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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

#441

Post by majormajor »

texaslonghorn5 wrote: post #341
commandlinefan wrote: post #323

Earlier quoted context omitted.

Wait, is this high school or college? That looks like 3 different courses you're listing there - I've never heard of a high school offering more than a single year of calculus.

Some schools which allow students to take calculus 1 and 2 before senior year also offer multivariate calculus (3), differential equations, and linear algebra courses to round out the fourth year of math. This is especially prevalent when students can take geometry in 8th grade which leads to Algebra II, Pre-Cal, Calculus, Advanced Math Electives as the four year progression.

My public high school in TX had that track.

Is this uncommon in California schools?

(I think the idea that it's in any means required to be able to do STEM in college is ludicrous, but having the option is great.)

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

#442

Post by dan-robertson »

selimthegrim wrote: post #346
bpoyner wrote: post #236

Earlier quoted context omitted.

That would drive my wife up the wall. Our school district in the Pittsburgh suburbs has 5 math tracks from grades 4-12. They just added linear algebra because so many kids were maxing out the available math curriculum.

And the course is what, elementary row operations?

My understanding is that in the US ‘linear algebra’ is used for both the thing that involves manipulating grids of numbers in various ways (so the basis is implicit), the thing that is a bi like algebra but for matrices and vectors, the thing you have in physics where linear maps have specific geometric meanings (so you care about being mostly basis-agnostic, and you care about how the objects change when you change basis), and the thing which is abstract algebra for vector spaces and so on.

When I was in school in the U.K. we did the first and second things, including eg multiplying matrices, eigenstuff, diagonalising them, inverting small matrices, some determinant/cross product stuff, and we maybe did the thing where you solve a first order linear ODE system by converting to matrix exponentiation, though I don’t quite remember. I think we just called it vectors and matrices.

There was some useful stuff there. The problem is that it was at a course so close to the leaves of the ‘x allowed to depend on material from y’ tree that we didn’t get to apply that much (related example: we had to waste a bunch of time on silly equations in physics because they couldn’t depend on us knowing about the y’ = kx ODE)

At university we did some courses in vectors and matrices / vector calculus that went down the practical route towards physics things and useful tools, and we had a course called ‘linear algebra’ that covered the abstract algebra side of things, where everything was lemmas/theorems/proofs beginning with e.g. suppose e1, e2, …, en is a basis for a vector space V over F, …. However it is certainly possible that the US terminology (linear algebra for everything) was more common outside of the courses I took.

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

#443

Post by s1artibartfast »

0000011111 wrote: post #141

Why can we do both? 1. Make it possible for HS students who are interested in Calculus to take the course under the instruction from a college profess on the high school campus. That way it would be set up for students to get college credit for the class and they would not need to travel to a college campus or deal with the AP exam system. 2. Make it possible for HS students who are not interested (Yet) or at all to…

My high school did exactly that in the 2000s. The local Community College teacher drove to the high school and taught a class. You got high school credit and college credit if you payed the $50 community College enrollment. No ap test required.

Students could also take additional ge's at college outside of school hours, and I entered University with about 80 credits

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

#444

Post by hintymad »

troupe wrote: post #437
hintymad wrote: post #400

Earlier quoted context omitted.

Education content is definitely ample now, including text books and references. we even have great communities to get answers to our questions. Unfortunately the bottleneck of education just switched to access to good teachers. A good teacher inspires students, identifies exactly why each student has difficulty understanding something, explains intuitions behind the most difficult concepts, designs highly tailored ho…

I understand what you are saying, but I would argue that lack of access to teacher is less of a bottleneck than drive, desire, and motivation. A motivated individual is going to have no trouble finding what they need to learn and places to ask questions for things they don't understand. I see where you are coming from on access to labs, chemicals, and equipment. But someone who has fully availed themselves of everyth…

I don’t disagree with you. I just think “drive, desire, and motivation” is part of one’s talent. The progressive policies will not hurt the best students because they students will find their resources anyway. It is the middle, the vast majority like me, who would get hurt. They would think that they got good education, and then realize that their understanding of maths is so shitty that they can’t even pass city college’s dead simple placement test. Oh, I didn’t make this up, either. NYT reported this miserable experience of a straight A student, and I was shocked to read it.

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

#445

Post by charlescearl »

In the last couple of months, two readings stay with me on challenging the notion that math/science are things that only “certain kinds of men” do (more a gendered stance in the u.s. than eastern europe / asia).

The first is The Dawn of Everything, by David Graeber. I’m left with the notion that what we now call science and mathematics emerged from tinkering, persistent experimentation done mostly by women, and that what we have now disciplined into mathematics emerges from the systematic study and production of pattern (basket making, the organization of communal structures), and Graeber seems to argue against the hierarchical gender divides when viewed across the broad stretch of human history.

Rachel Thomas https://www.fast.ai/2022/03/15/math-person/ also makes a case that math is something that all people do.

I think that the larger point both are making is that disciplines don’t have to be the way they are constructed now.

My only “political”’statement would be the hope that states (particularly the u.s.) would invest as deeply in mathematics education at the primary and secondary level, for all of its communities, at the level of investment in big science and big military projects.

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

#446

Post by zozbot234 »

AlchemistCamp wrote: post #427
andrewprock wrote: post #356

Earlier quoted context omitted.

No one is suggesting that all students take calculus in high school. What is being recommend is that no one take calculus in high school. Both of these ideas are bad, but only one of them informs the California Math Framework.

> No one is suggesting that all students take calculus in high school. It’s very commonly taught in 10th grade in France, Germany, Singapore and Taiwan (where I used to teach). It’s not universal by any means but as far as I can tell, the idea that calculus should be delayed until university is a nearly uniquely American idea. https://www.mathvalues.org/masterblog/calculus-around-the-wo...

"Very commonly" in STEM-focused prep schools (i.e. the "academic" part of the tracked education system that's common outside the US). Which leaves you with very roughly the same percentages as the U.S. approach where Calculus is an elective course.

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

#447

Post by wardedVibe »

zozbot234 wrote: post #157
wardedVibe wrote: post #95

Earlier quoted context omitted.

As a math PhD with dyscalcula, I'm very skeptical. I was nearly held back as a child because of poor arithmetic performance, and really only started to be above average when we started on algebra. Poor arithmetic isn't that uncommon among the mathematicians I know.

Did that dyscalculia prevent you from learning and attaining familiarity with the standard algorithms? That's the sensible goal of "drill and kill" in early grades, not doing routine arithmetic with high amounts of significant digits.

Nope, its literally recalling the times tables that I choke on. There were timed segments, and I couldn't keep up

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

#448

Post by cryptonector »

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…

> I think they truly believe they are doing the right thing.

The alternative would be awful, no?

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

#449

Post by hintymad »

charlescearl wrote: post #445

In the last couple of months, two readings stay with me on challenging the notion that math/science are things that only “certain kinds of men” do (more a gendered stance in the u.s. than eastern europe / asia). The first is The Dawn of Everything, by David Graeber. I’m left with the notion that what we now call science and mathematics emerged from tinkering, persistent experimentation done mostly by women, and that…

I also believe that maths and STEM is something that all people do. Well, maybe not all, but at least not just a few geniuses. For that matter, I believe the progressives prescribed the wrong solution. The ordinary people, those who are are not the top X% in schools, need the push from their teachers, need the challenges in course work to push themselves to truly learn, and need a certain repetitiveness to truly grasp the fundamental concepts and skills.

How do I know that? I was one of such students. I made it because my teachers pushed me. They used carefully designed homework to show me that I didn't really have the deep understanding of math as I thought. They used homework to show me that my understanding of Newton physics was inadequate. They used midterms to show me that I didn't really intuitively grasp algorithm analysis (I didn't know how to rigorously and succinctly argue that two pivots and one pivot are really the same in quicksort). I grew to enjoy STEM and CS precisely because I was lucky to have tough yet encouraging schools. Dumbing down courses would have taken away the push I needed, and I would likely have a lot more failures in my life.

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

#450

Post by Wohlf »

FredPret wrote: post #28
texaslonghorn5 wrote: post #13

Ultimately the solution is better STEM foundation at the very very early ages. Universal pre school would probably be very useful. Empirically [edit: n = 1 or 2], it seems that drilling basic arithmetic and then multiplication tables early in pre K and earlier elementary will give students a better intuitive math foundation to do algebra very well. That would enable everyone to go into more advanced classes at the sa…

I wish we did probability with equal gusto as kids. I very occasionally multiply 7 and 6 in my head, but have to reason with probabilities and statistics all day long.

Statistics is the only reason I was able to get over my math struggles in college.
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