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California needs real math education, not gimmicks

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Re: California needs real math education, not gimmicks

#191
post #153

Earlier quoted context omitted.

People with money homeschool, with much better results. There's even small homeschooling groups that pool resources to hire the best tutors money can buy. Homeschooling is exploding exponentially, doubling from 2012 to 2023 and a large portion of the parents who pulled kids from schools during COVID simply aren't going back. Understandable, because the quality of education is extremely poor. Unqualified parents homes…

> Homeschooling is exploding exponentially, doubling from 2012 to 2023 Two data points can't show something is exponential! Also, it can't possibly be exponential because the US population is not growing exponentially.

>Also, it can't possibly be exponential because the US population is not growing exponentially

This is completely wrong. The fraction of home-schooled students could e.g have been increasing from 0.02% to 0.04% to 0.08% to 0.16% even if the overall population wasn't growing at all, and that's considered exponential growth. Clearly there are indeed problems with US maths education.

Re: California needs real math education, not gimmicks

#192

California: one of the richest regions on Earth, with the highest taxes in the US, and math education worse than third-world countries.

Since we are talking about education, there is no such thing as "third world", for 32 years at least.

Re: California needs real math education, not gimmicks

#193

Earlier quoted context omitted.

> Homeschooling is exploding exponentially, doubling from 2012 to 2023 Two data points can't show something is exponential! Also, it can't possibly be exponential because the US population is not growing exponentially.

>Also, it can't possibly be exponential because the US population is not growing exponentially This is completely wrong. The fraction of home-schooled students could e.g have been increasing from 0.02% to 0.04% to 0.08% to 0.16% even if the overall population wasn't growing at all, and that's considered exponential growth. Clearly there are indeed problems with US maths education.

And then after another 6 doubling periods it'd get to 10%, will it? Exponential till it's not isn't exponential, it's logistic.

Re: California needs real math education, not gimmicks

#194
post #103

Earlier quoted context omitted.

Teachers appear to earn an average of $79k in California[0], and are eligible for a pension[1] that probably boosts their earnings to the equivalent of a six-figure job. Also, they get summers and holidays off. Not silicon valley engineer money, but not bad. [0]: https://www.niche.com/blog/teacher-salaries-in-america/ [1]: https://www.calstrs.com/retirement-benefits

> Also, they get summers and holidays off. Please don't perpetuate this. Any half decent teacher is going to spend summer looking at curriculum, block/lesson planning, in meetings, organizing their classroom, doing continuing education and training, etc. Sure, it's not as much work and it's more flexible during the summer, but it's by no means time off. Also, they work a lot more than 40 hrs/week during the school ye…

> Any half decent teacher is going to spend summer looking at curriculum, block/lesson planning, in meetings, organizing their classroom, doing continuing education and training, etc.

But the unions ensure that the NOT half decent teachers get paid the same, and they’re taking all that time as vacation. With such an incentive structure, it shouldn’t surprise anyone that there are a lot of NOT half decent teachers, and they get a lot of time off.

Re: California needs real math education, not gimmicks

#195
post #5

As someone with a PhD in education, anytime someone uses the phrase “real education” as an attack on new approaches to teaching and learning, it’s a gigantic red flag that their argument is unserious.

I haven't seen anything serious in the field of education. Education can and should be a science. There should be experiments to determine what works and what doesn't work. Instead, we have 5 different preschool pedagogies, 5 different elementary pedagogies, and 5 different secondary pedagogies, and nobody bothering to figure out what works at scale.

You're right-ish, but... the problems of educational sciences are plenty, but most importantly the impossibility to run proper experiments, and the almost complete lack of fundamental, reliable knowledge about human cognition and learning. The bottom line is that they have no idea how learning works, nor how teaching works. Their findings should not be used as evidence. Only the largest effects could be cautiously used as guidelines for gradual and reversible change.

Re: California needs real math education, not gimmicks

#197
post #158
post #23

Earlier quoted context omitted.

> why Algebra is required to understand basic stats I don't understand how you can say this. Literally every statistical concept is defined via formula, and to manipulate formulas correctly (or even really understand the concept) you need basic algebra. Going even further than that, if you have the most basic "business scenario word problem", like cells in excel that describe how many widgets are made per hour, how m…

I struggled a lot with Algebra, I forged my teacher's signature to not retake it for the third year in a row. I didn't really "get" it until I started programming and learning stats. That's when it all hit me, then I went back and had to relearn what the hell they were talking about during my middle school years. Also, once I got to Highschool math, Algebra 2 and PreCalc, it was very easy to simply memorize formulas…

Thanks for the detailed thoughts. It sounds like you had a uniquely poor experience with your math education which is too bad. Obviously you are plenty smart to handle the concepts themselves and once you had reason to apply them, you immediately "got it". I definitely don't disagree that the way the subjects are taught without context is part of the problem. I didn't really "get" calculus until I was forced to apply it to physics.

That said, specifically with respect to the content in Algebra, I wasn't really sure what we were talking about here, so I looked up the CA Common Core Algebra 1 concepts. [0]

> (1) deepen and extend understanding of linear and exponential relationships

> (2) contrast linear and exponential relationships with each other and engage in methods for analyzing, solving, and using quadratic functions

> (3) extend the laws of exponents to square and cube roots

> (4) apply linear models to data that exhibit a linear trend

This strikes me as a pretty reasonable terminal point for the general population, and I don't see how you are going to talk about anything but the most shallow statistical concepts without being comfortable with the machinery involved in the above. Perhaps you could use stats to make the content more relatable and teach both at the same time (over 2 years?), that would seem reasonable to me. But I think I would resist dropping the above concepts from the curriculum entirely in favor of a "stats light" course that literally only went into charts and basic descriptive stats.

Also, it's a bit of a cliche, but I do think it's worthwhile to teach some concepts for the sake of imparting a lesson on "how to think" and not just for the content itself. The quadratic formula feels like a good example of this. Literally nobody has reason to apply it, but the abstract reasoning skills involved in mastering it are foundational. Even if we cannot get 100% of everyone there, it's a laudable goal to me and one we should stick with.

[0] https://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardau...

Re: California needs real math education, not gimmicks

#198

In my younger years, particularly during my schooling, I held a deep resentment towards the educational system. It felt overtly clear to me, as a student, that schools failed to effectively foster learning and growth. However, my perspective has evolved over time. I've come to understand that the issues I observed are not unique to the school system but rather characteristic of large institutions as a whole. The perv…

I grew up in China and came to the same conclusion as yours! I never expect such a similarity. I've always thought that education in the US must be much better. After graduating from college, I realized that the problem I was facing was a systematic one of the whole society, rather than one limited to particular teachers, middle schools, or even the entire education system. Many people say Chinese maths education is…

I had the experience of going to US schools among competitive immigrants from Taiwan and HK(in the late 90's, i.e. they left while it was still under the British), and a little bit of mainland China as well.

Reflecting on it, it produced an odd dichotomy in classroom expectations where nobody was really on the same page: I'm fourth-generation American to a mixed European background - my mom insisted on me attempting advanced math, but in a distinctly Eastern European sense, with emphasis on learning theory, which wasn't anything like what I was confronted with at school, which was primarily computational drills that I didn't know how to prepare for and which my parents tried to pretend I could just power through, as my older brother did(he had more of a direct interest, and later confessed that he probably got through it all just with short-term memory, because he was diagnosed with ADHD as an adult and started medicating, and thought I should too). My classmates, meanwhile, had clearly normalized strict study habits but could not usefully communicate what they were to me, or maybe did not want to give up their secrets. And the teachers were just pleased that the class behaved so well and could withstand being assigned piles of homework, but they didn't have particularly advanced backgrounds themselves and often couldn't hold their own when challenged by the best students in the city.

And then I went off to college and the student body was now mostly white. I realized that this was a completely different vibe and I didn't understand that, either.

I think the places in which the US system manages to work are because sometimes the collision of varied cultures against the institutions produces useful sparks. The institution itself tracks political winds, which vary at the state and local level. Struggling schools have the usual issues of domestic insecurity spilling into the classroom, and being in the public school system, occasionally I would cross paths with those students instead of the "gifted and talented" track that I was on. But "good schools" tend to be "home owners association" schools, whipped into doing whatever the parents ask for, which usually amounts to fairy tale fantasies. When my mom started pressuring the faculty for me to stay in the advanced math track despite my not fitting there, it was, I now see, in this latter mode. Eventually, not getting the desired result, she insisted that I argue my own case, which of course I was terrible at, and left me confused, ashamed and other feelings which took years to work through. I just wanted to withdraw from everything at that point, but I was being hurried along. That is the one quality I would say tends to always be the case throughout, at least in the large schools I went to - nobody has time for anything, because everyone has a deadline to meet. It's mostly an illusion and busywork, but it nevertheless sucks out societal energy.

The elite students, some of whom I ran into in college, tend to have a path carefully paved for them through subtle signalling and tracking - opportunities and experiences that are just not the norm for anyone less wealthy. They aren't getting well-rounded educations either, rather, they are normalized to self-identify as strivers, which when combined with some early connections, is enough for most of the cohort to advance. I had a housemate who was an heir to an major beer company executive. He was an alcoholic and his dad was, too, and he bemoaned the idea that his summer job was being the boss to people ten decades older than him. His goal in getting a CS degree was to prove that he could do something for himself, essentially.

In the end, looking at it, the way the US system is set up is to not know you are in a rat race until it's too late and you're tracked at the bottom for reasons beyond your control.

Re: California needs real math education, not gimmicks

#199

Like a lot of education, California's is so tied up in so many ways that it takes books to understand. The first issue that springs to mind is the funding. Most funds in California do not stay local, they go to Sacramento and are then distributed out. If you're thinking that is a system ripe for abuse, then you are correct. The formulas and methods for determining funding aren't easy to grok. But then you add in all…

Funding is not the problem, at least not everywhere. My local school district (San Francisco) has:

- an annual operating budget of $1.2bn/year.

- ~50k K-12 students.

That's $24k per student per year.

Let's assume a teacher costs $150k/year and you want a low student:teacher ratio of 20:1.

Of the $24k, $7.5k is needed to pay 1/20th of the cost of the teacher.

You still have two thirds of the money left. Is that not enough to pay for management and facilities?

Re: California needs real math education, not gimmicks

#200

In my younger years, particularly during my schooling, I held a deep resentment towards the educational system. It felt overtly clear to me, as a student, that schools failed to effectively foster learning and growth. However, my perspective has evolved over time. I've come to understand that the issues I observed are not unique to the school system but rather characteristic of large institutions as a whole. The perv…

Indeed. And this is really the alignment problem of our time.
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