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

Not the OP, but I would weigh in with D) it's worth trying, and we should learn what we can, but the phenomena being studied are too complex and/or subjective to yield the kinds of rigorous results that we expect from the harder sciences, and the opinions of experts are therefore necessarily more infused with personal opinion and bias.

I think it is incumbent on all fields to be exceptionally clear about which of their results are rigorous, and which are outside the realm of rigorous knowledge. For example, as someone with expertise in CS, I can give you very reliable information about computability theory, and pretty reliable information about what is technically feasible to implement using current technology, but my opinion on fair moderation policies for social media are not really buttressed by my CS expertise. I wish public health officials (as just one example) were similarly clear about what they have expertise about (how disease spreads and what interventions will have what outcomes) and what is their personal opinion (cost/benefit analysis of different options, who should get vaccines first, etc).

Calculus is important, because in high school you only superficially know the breadth of the field you're interested in, where you may fit, and what you need to get there.

I unwittingly had a "low math" high school education, with pre-calculus only introduced spring of my last year. Freshman Engineering was a shock, with Calc, Physics, and Electrical Engineering using concepts I'd never heard of.

There's nothing worse than thinking you're accepted, prepared, and ready, and finding you're totally wrong.

I don't see a problem in that statement. The opposite would mean that you are born with ability and can't grow or improve it, which is absolutely false. The idea behind the statement is basically: people do not have to be naturally gifted to be good at math.

> I also don't think that criticism of a specific model of leveled courses should be used to dismiss all leveled courses. You talk about kids that are rushed ahead or that perform differently at different points in their math "career" - which could certainly be problematic if levels are rigid throughout the educational timeline and leave little choice to students.

But arguing for a gifted track IS rigid - it basically says "you must decide now if you're good at math, or not." That is deeply flawed. You can't add flexibility - you need algebra and geometry to do calculus. If you decide or become motivated too late (even if naturally gifted!), you have no recourse, as the "gifted track" starts before you can even know. The current system and system you advocate for could be removing huge numbers of potential STEM graduates from the mix.

> Yes sometimes it is implemented that way. But it is not impossible nor even particularly impractical to implement a more flexible levels system that would mitigate those concerns. There are schools that have done this well, California school system was not one of them. This proposal is throwing out the baby with the bathwater.

Not really - as is said in the framework, most foreign nations that outperform the US have a standard curriculum. So the problem isn't flexibility.

"The framework builds on the strategies used in a number of high-achieving jurisdictions (e.g., Estonia, Finland, Japan, and Korea) that pursue an integrated curriculum—connecting the domains of mathematics with one another as students collaborate in using data to solve real-world problems. These countries pursue a common curriculum in elementary and middle school, supporting more students in reaching higher level mathematics. The framework illustrates how this integrated approach with many different kinds of supports can be used to expand the number of students excelling in mathematics and heading for science, technology, engineering, and mathematics (STEM) careers."

Before I start, you really need to watch your tone and not pretend that you are a hunter on a hunt about to kill a nasty prey. My responses are clear, comprehensible and from your reply it is clear that you understood all of my points perfectly well, yet chose to use phrases like

1. If we are to assume you are being earnest

2. If you are going to dodge the question

etc.

I am a statistician and all of your questions have banal answers.

For individual differences you can plot the bell curve and the standard deviation gives you the individual variances.

I was clearly talking about population averages in 3.

> can you explain how much innate ability differences are a factor in intelligence differences (using it since you brought it up)? And how do you determine it?

AFAIK remember, heritable IQ/ height is estimated to be a bigger factor at an individual level. However, there is no existing causal methodology to determine it. Instead we have correlational regression models that make a lot of strong assumptions that are practical. There are various papers but it is clear that IQ is highly heritable like human height.

Also, I am going to replace "innate" ability with "inherited" ability because there is no methodology that can tell you how much of Roger Federer's tennis ability is "innate" and how much is "coached".

> talking about averages between groups

Your wording is ambiguous. But assuming you are talking about intergroup differences. When you sum up IQ or height within a group, the observation from regression models is that individual hereditary differences cancel out, and intergroup height and iq differences are easily explained by socio economic factors in a correlational regression model and heritable height/iq is an insignificant factor. Once again- this is not a causal model. Only correlational.

And this is just common sense. We know from life experiences that different people have differing IQs and heights from an early age. We are also aware of how important it is to have a school system - instead of just letting the kids figure things out on their own. The environment matters because we do have to work to nurture the inherent talents of a kid, otherwise that potential will be lost.

> please share how much of a factor innate ability differences are in intelligence within groups?

I expect the per sample standard deviation to be the same across different ethnic groups. For inherited "ability" i expect the total variance explained by "inheritance" factor to be the same across ethnic groups. I doubt if such an analysis has been conducted, because I don't see the value in this kind of subgroup analysis. Do you have any references to such studies? Have you seen data that contradicts this?

I love that response because I think it gets to the point and the problem.

Q1: "What is the worst-case runtime complexity of quick sort" is a question that has a rigorous answer that can be proven with fundamental scientific concepts.

Q2: "What is the programming language/framework we should use for this next project" is one that absolutely cannot.

Any answer to Q2 will invariably involve some personal opinion and bias, AND YET serious professionals with decades of experience - ones perfectly capable of answering Q1 would also be expected to weigh in on Q2, incorporating their knowledge, context, the skills of the rest of the team, the existing architecture, the requirements, etc, etc.

It would be absolutely arrogant to push back against the qualitative analysis of a senior software developer making a recommendation to Q2 with "That's just your own opinion and bias" - ESPECIALLY by someone outside the field who doesn't understand all the considerations being weighed.

I sympathize with your desire for health officials, but my theory is that everything about epidemiology, public health, disease spread, etc are all mostly Q2-category questions. You still need a PhD and rigorous understanding of all the Q1 questions but shaping public policy in a pandemic is all Q2.

Education is much the same way. Education of mathematics at scale is less about mathematics and more about people.