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

scottaaronson.blog

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

#131

Sorry for being out of the loop and asking a (possibly) dumb question: What is the stated reason that the CMF suggested these changes? Is it about budgets? Is it because some people might think these classes " aren't that important? ". The open letter seems to suggest that it's about closing gaps between privileged and less privileged - is that it? Honest question - I'm not trying to stir the pot.

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…

Yep, tracking students into systems like high/low early on makes it very hard to ever escape that track, as they're a sort of self-perpetuating system. That has downstream effects for one's entire life. It's a crude method of personalizing education within the context of factory education.

Downsides are that kids develop at different times, have different educational needs, have home life issues that can temporarily derail progress, etc and if those happen around the time kids are getting tracked, they may not reach their full potential.

A good education system would offer students a way to rise up whenever they're ready to rise up, let them learn at their pace, focus on mastery, build upon knowledge gained rather than schedule followed, etc. There's a lot of edtech out there that incorporate these concepts but school models struggle to integrate it into the (literally) old school way they operate. It's quite difficult to reorient school around these new concepts at scale, it has to be done school-by-school, leader-by-leader, school board by school board.

Agree its complex, as it may be the 'best of the worst' option for certain contexts. Anything involving balancing equity/access/etc is like that.

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

#132

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…

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.

Poor arithmetic actually drove me to learn how to program calculators and caused me to be interested in being a software engineer

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

#133
post #128
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…

Is calculus an important highschool goal? I feel like I may have benefited more if that time was spent on statistical literacy than calculus. I encounter stats very often in my adult life, calculus style problems are rare and I don't remember the formulas offhand, so end up just looking up what I need.

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.

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

#134

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…

Why wouldn't you just let everyone take the same class and the same exams, but let the kids who have interest do extra work? Want to do calculus a year early? Here's the book, here's the exercises, why would I stop you?

What you suggest is already the case. The book and exercises are "here" for you to do, nobody to stop you. It's called the internet. The calculus police doesn't come get you if you're reading a calc book in 10th grade. It's just that you don't have any way of getting instruction or school credit - so you are very unlikely to be successful, and not very likely to have your university credit you as having mastered the material without taking a college class.

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

#135
I think I can translate this:

It's saying that it is impossible to get the bulk of students (with the teachers we have) to complete the standard mathematics curriculum by the end of high school. This has always been true, in all countries, hence "streaming". But now they're saying let's do away with the advanced stream, therefore students can't complete the last part of the US mathematics curriculum (which is called "Calculus"). Rather than justify that move in terms of cost or fairness, we're going to say "because Calculus isn't important now".

This is obviously completely bogus. If their assertion that Leibnitz-style calculus isn't important now, they could replace it with Linear Algebra, Number Theory, or some other "important now" subject.

Add to that, the fact that in the US the names of high school mathematics classes are by convention. "Geometry" isn't all geometry, for example. And "Calculus" isn't all calculus. The classes are really : Math 1, Math 2, Math 3, Math 4, AP Math.

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

#136
post #94
post #61

Earlier quoted context omitted.

Sounds like more woke nonsense. Sounds nice and easy to a layman from a super high level but not practical or put through any kind of rigorous rational thought.

> Sounds like more woke nonsense You are right that this is a lot of nonsense. Specifically, 'you aren't good at math/math is hard' is the nonsense meme that gets hammered into student heads so frequently during school that most of them actually start to believe it. It's not some kind of novel woke nonsense, though, it's how math instruction on this continent has been happening over the past X decades. The wokies are…

'you aren't good at math/math is hard' may be nonsense, no doubt.

'you can be good at math/math is easy' may be an equal nonsense.

This seems to be a symmetrical situation to me. You can absolutely underrate or overrate a person's abilities to do X. I don't see how one is preferable to the other. Both are pretty destructive when taken to their extreme logical conclusions. For example, from the relative underrepresentation of blacks in advanced math classes, you can draw a conclusion that math as a science is inherently racist/white supremacist. Such sentiments can be sometimes seen in discussions and I consider them dangerous, toxic nonsense.

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

#137
post #38

Earlier quoted context omitted.

Pre-K (4 year olds) seems a bit young for teaching multiplication tables.

In context I meant get really good at addition/subtraction starting pre K and then multiplication once +/- is mastered. Though empirically, I don't know about age 4 but kindergarten is definitely not too young for learning up to 12*12. And once you figure out multiplication and eventually mental division, it's not too big of a leap to have one variable algebra with "move a plus to the other side to become minus" etc.…

My sixth grader and first grader score in the 90+ %ile in mathematics and didn't come close to learning multiplication up to 12 in kindergarten. In fact, the topic isn't even covered until second grade at the earliest.

I think establishing a foundation of addition and subtraction takes far longer for children to master than you're considering, especially since there is evidence that children of this age appear to intuitively view numbers logarithmically rather than linearly [0].

I suppose you could take advantage of this by somehow prioritizing multiplication and division over addition and subtraction, but I think there's too much value in comprehension of linear numbers and addition/subtraction since that is the lion's share of interactions they will experience at that age.

On the other hand, if you're merely talking about abstracting multiplication and division into patterns, then I wholeheartedly agree with you, and there is evidence supporting this [1]. Although pattern identification is already part of kindergarten/1st grade curriculum here.

Ultimately, IMO the most important aspect of education in general is covered in the open letter linked to the OP:

> There cannot be a “one size fits all” approach to K-12 mathematical education.

My children have thrived with their current math curriculum, and I know some of their classmates have struggled in contrast. One size does not fit all in education, nor in many aspects of life.

0: https://news.mit.edu/2012/thinking-logarithmically-1005 1: https://www.tandfonline.com/doi/abs/10.1080/15248372.2012.68...

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

#138

Earlier quoted context omitted.

What is wokeness in this instance?

Math perpetuates an -ism so we must change math.

Was some of the false statements said about Common Core match "woke" according to that definition?

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

#139
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…

My guess is the intention is to be able to say that the framework benefits disadvantaged people. But like almost any policy like this all it does at best is pull down people at the top, at worst pulls down everyone making the situation worse for everyone. You can have separation of education by ability, and progress, or you can have equality, and everyone being pulled down to the same low level. And suffering for eve…

> You can have separation of education by ability, and progress, or you can have equality, and everyone being pulled down to the same low level.

This seems a little off. What we're talking about (and what it seems like you're defending) is directing more resources towards the most gifted. It's fine to believe that, but it's an argument to give the most to those who have the most. Nobody is pulling anyone down, and communists are as happy to grant power and resources to those with aptitude and connections as capitalists are.

edit: with the constant attacks on teachers, it might be more realistic to stop aiming for calculus in high school. Any kid who manages it within a gutted public system would have gotten there anyway, no matter what situation they found themselves in. They can download calculus books and calculus lectures now; with the internet a feral education is within everyone's reach.

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

#140
post #129
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'll bite. Why is calculus a goal?

Because, without it you will be at a great disadvantage in entering any STEM undergraduate program in the US.
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