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An update on the campaign to defend serious math education in California

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Re: An update on the campaign to defend serious math education in California

#201

Post by zdragnar »

H8crilA wrote: post #159
kurthr wrote: post #27

From the original letter: While well-intentioned, we believe that many of the changes proposed by the CMF are deeply misguided and will disproportionately harm under-resourced students. Adopting them would result in a student population that is less prepared to succeed in STEM and other 4-year quantitative degrees in college. The CMF states that 'many students, parents, and teachers encourage acceleration beginning i…

What does "calculus" here mean? I'm not American, no idea what's included in that word and what's outside, in this context. Does it mean limits, derivatives, integration (Newton), maybe even some high level talk about ODEs for the "very best" schools? Anything more, anything less? Also, in case anyone is also wondering, 8th grade means 13-14 years old.

At my US school around the year 2000, precalc was one option for seniors, which primarily focused on limits and derivatives. The more advanced pace AP calc course also went into integrals. Beyond that I don't really recall, but by that point you also had gone through courses focusing on basic geometry, basic algebra (using variables, factoring), and a course dedicated to trigonometry (mostly memorizing the rules around figuring out angles).

There were some other courses that had math involvement, but were more business oriented (finance / accounting type stuff) and I don't recall if they counted towards core math credit requirements.

Re: An update on the campaign to defend serious math education in California

#202

Post by 300bps »

ckemere wrote: post #85
ckemere wrote: post #46

Text from the CMF: > "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 schoo…

Update - having re-read the first post about this, it seems that the issue of resources is exactly the problem. I think that opponents of the CMF would prefer to see More Resources put into careful, thorough elementary/middle school math so that middle schoolers would thrive in 8th grade Algebra. And in their view, the CMF simply lowers the bar, masking the need for more resources. I agree with that!

masking the need for more resources.

Want to know the one resource that schools can never give students? Parental involvement. It also happens to be the #1 variable in success for students.

If parents aren't checking their children's grades on a daily basis, asking what they're studying, staying in frequent communication with teachers and the school, there is nothing that is going to replace that.

My oldest son was on a robotics team during high school in which we were a minority. All the other parents, their kids were studying calculus by the end of high school. I asked every one of them how their kid was able to do that and each one of them shrugged and said, "nothing".

To them, "nothing" was their child spending 2 hours per day at Kumon after school and a few hours on the weekend in addition to their constant checking of their work and insistence on academic excellence.

Re: An update on the campaign to defend serious math education in California

#203

Post by zozbot234 »

pishpash wrote: post #158
jeffbee wrote: post #142

Earlier quoted context omitted.

I had calculus before college, got a 5 on the AP calculus exam, and it did not seem to have prepared me in any way for college-level calculus. I always thought that had been a total waste of one of my senior year class periods.

That's a totally different argument. I mean, did arithmetic "algebra" prepare you for abstract algebra or even linear algebra in college?

Actually, yes. The rules for manipulating 'expressions' with 'variables' in school algebra describe what are called "free objects" over some set of "generators". The whole setting generalizes pretty well.

Re: An update on the campaign to defend serious math education in California

#204

Post by throwawayboise »

spicymaki wrote: post #75

The tension here is that educational achievement is a proxy measurement for IQ and in capitalist societies IQ is directly correlated with income. The cultural ideal here in the US is that hard work, effort, and grit is what is necessary for success. It is supposed to be purely egalitarian; you get what you give. However whether you are born with a high IQ is purely random, and even worse IQ is heritable. This is crea…

High IQ by itself doesn't get rewarded very much without hard work, effort, and grit. If you have all of that, yes you'll be rewarded more than others who lack one or more of those qualities. And you should be.

Re: An update on the campaign to defend serious math education in California

#205

Post by innagadadavida »

FFRefresh wrote: post #166
kurthr wrote: post #27

From the original letter: While well-intentioned, we believe that many of the changes proposed by the CMF are deeply misguided and will disproportionately harm under-resourced students. Adopting them would result in a student population that is less prepared to succeed in STEM and other 4-year quantitative degrees in college. The CMF states that 'many students, parents, and teachers encourage acceleration beginning i…

I don't doubt that the people crafting these proposals care. I think they truly believe they are doing the right thing. I personally think it's just increasingly popular, mistaken moral beliefs that inform these types of proposals. Some of the underlying beliefs: 1. Blank slate - All humans are of equal ability 2. Any observable differences between humans are merely the result of social factors 3. Any observable diff…

You are leaving out who is involved and what commercial interest will be benefitted from these policies. It is likely those commercial interests are the ones sponsoring and pushing these by finding sympathetic folks.

The important thing to note here is- if you reduce the bar in high schools, a lot more students will end up in college - more money will spent, more loans will be written out etc.

Re: An update on the campaign to defend serious math education in California

#206

Post by pishpash »

acomjean wrote: post #106
cortesoft wrote: post #48

Earlier quoted context omitted.

I believe the gist of the argument is that when you split students into 'normal' and 'advanced' classes at a young age, the students who are not put into the advanced classes will believe they are just naturally not good at math and will give up on trying to get better because they will think they just "don't have a math brain". Here is a short blurb about the idea: > The framework would not forbid districts from acc…

I was in the "middle" tier math program in high school. But around sophomore year I wanted to get more into science/engineering but you can't switch tiers or catch up to those ahead of you, no matter if you're making extra effort and doing well. It was frustrating. In my case I got a letter about summer school at a local university. So I pre-calced over summer school to get moved into calculus in high school. It hone…

Many public schools take local college credits. There is always a path.

Re: An update on the campaign to defend serious math education in California

#207

Post by cowboysauce »

H8crilA wrote: post #159
kurthr wrote: post #27

From the original letter: While well-intentioned, we believe that many of the changes proposed by the CMF are deeply misguided and will disproportionately harm under-resourced students. Adopting them would result in a student population that is less prepared to succeed in STEM and other 4-year quantitative degrees in college. The CMF states that 'many students, parents, and teachers encourage acceleration beginning i…

What does "calculus" here mean? I'm not American, no idea what's included in that word and what's outside, in this context. Does it mean limits, derivatives, integration (Newton), maybe even some high level talk about ODEs for the "very best" schools? Anything more, anything less? Also, in case anyone is also wondering, 8th grade means 13-14 years old.

It varies throughout the country. But for me it was:

* Calculus I: limits, derivatives, integrals

* Calculus II: More integration techniques (substitution, by parts, table), infinite series and convergence, basic numerical methods

* Calculus III: multi-variable calculus (partial derivatives, multiple integrals), vector calculus (gradient, divergence, curl, surface and line integrals)

ODEs were a class you could take after Calc II.

Re: An update on the campaign to defend serious math education in California

#208

Post by afiori »

hnrj95 wrote: post #172
zozbot234 wrote: post #133

Earlier quoted context omitted.

Stats requires calculus; you can't even define a probability distribution without some pretty advanced notions of real analysis. Discrete math, linear algebra etc. are viable alternatives.

i’d argue that you can’t properly define probability without notions in measure theory, which is obviously far too advanced for a high school student. i’m not an educator, but some middle ground needs to be struck. i think it’s clear to many that the quality of education in american colleges far exceeds the quality of education in the average middle or high school. that’s the issue, imo

You can do quite a lot of useful stuff with just https://en.wikipedia.org/wiki/Cumulative_distribution_functi...

You only need measure theory when working with something that is not easily replaceable by R^n, Z^n, or finite sets to meaningfully define integration, otherwise (in)finite sums and Riemann integration get you very far.

I am a bit rusty on my advanced probability theory, but IIRC the only thing that required* measures was defining conditional probabilities and expected values on zero-probability events.

Of course redoing that class without Lebesgue integration sounds excruciatingly painful.

* Not just to make proofs nicer and theorems more powerful

Re: An update on the campaign to defend serious math education in California

#209

Post by spywaregorilla »

kurthr wrote: post #27

From the original letter: While well-intentioned, we believe that many of the changes proposed by the CMF are deeply misguided and will disproportionately harm under-resourced students. Adopting them would result in a student population that is less prepared to succeed in STEM and other 4-year quantitative degrees in college. The CMF states that 'many students, parents, and teachers encourage acceleration beginning i…

I don't think calculus should be a goal to be honest. Or at least not as taught. Calculus could be greatly condensed to a shorter theoretical view. The ideas of understanding differentiation and integration are great. Memorizing the rules of doing it is pretty painful and likely won't stick. But that's the bulk of classroom time, homework, and testing.

Re: An update on the campaign to defend serious math education in California

#210

Post by cool_dude85 »

devindotcom wrote: post #179
FFRefresh wrote: post #166

Earlier quoted context omitted.

I don't doubt that the people crafting these proposals care. I think they truly believe they are doing the right thing. I personally think it's just increasingly popular, mistaken moral beliefs that inform these types of proposals. Some of the underlying beliefs: 1. Blank slate - All humans are of equal ability 2. Any observable differences between humans are merely the result of social factors 3. Any observable diff…

Quoted post unavailable.

No, even Ayn has never claimed to be a psychic, able to penetrate the deepest thoughts of school board members to distill their entire world view down to a bulleted list.
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