First of all if it was truly "New Math" that you were talking about, that was generations ago. And the classic that took it down was https://www.amazon.com/Why-Johnny-Cant-Add-Failure/dp/039471... - which was written by a math professor. Almost certainly what you're talking about is Common Core, not New Math.
So let's move on and pretend you talked about what you probably meant to talk about.
It is easy for you to dismiss the concerns of math illiterates whose kids failed to learn. But I've got an advanced math degree, and I assure you my complaints do not come from a lack of comprehension. Please do not dismiss them.
Next, Common Core was multiple things. Officially it was a set of national standards. That set of standards could theoretically have been met by a variety of different programs. But there was also a set of textbooks produced that had Common Core all over the titles, which necessitated extensive retraining of teachers in programs that also had Common Core all over the name. And the entire package - standards, textbooks, training and the changed classroom process - were all generally called Common Core.
I bring this up because I'm going to talk about what actually happened. And I've seen a lot of defenders try to sidestep by pointing to the standards and talking about how many ways that they could have been met. Yes, there is a theory under which it could have been great. But that isn't what happened. And the complaints are about what happened.
What I observed with my own child is this. I don't know how well his 3rd grade teacher understood math in the first place - given how many teachers in practice can't tell you whether 3/5 is larger than 2/3, odds are not great. However her retraining in Common Core apparently left her confused about everything except how to convey a general sense of enthusiasm. Therefore my son got shown 3 ways to do long division, none of which he understood, and I suspect none of which SHE understood. Given the plethora of problems that he had to do (from his point of view) with random techniques, he learned none of them. He managed to still score in the top 5% on state tests, but only because he was good at doing problems in his head. He was missing basic skills like how to write anything down, which I had to fix a couple of years later with extensive tutoring to teach him what school was supposed to.
Talking to other parents, the biggest difference between our experience and theirs is that my son got the tutoring he needed. Common Core was an unmitigated disaster in practice.
Now, you say, these are teething problems and could have been addressed if the program ran on long enough? I disagree. This was an entirely predictable disaster, intentionally created by major players in the education disaster, which is only one of many waves of disasters. From the actual New Math disaster, they learned that there is good money to be made from rewriting all the textbooks, giving expensive training, redoing the tests, and so on. And when you take advantage of a particular reform wave for enthusiasm, you guarantee that the rollout will be bad enough to generate a backlash. A backlash that generates its own reform wave, which all the same institutions fall over backwards to assist, guaranteeing a new set of textbooks, retraining, new tests, and so on. Very profitable for them, and since most parents only get to see 1 or 2 iterations, few put blame where blame belongs for the disaster that kids go through. But if you come from a family with a lot of teachers like I do, you get more perspective.
Anyways, back to what happens. You admit that it is a problem that it is unfamiliar to parents. But that problem is much bigger than you acknowledge. For a variety of societal reasons, schools ignore the general ineffectiveness of homework and assign lots of it. Research shows that this moves the responsibility of teaching from schools to families. (With corresponding impacts on families that lack the skills, but let's not digress.) And so if the parents don't know the techniques taught, the parents can't help. It is essential that either schools not assign homework to 3rd graders, or they assign homework that parents can help with.
And with Common Core, they assigned homework that parents couldn't help with. I know, I tried. My son would come with a worksheet with lots of boxes where you were supposed to write the right thing in each box to practice the technique. The problem was that my son didn't know what technique he was supposed to write down. I looked at it and found at least TWO techniques that could have been used to fill out on that worksheet. I had no idea which one the teacher intended so couldn't help. (Turns out that the teacher intended a third - there are lots of techniques that work.) And so there was absolutely no way that this homework could serve any useful purpose other than performative art.
Moving on, let's discuss the issue of the techniques.
Common Core advocates preached the value of understanding multiple approaches for the same problem - that when you do you understand better. And also pointed out that different students find different approaches click, and so theorized that showing multiple approaches would let students find what worked for them, and create mastery. Indeed each technique was mathematically sound, and each also had some evidence of effectiveness. Plus pilot programs found that people who understood this approach were effective.
What's wrong with this picture?
First, knowing multiple techniques and fluidly switching between them is a result of mastery, it is not a path to it. For absolute beginners it is more important to master one way of doing it, then elaborate. There are many techniques that could work, and which one you pick first doesn't matter as much as that you DO only pick one.
Second, results about what works when experts teach are meaningless. Experts teaching something that they are passionate about do well regardless of what methodology they do or don't use. Therefore their success is both expected, and not a predictor of success when you roll the program out.
Third, the multiple techniques idea is incredibly demanding on the teacher. The teacher has to know all of the techniques well enough to recognize which one a given student is clicking with so that the teacher can focus on what that student needs. Most teachers do not have this level of mastery - my son's clearly did not. And even if the teacher does, this is an incredible level of individual attention to demand when faced with realistic class sizes.
The result is that all techniques got shown to all students, most of whom mastered none of them. And the students failure to master any technique was a predictable disaster. Indeed from my perspective as someone with exposure to the reform cycle, almost certainly an institutionally intended one.
And finally, let's talk about your "significant data to back that up" point about Common Core. To a first approximation, there is zero data to back that up for Common Core as it was implemented. As I already indicated, the kinds of evidence that existed in advance of the standards being finalized are not ones that we rationally should expect to translate to practice in the classroom. Furthermore from first principles we should distrust any big bang, rewrite everything, reform. Changing everything is inherently risky because any mistake cascades. As I noted at https://news.ycombinator.com/item?id=34631838 we should do the simple thing first, get feedback, and iterate.
And if you ARE going to do a big bang upgrade, you should upgrade to something WITH REAL WORLD EVIDENCE OF EFFECTIVENESS! There may still be teething pains. But you've got good reason to believe that there won't be inherently shortcomings in the approach itself.
If they had done that, the single program with the best data that I'm aware of is https://en.wikipedia.org/wiki/Singapore_math. Note the focus on greater mastery of fewer techniques, each of which is mastered through multiple modalities. Yes, the Common Core people said that they included techniques from that, so they were at least as good. But including something plus a lot of other things doesn't actually work when the thing you're including works BECAUSE IT IS SIMPLE. Lose the simple, and you lose what works about it.
But, of course, Singapore math will never be adopted. Why? Because those with political influence in the educational sector wouldn't get to write new textbooks, do retraining, or rewrite tests - those things already exist. Worse yet all evidence suggests that it would work. Which would end the reform gravy train that the industry has depended on for decades.
It is worthy of note that Common Core had both math and English standards. I only talked about math. The English disaster was a little different, but just as predictable. https://www.brookings.edu/blog/brown-center-chalkboard/2021/... goes into this a little bit.
First of all if it was truly "New Math" that you were talking about, that was generations ago. And the classic that took it down was https://www.amazon.com/Why-Johnny-Cant-Add-Failure/dp/039471... - which was written by a math professor. Almost certainly what you're talking about is Common Core, not New Math.
So let's move on and pretend you talked about what you probably meant to talk about.
It is easy for you to dismiss the concerns of math illiterates whose kids failed to learn. But I've got an advanced math degree, and I assure you my complaints do not come from a lack of comprehension. Please do not dismiss them.
Next, Common Core was multiple things. Officially it was a set of national standards. That set of standards could theoretically have been met by a variety of different programs. But there was also a set of textbooks produced that had Common Core all over the titles, which necessitated extensive retraining of teachers in programs that also had Common Core all over the name. And the entire package - standards, textbooks, training and the changed classroom process - were all generally called Common Core.
I bring this up because I'm going to talk about what actually happened. And I've seen a lot of defenders try to sidestep by pointing to the standards and talking about how many ways that they could have been met. Yes, there is a theory under which it could have been great. But that isn't what happened. And the complaints are about what happened.
What I observed with my own child is this. I don't know how well his 3rd grade teacher understood math in the first place - given how many teachers in practice can't tell you whether 3/5 is larger than 2/3, odds are not great. However her retraining in Common Core apparently left her confused about everything except how to convey a general sense of enthusiasm. Therefore my son got shown 3 ways to do long division, none of which he understood, and I suspect none of which SHE understood. Given the plethora of problems that he had to do (from his point of view) with random techniques, he learned none of them. He managed to still score in the top 5% on state tests, but only because he was good at doing problems in his head. He was missing basic skills like how to write anything down, which I had to fix a couple of years later with extensive tutoring to teach him what school was supposed to.
Talking to other parents, the biggest difference between our experience and theirs is that my son got the tutoring he needed. Common Core was an unmitigated disaster in practice.
Now, you say, these are teething problems and could have been addressed if the program ran on long enough? I disagree. This was an entirely predictable disaster, intentionally created by major players in the education disaster, which is only one of many waves of disasters. From the actual New Math disaster, they learned that there is good money to be made from rewriting all the textbooks, giving expensive training, redoing the tests, and so on. And when you take advantage of a particular reform wave for enthusiasm, you guarantee that the rollout will be bad enough to generate a backlash. A backlash that generates its own reform wave, which all the same institutions fall over backwards to assist, guaranteeing a new set of textbooks, retraining, new tests, and so on. Very profitable for them, and since most parents only get to see 1 or 2 iterations, few put blame where blame belongs for the disaster that kids go through. But if you come from a family with a lot of teachers like I do, you get more perspective.
Anyways, back to what happens. You admit that it is a problem that it is unfamiliar to parents. But that problem is much bigger than you acknowledge. For a variety of societal reasons, schools ignore the general ineffectiveness of homework and assign lots of it. Research shows that this moves the responsibility of teaching from schools to families. (With corresponding impacts on families that lack the skills, but let's not digress.) And so if the parents don't know the techniques taught, the parents can't help. It is essential that either schools not assign homework to 3rd graders, or they assign homework that parents can help with.
And with Common Core, they assigned homework that parents couldn't help with. I know, I tried. My son would come with a worksheet with lots of boxes where you were supposed to write the right thing in each box to practice the technique. The problem was that my son didn't know what technique he was supposed to write down. I looked at it and found at least TWO techniques that could have been used to fill out on that worksheet. I had no idea which one the teacher intended so couldn't help. (Turns out that the teacher intended a third - there are lots of techniques that work.) And so there was absolutely no way that this homework could serve any useful purpose other than performative art.
Moving on, let's discuss the issue of the techniques.
Common Core advocates preached the value of understanding multiple approaches for the same problem - that when you do you understand better. And also pointed out that different students find different approaches click, and so theorized that showing multiple approaches would let students find what worked for them, and create mastery. Indeed each technique was mathematically sound, and each also had some evidence of effectiveness. Plus pilot programs found that people who understood this approach were effective.
What's wrong with this picture?
First, knowing multiple techniques and fluidly switching between them is a result of mastery, it is not a path to it. For absolute beginners it is more important to master one way of doing it, then elaborate. There are many techniques that could work, and which one you pick first doesn't matter as much as that you DO only pick one.
Second, results about what works when experts teach are meaningless. Experts teaching something that they are passionate about do well regardless of what methodology they do or don't use. Therefore their success is both expected, and not a predictor of success when you roll the program out.
Third, the multiple techniques idea is incredibly demanding on the teacher. The teacher has to know all of the techniques well enough to recognize which one a given student is clicking with so that the teacher can focus on what that student needs. Most teachers do not have this level of mastery - my son's clearly did not. And even if the teacher does, this is an incredible level of individual attention to demand when faced with realistic class sizes.
The result is that all techniques got shown to all students, most of whom mastered none of them. And the students failure to master any technique was a predictable disaster. Indeed from my perspective as someone with exposure to the reform cycle, almost certainly an institutionally intended one.
And finally, let's talk about your "significant data to back that up" point about Common Core. To a first approximation, there is zero data to back that up for Common Core as it was implemented. As I already indicated, the kinds of evidence that existed in advance of the standards being finalized are not ones that we rationally should expect to translate to practice in the classroom. Furthermore from first principles we should distrust any big bang, rewrite everything, reform. Changing everything is inherently risky because any mistake cascades. As I noted at https://news.ycombinator.com/item?id=34631838 we should do the simple thing first, get feedback, and iterate.
And if you ARE going to do a big bang upgrade, you should upgrade to something WITH REAL WORLD EVIDENCE OF EFFECTIVENESS! There may still be teething pains. But you've got good reason to believe that there won't be inherently shortcomings in the approach itself.
If they had done that, the single program with the best data that I'm aware of is https://en.wikipedia.org/wiki/Singapore_math. Note the focus on greater mastery of fewer techniques, each of which is mastered through multiple modalities. Yes, the Common Core people said that they included techniques from that, so they were at least as good. But including something plus a lot of other things doesn't actually work when the thing you're including works BECAUSE IT IS SIMPLE. Lose the simple, and you lose what works about it.
But, of course, Singapore math will never be adopted. Why? Because those with political influence in the educational sector wouldn't get to write new textbooks, do retraining, or rewrite tests - those things already exist. Worse yet all evidence suggests that it would work. Which would end the reform gravy train that the industry has depended on for decades.
It is worthy of note that Common Core had both math and English standards. I only talked about math. The English disaster was a little different, but just as predictable. https://www.brookings.edu/blog/brown-center-chalkboard/2021/... goes into this a little bit.