The New California Math Framework: Another Step Backwards?

Once again we are tinkering with primary and secondary school math education in the US. Recently California passed a controversial math framework for its schools. Of concern is its possible detrimental effect on math-intensive careers and the possible adoption by many other states.

At the heart of the framework is the philosophy that the student should discover the importance of math in their lives. buy showing how math can be used to promote justice and egalitarianism. It would delay the introduction of algebra to the freshman year in HS for most students and promote data science courses recognizing their importance in our economy. it would replace calculus or limit its access with statistics courses or some math courses focusing on data science.

Synopsis of the California Math Framework

https://www.edweek.org/teaching-lea...-new-math-framework-heres-whats-in-it/2023/07

A critique

https://blog.independent.org/2023/0...26XWq6wMX893keRDalbju4dxeaJ5djocaApzWEALw_wcB

Stanford University Mathematician Brian Conrad's Atlantic article on this subject.

My position on education is that it should avoid wasting students time.

If 15% of the students who make it through High School are good at algebra, trigonometry, geometry, and logic, that is fine. The rest can hang out with basic add, subtract, and percentages.

I have tutored several kids and adults on High School level math. Imposing the "heavy" stuff on students with no current inclination is bizarrely bonkers. Most of the time you can tell within 15 minutes ... 20 minutes tops when the time is not right for them - and perhaps it never will be. If you don't catch it in that first session, the second day will be telling. In some cases, it's like starting all over from scratch. In other cases, you can build up one day to the next. If you can build up knowledge and technique from one day to the next, go for it.

If you can't, persisting is torture and wasted time. Let the student move on and find what suits them.

My other comment about math education is that more emphasis should be placed on statistics. For most people, it will be more important than calculus.

The chase for equity in its own right is worrying. I wish there was at least some honesty from those doing the chasing. For example, an admission of the negative side effects, such as removing opportunities from high-achieving students. Instead we get bad or even fake research to bolster the chase, and an objective evaluation of the outcomes is replaced with pointing out the goodness of the goals.

School boards are political bodies.

"Equity" sells. Easier curricula sells. The fact that advantaged students can escape the public school system entirely, get a better education, and advance in society faster than those they left behind actually reduces equity matters not. By that time, the school board's responsibility is hard to assess, and in any event they have likely moved on - perhaps to sewer commissioner or something.

.Scott said:

If 15% of the students who make it through High School are good at algebra, trigonometry, geometry, and logic, that is fine. The rest can hang out with basic add, subtract, and percentages.

And, based on this and the rest of your post, I gather that you are fine with CA's concept of teaching to the lowest common denominator and totally ignoring education for the good math students (15% in your estimation). I understand your premise but I disagree with your conclusion. I would HATE for any of my kids to have gone through an educational system with such an abysmal plan.

We as a society and a country need well qualified STEM people. I don't want the bridges I travel over or the airplanes I fly on to be designed by people who have a very rudimentary understanding of actual math but a great feel for societal values. This whole plan is going to help China (and others) eat our lunch in the long run.

phinds said:

And, based on this and the rest of your post, I gather that you are fine with CA's concept of teaching to the lowest common denominator and totally ignoring education for the good math students (15% in your estimation).

That "15%" was a generous estimate for what is required, not what is available.
The points behind that "15%":
* Before criticizing "only 15%", check out the 2022 US Bureau of Labor Statistics. I don't think you'll find many workers operating beyond the arithmetic mark.
* If a student is absorbing the material, go for it. If they aren't, make sure they have alternatives - and let them move on - immediately.

Let me add this: For those of us taking 19th Century US Literature and coming to only one emphatic conclusion: that we are not the authors intended audience; take this item and everything like it off of our required college curriculum. Replace it with more pertinent subject matter like requirements writing, detailed design development and maintenance, and resume writing. That'll give us more time to design your bridges.

.Scott said:

* If a student is absorbing the material, go for it. If they aren't, make sure they have alternatives - and let them move on - immediately.

But that is exactly what they are NOT going to do.

.Scott said:

Replace it with more pertinent subject matter like requirements writing, detailed design development and maintenance, and resume writing. That'll give us more time to design your bridges.

Which will be irrelevant if your math skills are useless.

phinds said:

But that is exactly what they are NOT going to do.

When I say "move on", I mean to non-math topics. Anything where the student can make good progress.

phinds said:

Which will be irrelevant if your math skills are useless.

I was offering these as alternatives to 19th Century Literature to those who are gaining ground with STEM. In other words, if someone is good at STEM topics, focus on STEM-supporting topics. If someone wants "well rounded" education to be offered, round it out with non-math oriented STEM-supporting topics. Don't push poetry, foreign languages, etc.

.Scott said:

If 15% of the students who make it through High School are good at algebra, trigonometry, geometry, and logic, that is fine. The rest can hang out with basic add, subtract, and percentages.

I don't completely agree with everything you said but it's odd how few people talk about this here... People keep trying to convince students math is really important and practically useful to their lives. This is complete nonsense for the vast majority of the students. The one thing they may need sometimes after arithmetic is statistics, and that is not taught much.

It's not exactly that I'm against a hard curriculum, but it should be reoriented in a way that admits a big part of it is education for education's sake, a concept which however I've noticed is not popular in anglo countries. But starting from the notion that students should learn things for the sake of learning more about the world and not some weird notion that they will all build a bridge the moment they step out the classroom or that they are part of some race with China or *insert boogeyman country*, should probably lead to different conclusions about the teaching methods and curriculum. I don't think this new California curriculum is good but I also don't agree with the reaction to it, the pure STEM worship and this notion that the main thing schools should be doing is producing students who mastered basic calculus at all.

phinds said:

I don't want the bridges I travel over or the airplanes I fly on to be designed by people who have a very rudimentary understanding of actual math but a great feel for societal values.

Until someone can demonstrate even a single example in recent memory where a bridge collapsed or an airplane crashed because the people who designed them misremembered math they learned at school, this weird argument should stop being used. A lot more bridges have collapsed because of politics and poor societal values.

Well, the Laufenberg Bridge didn't collapse in 2004, but due to an arithmetic error, the two ends would not have met up. The error was not caught until mid-construction.

Then there was AC143 which ran out of fuel mid-flight because of an arithmetic error. Amazingly, everybody survived.

The Mars Climate Orbiter became the Mars Surface Impactor because of an arithmetic error.

These don't involve fatalities. If you insist on fatalities, there is the Scud attack on a Saudi Arabian US barracks where the Patriot defense system failed to intercept it because of an arithmetic error. Killed 27.

Then there is the Vasa, a 17th century warship which is now a museum ship in Sockholm. The ship was lost and ~30 people died because of a failure to correctly convert from a Dutch Foot to a Swedish Foot.

AndreasC said:

Until someone can demonstrate even a single example in recent memory where a bridge collapsed or an airplane crashed because the people who designed them misremembered math they learned at school, this weird argument should stop being used.

That' a bogus straw-man. I'm saying I don't want it to happen in the future.

There are a number of intertwined ideas here.

• One is the question of what should be taught.
• Another is the question of how much should be taught.
• Yet another is the question of what the right balance is between teaching facts and teaching how to reason and learn.
• And yet another is if there are different answers to the above questions for different students, who decides and when.

There are some pernicious ideas out there that I would like to come out against.

One is that excellence in education, especially in math, is somehow racist, sexist, heteronormative, cisgendered, etc. Setting a high bar is somehow unfair to minority groups who Everybody Knows Are Just Not Good At Math. The proponents of this idea make a big deal of being inclusive, but this ideology is racist, sexist, and every other kind of -ist you can think of.

Another is that we should "track" students. As Matt Groening described it "The gold track kids will go to Room 106, the silver track kids will go to Room 107, and the brown track kids will go to the basement." We're talking about high school here - do we really want to determine the adult fate of kids when they are 13?

Finally, and perhaps worst of all, is that not everybody needs a solid education. We can have some people be the engineers and the rest baristas. HG Wells warned us about them, with Morlocks and Eloi. Remember, the Eloi were food.

Vanadium 50 said:

• One is the question of what should be taught.
• Another is the question of how much should be taught.
• Yet another is the question of what the right balance is between teaching facts and teaching how to reason and learn.
• And yet another is if there are different answers to the above questions for different students, who decides and when.

And with the California program How it should be taught or not.

Vanadium 50 said:

Another is that we should "track" students. As Matt Groening described it "The gold track kids will go to Room 106, the silver track kids will go to Room 107, and the brown track kids will go to the basement." We're talking about high school here - do we really want to determine the adult fate of kids when they are 13?

This is a problem that I have with current educational programs. I would bet that if I were tracked I would not have become a physicist. I was a late bloomer. It took me all of HS and the help of my physics teacher to sort out most of my life plan. Back in the Sputnik era the HS curriculum probably had not changed in decades. Math facts in elementary school slowly transitioned to Algebra I in freshman HS, then geometry, algebra II, trig, and finally, for me, solid geometry (I had little idea of calculus until college) I ended up taking more math than physics courses in college and ended up doing quite well thank you very much. Interestingly the Cal program actually deemphasizes tracking but ends up mudding the math education waters for most students.

The California University system seems to remain a staunch supporter of traditional math methods going so far as to not grant math credit for the new data science courses that are proposed in the new framework.

phinds said:

That' a bogus straw-man. I'm saying I don't want it to happen in the future.

So in all the world so far, in every place, the teaching of mathematics has been up to par and it's only now that you're worried California will start observing mass bridge collapses due to bad high school math standards?

There are tons of reasons why catastrophic accidents happen, it's never because someone didn't learn properly in high school. There are a billion steps between school and designing bridges.

Clearly there will continue to be nothing but disagreement in this thread. I'm outta here.

Vanadium 50 said:

Well, the Laufenberg Bridge didn't collapse in 2004, but due to an arithmetic error, the two ends would not have met up. The error was not caught until mid-construction.

Then there was AC143 which ran out of fuel mid-flight because of an arithmetic error. Amazingly, everybody survived.

The Mars Climate Orbiter became the Mars Surface Impactor because of an arithmetic error.

These don't involve fatalities. If you insist on fatalities, there is the Scud attack on a Saudi Arabian US barracks where the Patriot defense system failed to intercept it because of an arithmetic error. Killed 27.

Then there is the Vasa, a 17th century warship which is now a museum ship in Sockholm. The ship was lost and ~30 people died because of a failure to correctly convert from a Dutch Foot to a Swedish Foot.

Right, do you think these arithmetic errors happened because someone did not have an adequate elementary school education or because someone was careless? Because I seriously doubt the engineers didn't know elementary school math. All of your examples except one have to do with people being careless regarding conversions or outright forgetting to convert because they were put in a setting other than what they were used to for years, or bad communication. I looked up the Scud attack thing and it wasn't due to someone messing up elementary school math at all, it was a rounding error in some computer program. You don't learn that in school.

I am not saying errors don't happen. I am saying that they have nothing to do with the school education of the people involved and there is no way to cure them by better teaching in schools. What they learned decades ago in elementary school is absolutely the last thing that mattered in the failure. What does happen a lot more is when people cut corners, communication breakdowns, and political decisions. You don't normally learn these things in math class.

A very recent mass casualty accident regarding infrastructure in my country was two trains that collided head on, leading to 57 deaths. Did someone mess up their highschool algebra? No, it's simply that the sole responsibility for coordinating what train goes on what track was put on a single station master, and there was no automated control system, no failsafe, or any sensors on the tracks that would alert the drivers of either train that there was another train on the track, or anything like that. Why? Because politicians completely ignored this issue that had been pointed out again and again for years as they were cutting corners, and so were some private firms involved in the same thing. People make errors, that's gonna happen regardless of school education. But what is really needed is that people properly cooperate so they can check on each other, and do what is necessary instead of cutting corners, and better decision taking. Of course learning really basic math well in school is a good thing, but the engineers who end up dealing with these things know basic math to the level expected by school. That's not where things go bad. It's preferrable for an educational system to produce fewer incurious, unempathetic self centered psychos than people better at basic math in my opinion.

gleem said:

This is a problem that I have with current educational programs. I would bet that if I were tracked I would not have become a physicist. I was a late bloomer.

Yeah, it's kind of a shame. School is probably the last place in life where the students can afford to get second chances, and will be treated more or less equally. Why take it away?

Aye, no true Scotsman puts sugar on his porridge!

Vanadium 50 said:

Aye, no true Scotsman puts sugar on his porridge!

Excuse me, but in reply to the point I brought up you didn't give an example of people inadequate at basic math messing up, you just googled "accidents because of arithmetic mistakes", so you ended up also including arithmetic mistakes made by computer programs, which is completely irrelevant to the point I brought up. I would appreciate if you engaged more with my central point, which is that basic math is basic, and by the time anyone gets to design anything critical, they have learned it to the level expected by schools. What would the conclusions even be from your examples? That Canada has inadequate math education? Canada ranks really, really high in relevant rankings. Same with Switzerland and to a lesser extent Germany. Wouldn't you expect more of these errors happening in places with poorer educational systems if that's what is at fault?

AndreasC said:

There are tons of reasons why catastrophic accidents happen, it's never because someone didn't learn properly in high school. There are a billion steps between school and designing bridges.

High school years are still formative times for human development. Perhaps not the subject but how things are taught and what is expected of them have lasting effects. Superficiality in HS if tolerated will persist. If certain courses are pivotal later in life but are sufficiently neglected, downplayed, or ignored the attitude can have deleterious results later on.

Think of a fatal flaw in one's ability or attitude. It is hidden until the right circumstance puts it "on stage" with a resulting tragedy. IMO many problems have resulted from the indulging of youth in yet-to-be-understood aspirations. I recall in the 70's the cry for relevant courses or real-world problems neglectful of the need for understanding the past or past approaches.

AndreasC said:

I am not saying errors don't happen. I am saying that they have nothing to do with the school education of the people involved and there is no way to cure them by better teaching in schools.

It could be because the student wasn't paying attention when certain subjects were taught in school. As part of the worldwide earthquake notification drills yesterday, here in California we were all supposed to get a cellphone notification at 10:19AM with a test message, but many of us got it at 3:19AM instead because the person in California scheduling the alert message didn't understand the difference between UTC and PDT. He should have been paying more attention in class when they covered that...




https://www.cbsnews.com/sanfrancisco/news/myshake-app-earthquake-alert-test-mistake-overnight/

gleem said:

High school years are still formative times for human development. Perhaps not the subject but how things are taught and what is expected of them have lasting effects. Superficiality in HS if tolerated will persist. If certain courses are pivotal later in life but are sufficiently neglected, downplayed, or ignored the attitude can have deleterious results later on.

Think of a fatal flaw in one's ability or attitude. It is hidden until the right circumstance puts it "on stage" with a resulting tragedy. IMO many problems have resulted from the indulging of youth in yet-to-be-understood aspirations. I recall in the 70's the cry for relevant courses or real-world problems neglectful of the need for understanding the past or past approaches.

I actually don't really disagree with this much. I mean, I agree that they are formative years, and that there may be all sorts of nasty consequences later down the road. It's just that I really don't think average subject knowledge in school has anything to do with things such as catastrophic accidents etc. After all the students who end up in engineering critical infrastructure are typically the ones who did well in school. And even if they didn't, they learned that stuff well later. Their values matter though, and sure, that comes from school too. Not necessarily related to how well the subject knowledge is transmitted though.

AndreasC said:

you just googled

Really? Do you have a keylogger installed on my computer? (And I've discussed the AC flight here in the past - how did I know then that you were going to ask that now?)

If you're going to make sh... er...stuff up,, there's no point in discussing anything with you. Bye,

The more I try to read this topic of posts, the more tiring and confusing it becomes. I did not even yet try to read the links given in the post #1.

Some years (decades) ago, schools taught basic arithmetic, general mathematics and then bordering junior high and high school gave the college prep. sequence of Algebra 1, Geometry, Algebra 2, Pre-Calc./Math Analysis often including Trigonometry. The college preparatory sequence was for the either more motivated students or the prospective S.T.E.M. students.

Some years after that wonderful set of arrangements, there came "everybody must have at least one Algebra course" and the "Integrated Mathematics" curriculums which were, ... problematic.

symbolipoint said:

The more I try to read this topic of posts, the more tiring and confusing it becomes. I did not even yet try to read the links given in the post #1.

I only gave a broad idea of what this new math framework California will implement. The links should be read. The first which I guess is supposed to give a basic idea of the philosophy behind this program really just talks around it in very general terms often so the reader may only hear what they want to.

The critiques are more specific and thus more revealing of the goals of the framework which ignores established educational psychology principles for math instruction., delaying math facts until later on in school. I might add that will reduce the amount of time therefore the practice of the use of these facts and associated algorithms resulting in less proficiency.

Interestingly the framework notes that the implementation will be the most challenging part.

The critiques note that California has 6 million students in school and thus will impact the country as a whole. Think of the rush of publishers of textbooks to get their books adopted by the system and I am sure hopeful that other states will follow suit. Recall Feynman's experience reviewing math and science books for the California educational system.

gleem said:

Recall Feynman's experience reviewing math and science books for the California educational system.

I found this link -- http://calteches.library.caltech.edu/2362/1/feynman.pdf

Mark44 said:

I found this link -- http://calteches.library.caltech.edu/2362/1/feynman.pdf

Actually, I was thinking of this one. https://www.rangevoting.org/FeynTexts.html

gleem said:

Actually, I was thinking of this one. https://www.rangevoting.org/FeynTexts.html

I read both articles, the one whose link I posted and the one you gave. I'm not sure, but I think the article you posted was also in "Surely You're Joking, Mr. Feynman." I recently reread that book and might have seen it as part of that book.

@gleem
I just started reading the first article linked in post #1. Still is long but what I take from it so far seems promising. I feel like the idea is the article means, "time to teach Mathematics the way Mathematics should be taught", maybe like it was in the mid 1960's to early 1970's.

The section in the article, "High School Course Sequencing" is a part of the article also which seems like a basic good idea.

symbolipoint said:

I just started reading the first article linked in post #1. Still is long but what I take from it so far seems promising. I feel like the idea is the article means, "time to teach Mathematics the way Mathematics should be taught",

@symbolipoint Do you still think it's your father's or grandfather's math?

gleem said:

@symbolipoint Do you still think it's your father's or grandfather's math?

I can only give my impression from the brief reading I started from the article. The reality of what is REALLY happening, I do not know.

If the current changes mean my grandfather's Mathematics, then I would say, that curriculum would be forced 'tracking'. I am unsure if he had the option of a formal course sequence of Algebra 1, Geometry, Algebra 2, Pre-Calc/Math Analysis.

Looking again briefly in the first article, the section called Inquiry-based Instruction; that is a way that teachers and students could get lost if the teacher forgets about recognizing and aiming for the Standards.

@gleem and other interested members on the topic;
Maybe not all students will be ready for Calculus in high school. That to me does not mean that "data science" should be a replacement for Calculus. Students could still be working very hard to get through Algebra 1/Algebra 2/Geometry/Trigonometry-Mathematical Analysis.

symbolipoint said:

@gleem and other interested members on the topic;
Maybe not all students will be ready for Calculus in high school. That to me does not mean that "data science" should be a replacement for Calculus. Students could still be working very hard to get through Algebra 1/Algebra 2/Geometry/Trigonometry-Mathematical Analysis.

Maybe I am missing the point. Could Statistics be one of the options for "College Preparatory Mathematics" courses?