6 ms·

Throwing out units 6,7,8 is a horrible, horrible idea. That’s the only useful part of the curriculum. In fact, most of the rest of the sections are not even sta

by dxbydt 2y ago

Throwing out units 6,7,8 is a horrible, horrible idea. That’s the only useful part of the curriculum. In fact, most of the rest of the sections are not even stat. They are just plain math. Rest of your suggestions are just plain wild. If there is some unicorn high schooler out there who meets your wild template - knows no calculus but knows rejection sampling and MH - I would like to see which foolish employer hires this clown.

Onavo 2y ago
> Rest of your suggestions are just plain wild. If there is some unicorn high schooler out there who meets your wild template - knows no calculus but knows rejection sampling and MH - I would like to see which foolish employer hires this clown. The point is to build intuition, those take time and unless the student is particularly mathematically inclined, you can't rush it. That's why you have to start in high school. Right now, the focus of pre calc is to induce them into calculus through slopes, limits, and derivatives. But a good chunk of high level statistics don't need that to build intuition. For example, we generally teach students y=mx+b in middle school and high school. This is considered a perfectly normal part of math education. It's accepted that the students may not understand the full meaning of linearity and regression at first, but at higher levels the formula would be second nature to them. This is the point I am trying to make about statistical learning (not specifically Bayesian theory in particular, but the key concepts around it). Generative ML and stuff like LLMs require a specific frame of mine and view of the world, and it's best to develop it early. The way we are teaching statistical learning theory, at the lower levels, is essentially dumping a massive bag of tricks on them and hoping for the best. We need to change that approach and start treating it like pre-calc and algebra, something to be taught level by level, with building intuition as a core focus. It's not easy to communicate the idea that "the next word prediction of the LLM (depending on the model) is generally the joint probability of all other words that come before it by sampling from a multidimensional probability distribution" to most 14-16 year olds.
- dxbydt 2y ago
  I think this is a very constructive proposal. I am definitely on board with it. I don't see why we should shoehorn these topics into ap-stats. That curriculum is entirely based on classical statistics, which is very useful for what it does. But suppose there were an ap-ml, where we have word prediction of LLMs, maybe an attempt to teach multi-dim distributions without calculus (ha! I'm seriously skeptical of that, but its your idea), rejection sampling and a suite of easy to code mcmc recipes - MH, Gibbs, Slice Sampling, Importance Sampling, and a dash of Bayesian theory - if there were such a course, it would be quite popular among the high schoolers I work with. btw, college board does revamp ap curriculum quite often. AP African American Studies was introduced last year. Maybe AP-ML is on the cards.
  - Onavo 2y ago
    What's your email?

by dxbydt 2y ago

Onavo 2y ago

> Rest of your suggestions are just plain wild. If there is some unicorn high schooler out there who meets your wild template - knows no calculus but knows rejection sampling and MH - I would like to see which foolish employer hires this clown. The point is to build intuition, those take time and unless the student is particularly mathematically inclined, you can't rush it. That's why you have to start in high school. Right now, the focus of pre calc is to induce them into calculus through slopes, limits, and derivatives. But a good chunk of high level statistics don't need that to build intuition. For example, we generally teach students y=mx+b in middle school and high school. This is considered a perfectly normal part of math education. It's accepted that the students may not understand the full meaning of linearity and regression at first, but at higher levels the formula would be second nature to them. This is the point I am trying to make about statistical learning (not specifically Bayesian theory in particular, but the key concepts around it). Generative ML and stuff like LLMs require a specific frame of mine and view of the world, and it's best to develop it early. The way we are teaching statistical learning theory, at the lower levels, is essentially dumping a massive bag of tricks on them and hoping for the best. We need to change that approach and start treating it like pre-calc and algebra, something to be taught level by level, with building intuition as a core focus. It's not easy to communicate the idea that "the next word prediction of the LLM (depending on the model) is generally the joint probability of all other words that come before it by sampling from a multidimensional probability distribution" to most 14-16 year olds.

dxbydt 2y ago
I think this is a very constructive proposal. I am definitely on board with it. I don't see why we should shoehorn these topics into ap-stats. That curriculum is entirely based on classical statistics, which is very useful for what it does. But suppose there were an ap-ml, where we have word prediction of LLMs, maybe an attempt to teach multi-dim distributions without calculus (ha! I'm seriously skeptical of that, but its your idea), rejection sampling and a suite of easy to code mcmc recipes - MH, Gibbs, Slice Sampling, Importance Sampling, and a dash of Bayesian theory - if there were such a course, it would be quite popular among the high schoolers I work with. btw, college board does revamp ap curriculum quite often. AP African American Studies was introduced last year. Maybe AP-ML is on the cards.
- Onavo 2y ago
  What's your email?