under the current approach. What's not at all clear (again) is how they identify
students who are perfectly capable of handling the path to complete calculus by the end of high school.
I have no problem with assuming most students may benefit from a slower pace; I have big problems with
making it difficult for good students to establish their ability to go at an "accelerated" pace.
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In chapter 8, the draft framework notes: "Since achieving a solid foundation in mathematics is more important for long-term success than rushing through courses with a superficial understanding, it would be desirable to consider how students who do not accelerate in eighth grade can reach higher level courses, potentially including Calculus, by twelfth grade. One possibility could involve reducing the repetition of content in high school, so that students do not need four courses before Calculus. Algebra 2 repeats a significant amount of the content of Algebra 1 and Pre-calculus repeats content from Algebra 2. While recognizing that some repetition of content has value, further analysis should be conducted to evaluate how high school course pathways may be redesigned to create a more streamlined three-year pathway to pre-calculus / calculus or statistics or data science, allowing students to take three years of middle school foundations and still reach advanced mathematics courses."
While encouraging greater access to calculus, the framework also presents research that the "rush to calculus" without depth of understanding is not helpful to students' long-term mathematics preparation. Data shows that about one-half of all high school students who take calculus repeat the course in college or take pre-calculus in college.
The Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) issued a joint statement that included the premise: "Although calculus can play an important role in secondary school, the ultimate goal of the K–12 mathematics curriculum should not be to get students into and through a course in calculus by twelfth grade but to have established the mathematical foundation that will enable students to pursue whatever course of study interests them when they get to college." (See MAA and NCTM Joint Statement ).
Similarly, the University of California's board of admissions "strongly urges students not to race to calculus at the cost of full mastery of the earlier math curriculum. A strong grasp of these ideas is crucial for college coursework in many fields, and students should be sure to take enough time to master the material. Choosing an individually appropriate course of study is far more important than rushing into advanced classes without first solidifying conceptual knowledge."
Again, this is stating the obvious. But the bigger reality is that most students who struggle with math in school aren't likely to be heading for highly
quantitative careers. (If there's evidence to the contrary, I'd love to see it.) Just because they go slower so they end up with a better grasp of it, (which is great), doesn't mean they're going to be much more keen on doing
a lot more of it at a higher level.
Well known info: https://www.usatoday.com/story/news/education/2023/03/30/poor-rural-students-fewer-advanced-math-courses-stem/11565375002/
Quote from: marshwiggle on March 28, 2023, 09:28:59 AM
Quote from: Parasaurolophus on March 28, 2023, 09:21:29 AM
Quote from: ciao_yall on March 28, 2023, 08:13:05 AM
Quote from: marshwiggle on March 27, 2023, 08:51:43 AM
Quote from: apl68 on March 27, 2023, 07:39:22 AM
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.
Surely the biggest perverse incentive is it creates an incentive for mediocrity. The top students are given every incentive to not apply themselves - there's no grade incentive, as A really is Average these days, there's no incentive of moving on to fresh material instead of lingering with the same old stuff they've already mastered, and instead they're basically punished by being used as unpaid tutors - on top of possible ostracism by their peers. If you have some talent, but don't apply yourself, you'll still get an A, you'll be a bit less bored with the same old material because you probably ignored it the first time around anyway, and the teacher will largely ignore you instead of asking you to do unpaid work that will help make you a social pariah. This is a system designed to dull diamonds (I don't think it's polishing pebbles at all - it's not even making everyone mediocre, it's setting mediocrity as the ceiling).
For college students who do not need to take any given subject for their major and/or professional career objectives, which subjects do we feel that a liberal arts student should nonetheless be required to take a course in, and why?
Are you asking what general education requirements lib arts students should take from outside their major?
Foreign languages
At least one freshman level science sequence