In the Name of Equity, California Will Discourage Students Who Are Gifted at Math

[Loren Pechtel]

This makes sense when I relate it to my personal experience in high school and university mathematics. I took the advanced stream in high school, where we were introduced to calculus in Year 12, if I remember correctly. It was, as this paper describes, "significantly procedural": we learned how to do differentiation and integration, but we weren't taught what it meant. When I took mathematics (and programming, and analog electronics) at university, we had to apply calculus to real world engineering problems. The only useful things that I retained from high school was the notation and the handful of rules I'd learned by rote. (Power rule, chain rule, open vs. closed limits, etc.) I had to develop my intuitive understanding of calculus at university.

It doesn't make sense in my experience. I AP-tested out of calc 1 at college, for calc 2 I don't feel it was any different than what I had in high school, just going into more complex stuff. Still rote memorization, but I had no problem with applying it.

Without an intuitive understanding of mathematics, it's useless, because you won't recognise calculus solutions to problems out in the real world. Teaching students the procedure of solving calculus problems makes them very good at solving neat, pre-made calculus problems you put in front of them. but it doesn't teach them how to construct the calculus problem in the first place.

A failing I have seen throughout most education, especially in STEM areas.

Personally, I took calculus in Year 12 despite the fact that I didn't do any accelerated maths in middle school. The education system here just didn't offer it. I was taught maths in a heterogeneous class up until senior school, at which point students chose one of three different streams: easy maths, hard maths or a double dose of hard maths. So I can say from experience that there is nothing wrong with making middle school maths heterogeneous, since I've lived it and it seemed to work fine. It didn't stop anyone from becoming scientists or engineers.

(Different country, obviously, but Year 12 is still Year 12, and middle school is still middle school.)

When you make class too easy you hurt the good students by making them bored and not interested in it anymore.

 

[Loren Pechtel]

To me it comes down to a deficiency in how we teach. Rather than starting to draw connections in the mechanics of numbers, connections which will later become algebraic understandings... We teach memorization and rote. This has always been the case such that those most capable of learning are not presented bread crumbs that will put them meaningfully on the path to the greater enlightenment that is "understanding mathematics".

It's not that I believe students so coddled are incapable of discovery; those who must discover shall! But they shall discover more if they shall find themselves further along the path as their drive to discovery blooms.

Anyway, I think that the current "intuitive" math is definitely better than rote math, but both still must take a seat to process math. Because process math is where proof comes from and proof is where applications become possible.

This I will definitely agree with. How to apply it to the real world gets short shrift--but this is nothing specific to accelerated math classes or even accelerated classes in general.

 

[J842P]

This makes sense when I relate it to my personal experience in high school and university mathematics. I took the advanced stream in high school, where we were introduced to calculus in Year 12, if I remember correctly. It was, as this paper describes, "significantly procedural": we learned how to do differentiation and integration, but we weren't taught what it meant. When I took mathematics (and programming, and analog electronics) at university, we had to apply calculus to real world engineering problems. The only useful things that I retained from high school was the notation and the handful of rules I'd learned by rote. (Power rule, chain rule, open vs. closed limits, etc.) I had to develop my intuitive understanding of calculus at university.

Without an intuitive understanding of mathematics, it's useless, because you won't recognise calculus solutions to problems out in the real world. Teaching students the procedure of solving calculus problems makes them very good at solving neat, pre-made calculus problems you put in front of them. but it doesn't teach them how to construct the calculus problem in the first place.

I was on an accelerated math track since middle school and ended up taking AP Calculus in 11th grade. It was my worst grades in my entire educational career. I didn’t understand what we were doing or why. Then in 12th grade I took Physics and all of a sudden I had a context for the calculus.

In college I got my degree in physics and obviously had to take calculus again and did fine with it. I can’t think of any benefit I gained from taking calculus in 11th grade and all it did was hurt my GPA.

Just my anecdotal ‘evidence’.

My anecdote: I took calc in 11th grade. Did well on it and the related AP test. Started college in more advanced math classes, although, I re-took linear algebra for the easy A. Preventing me from taking accelerated math classes would have been profoundly stupid.

Of course, I studied biology, and math was just something I took for fun, I already had all my math requirements from high school.

I don't think I'm very good at math, either. I would say, middling but motivated.

 

[Jarhyn]

To me it comes down to a deficiency in how we teach. Rather than starting to draw connections in the mechanics of numbers, connections which will later become algebraic understandings... We teach memorization and rote. This has always been the case such that those most capable of learning are not presented bread crumbs that will put them meaningfully on the path to the greater enlightenment that is "understanding mathematics".

It's not that I believe students so coddled are incapable of discovery; those who must discover shall! But they shall discover more if they shall find themselves further along the path as their drive to discovery blooms.

Anyway, I think that the current "intuitive" math is definitely better than rote math, but both still must take a seat to process math. Because process math is where proof comes from and proof is where applications become possible.

This I will definitely agree with. How to apply it to the real world gets short shrift--but this is nothing specific to accelerated math classes or even accelerated classes in general.

My point is that accelerating math is being done very wrong. It should start with care in elementary school to identify those who are "breaking rules, but making sense", and displaying the budding of original thought. Maybe I draw from my own life too much, but there is maybe somewhere between 1:25-1:100 of people who display, for instance, an instant recognition of how pointers work. They are ahead of the game as far as abstract thought of whatever type. But that is hard to identify. It can be easy to discount the fact that a fourth grader is doing algebraic calculations because when a fourth grader does it, it won't look like algebra. Instead, it will be something primitive or even silly-sounding. It may seem like a regression, even. Because obviously, fourth graders don't know algebra; they haven't learned it yet. And no two discoveries of the same idea are likely to be immediately identifiable as "same" especially in such early or "clean" environments.

It can't be tested for, not well at any rate. It has to be observed, and the people observing have to care, and then also know what to do when they find one out in the wild.

I once took a class called "exceptional child" that I had every hopes would cover such a topic. Ultimately my disgust with the lack of such a concept in education is what drove me to only minor in psychology.

 

[barbos]

My point is that accelerating math is being done very wrong. It should start with care in elementary school to identify those who are "breaking rules, but making sense",

Most in education is done very wrong. In university math, they often intentionally do it in unnecessary abstract way, just to weed out the weak, I think. It was annoying, but once you learn that it gets easier. And after a while you realize most of the math is obvious and start to wonder why could not they start with simple explanations. Physics also suffer from that. I remember reading analytical mechanics (By Landau). It was "Here is the Least Action Principle, lets do some math, shall we?". No explanation, not even hint of realization that readers might have questions there and few historical references would help explain who and why came up with this idea. One has to wait until at least optics/electrodynamics or better quantum mechanics to figure out why that principle.

 

[Jarhyn]

My point is that accelerating math is being done very wrong. It should start with care in elementary school to identify those who are "breaking rules, but making sense",

Most in education is done very wrong. In university math, they often intentionally do it in unnecessary abstract way, just to weed out the weak, I think. It was annoying, but once you learn that it gets easier. And after a while you realize most of the math is obvious and start to wonder why could not they start with simple explanations. Physics also suffer from that. I remember reading analytical mechanics (By Landau). It was "Here is the Least Action Principle, lets do some math, shall we?". No explanation, not even hint of realization that readers might have questions there and few historical references would help explain who and why came up with this idea. One has to wait until at least optics/electrodynamics or better quantum mechanics to figure out why that principle.

I would LOVE a math class where, instead of "let's get to derivatives", it's "let's do X" where "X" is some task that requires knowing derivatives.

 

[Loren Pechtel]

My point is that accelerating math is being done very wrong. It should start with care in elementary school to identify those who are "breaking rules, but making sense",

Most in education is done very wrong. In university math, they often intentionally do it in unnecessary abstract way, just to weed out the weak, I think. It was annoying, but once you learn that it gets easier. And after a while you realize most of the math is obvious and start to wonder why could not they start with simple explanations. Physics also suffer from that. I remember reading analytical mechanics (By Landau). It was "Here is the Least Action Principle, lets do some math, shall we?". No explanation, not even hint of realization that readers might have questions there and few historical references would help explain who and why came up with this idea. One has to wait until at least optics/electrodynamics or better quantum mechanics to figure out why that principle.

I would LOVE a math class where, instead of "let's get to derivatives", it's "let's do X" where "X" is some task that requires knowing derivatives.

Seconded. To the extent possible all education should be handled this way. I think math is the field to which this could be applied the best, though, as it's nature is very abstract but even a beginner student can apply it in meaningful ways.

 

[RVonse]

A truly gifted child can teach themselves calculus with internet access.

They need more exposure to history, morality and ethics.

As all of that, too, is available with the internet, what’s the point of school?

So they can be indoctrinated with liberal propaganda.

 

[Trausti]

A truly gifted child can teach themselves calculus with internet access.

They need more exposure to history, morality and ethics.

As all of that, too, is available with the internet, what’s the point of school?

So they can be indoctrinated with liberal propaganda.

Eh, the honest answer is that the main function of public schools is daycare. But what else ya gonna do with your kids?

 

[Emily Lake]

This makes sense when I relate it to my personal experience in high school and university mathematics. I took the advanced stream in high school, where we were introduced to calculus in Year 12, if I remember correctly. It was, as this paper describes, "significantly procedural": we learned how to do differentiation and integration, but we weren't taught what it meant. When I took mathematics (and programming, and analog electronics) at university, we had to apply calculus to real world engineering problems. The only useful things that I retained from high school was the notation and the handful of rules I'd learned by rote. (Power rule, chain rule, open vs. closed limits, etc.) I had to develop my intuitive understanding of calculus at university.

Without an intuitive understanding of mathematics, it's useless, because you won't recognise calculus solutions to problems out in the real world. Teaching students the procedure of solving calculus problems makes them very good at solving neat, pre-made calculus problems you put in front of them. but it doesn't teach them how to construct the calculus problem in the first place.

I was on an accelerated math track since middle school and ended up taking AP Calculus in 11th grade. It was my worst grades in my entire educational career. I didn’t understand what we were doing or why. Then in 12th grade I took Physics and all of a sudden I had a context for the calculus.

In college I got my degree in physics and obviously had to take calculus again and did fine with it. I can’t think of any benefit I gained from taking calculus in 11th grade and all it did was hurt my GPA.

Just my anecdotal ‘evidence’.

I was in accelerated classes through elementary and middles school too. I took AP Calc and Physics in my senior year. Having the two together definitely made for a better understanding of the math. On the other hand, taking Thermodynamics in college before taking Differential Equations was a disaster.

Either way... holding back students with good minds is a stupid idea. Everyone has strengths and weaknesses, and their strengths should be fed while their weaknesses are bolstered so they're less of a hindrance. I can't imagine trying to make it policy to not let athletically gifted students participate in sports because other kids are uncoordinated (that would be me), or not allowing good theater students to participate in plays because others are completely unconvincing when they read scripts (also me), or not allowing students to participate in choir because other students are tone-deaf af (also me).

Dumb idea is dumb.

 

[Gospel]

So they can be indoctrinated with liberal propaganda.

Eh, the honest answer is that the main function of public schools is daycare. But what else ya gonna do with your kids?

The schools aren't doing so great, but whatever they're doing now it's better than what Americans used to do with them in the past.

 

[J842P]

My point is that accelerating math is being done very wrong. It should start with care in elementary school to identify those who are "breaking rules, but making sense",

Most in education is done very wrong. In university math, they often intentionally do it in unnecessary abstract way, just to weed out the weak, I think. It was annoying, but once you learn that it gets easier. And after a while you realize most of the math is obvious and start to wonder why could not they start with simple explanations. Physics also suffer from that. I remember reading analytical mechanics (By Landau). It was "Here is the Least Action Principle, lets do some math, shall we?". No explanation, not even hint of realization that readers might have questions there and few historical references would help explain who and why came up with this idea. One has to wait until at least optics/electrodynamics or better quantum mechanics to figure out why that principle.

Yeah, honestly, a lot of vector calculus went over my head when I was exposed to without physics. It all just seemed completely arbitrary. Then when I took E&M, it was like, "oh, that's what all that was for".

 

[Shadowy Man]

My point is that accelerating math is being done very wrong. It should start with care in elementary school to identify those who are "breaking rules, but making sense",

Most in education is done very wrong. In university math, they often intentionally do it in unnecessary abstract way, just to weed out the weak, I think. It was annoying, but once you learn that it gets easier. And after a while you realize most of the math is obvious and start to wonder why could not they start with simple explanations. Physics also suffer from that. I remember reading analytical mechanics (By Landau). It was "Here is the Least Action Principle, lets do some math, shall we?". No explanation, not even hint of realization that readers might have questions there and few historical references would help explain who and why came up with this idea. One has to wait until at least optics/electrodynamics or better quantum mechanics to figure out why that principle.

Yeah, honestly, a lot of vector calculus went over my head when I was exposed to without physics. It all just seemed completely arbitrary. Then when I took E&M, it was like, "oh, that's what all that was for".

When I was a TA for freshman physics and they were learning E&M with integrals I would tell my physics majors that this will all be much easier once they learn vector calc.

 

[Politesse]

The schools aren't doing so great, but whatever they're doing now it's better than what Americans used to do with them in the past.

Still a very common view as to the essential purpose of education, I assure you. They've just classed up the language they use to describe what they want.