There's a lot of these math "tricks" or "shortcuts" that sound crazy at first listen, but then with practice, they turn out to be quite useful. I forget what the most recent brouhaha was called, but when I finally read up on what this "new" math being taught was, I just rolled my eyes. The problem with the recent teaching kids shortcuts to me was that they were seemingly only teaching the shortcut rather than teaching the long way so there's a proper understanding before teaching the shortcut.
In high school, I participated in an event called Number Sense. 10 minutes to answer up to 80 questions. Catch was no scratch paper, no errant marks, no erasing, no modifications for anything. If you tried to turn a 7 into a 9, it was marked wrong. squares and roots were common. 3 digit numbers multiplied by 3 digit numbers. lots of things that once you knew the shortcuts made it very possible to do this.
Did they only teach the shortcuts? It seems just as likely to me that they taught all the way through, but the parents only started complaining because, without seeing the whole development, they weren’t able to come up with the shortcuts on their own.
The solution of course is for the parent to read, like, a paragraph from their kid’s textbook.
They did not only teach short cuts. New math actually does a much better job of helping kids understand how it works rather than memorize rules and it has significant data to back that up. It’s basically better in every way except that it is unfamiliar to parents.
People are just averse to change. I can’t tell you how many math-illiterate middle aged people I know who have said something like “If it ain’t broke don’t fix it” about new math. Then I ask them some simple multiplication problem they can’t do in their head and point out that maybe it is broken and that’s why they’re not good at math.
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.
> given how many teachers in practice can't tell you whether 3/5 is larger than 2/3,
Your claim is that math education was better before Common Core, when, as you say, not even teachers understood the fractions they needed to teach?
The Eureka books show how to solve the problems on the page adjacent to the homework. Eureka website has free parent resources on websites.
If your teacher is sending home mystery homework, that's just a bad teacher.
Your claim is that math education was better before Common Core, when, as you say, not even teachers understood the fractions they needed to teach?
I made no such claim.
To the contrary I pointed at a 50 year old book on how bad math education was, and said that there have been wave after wave of reforms since, each driven by the failures of the previous one. From this you should infer that I think math education has been broken for a very long time. Only the details of how it is broken change.
Furthermore you point out the past failures of teachers to understand the fractions that they needed to teach. But you haven't said anything to indicate we should believe that it has improved since. I don't believe it has improved. Teachers STILL don't understand fractions properly.
The Eureka books show how to solve the problems on the page adjacent to the homework. Eureka website has free parent resources on websites. If your teacher is sending home mystery homework, that's just a bad teacher.
Classic. Just blame it on the teacher.
She didn't pick the textbook, and printed out the prepared homework sets which went with the textbook. She also didn't have a choice about how much homework - that was school policy. As was not having the kids carry their textbookshome.
While there were problems with the teacher, this one really can't be blamed on her.
But it gets better. My son was in this course in 2012. According to https://deutsch29.wordpress.com/2019/10/06/a-great-minds-com..., the contract to create that website was awarded in 2012. We would have needed access to a time travel machine to take advantage of a website that did not yet exist! (I don't remember what textbook we had, but it certainly did not then have a website associated with it.)
So stop blaming the teacher, who was essentially also a victim of the system. Instead read through my explanation of why disaster was guaranteed from the start.
I've said this before, but public education seems to be in a death spiral of:
1. Reduce teacher autonomy
2. A lot of the better teachers dislike this, so move on
3. Decide that the teachers remaining aren't competent enough, so reduce their autonomy
4. GOTO 2
Not being able to decide how much, and what homework to assign is beyond absurd for someone who is so least ostensibly a teacher. If you are dictating what they are doing to that detail, stop requiring a college degree and call them day-care providers.
You're missing the step where Teachers College of Columbia University first hijacked the teaching profession for a specific progressive philosophy that aspired to a scientific approach to education, but went with pseudoscience around things like "learning to learn" instead. This provided fertile ground for fad after fad that later swept teaching. This created grounds to want to restrict teacher autonomy in the first place.
I recently re-read To Kill a Mockingbird and was surprised to find a first hand account of what an initial encounter with this philosophy was like back in the 1930s.
What I'm seeing from your long essay is that the common core curriculum is indeed great but average teachers are too stupid / mathematically illiterate to teach it, so we would be better settling for mediocrity instead.
What I'm seeing from your long essay is that the common core curriculum is indeed great...
That summary is woefully incorrect.
I will grant that Common Core had well-meaning people, some good math, and interesting pedagogical theories behind it. But it was broken on every other level. "Great" is hardly the last adjective that I'd use for it.
I believe that its pedagogical theories don't work in practice for children. The process by which it was created guaranteed that its standards would not be achievable in practice. The process by which the textbooks were created guaranteed that they would mostly consist of rough spots which would need a lot of ironing out for their target audience. The process by which teachers were trained was supported by decades of practice in creating enthusiasm for bad ideas, and the teachers showed it. And the inevitable failures of real teachers to deliver would guarantee that they could be blamed for the eventual failure of the whole endeavor.
...but average teachers are too stupid / mathematically illiterate to teach it...
What did I just say about blaming teachers for a multi-level disaster that was doomed from the start? How convenient of you to provide a demonstration.
...so we would be better settling for mediocrity instead.
HAH!
I discussed Singapore math briefly at the end. According to https://factsmaps.com/pisa-2018-worldwide-ranking-average-sc... Singapore is currently #2 in the world for delivered results on elementary school math education. But the #1 country, China, adopted the same techniques. Individual schools in the USA that adopted that technique have also had great success.
If we care about actual evidence over rhetoric, we should choose what has proven to be excellent in practice. Which is NOT Common Core.
> Then I ask them some simple multiplication problem they can’t do in their head
to be fair, it does require some practice. the stuff i used to do in my head is long since idle. there have been times i've struggled to remember the shortcut to the point i could have done it the long way faster.
the one that gets me is the simple ability (or lack of) to be able to calculate tips and other percentages. regardless of how you feel about tips, it is definitely something we do a lot. except, now, we don't and we have apps to do it for us. we can't figure out quickly what 25% off would make the price. so many day to day things like that is the worrying bit to me. not how quickly can Karen estimate the square root of a 3 digit number, because why would Karen even be in that situation. Karen is interested in 25% off, but can't without her phone. i've already decided the price still isn't worth and a have moved on before she can even unlock her device.
Not being able to figure out a tip does annoy me a bit, because when you know how 10% works then you've got all you need, just halve it and add it back on and you've got your minimum 15%, or double it for 20%.
It's not like that requires practice. Maybe to do it quickly, but moving a decimal place over in your head or halving or doubling is about as easy as it gets.
I don't want to disparage people who aren't good at math (compared to many here I'm like a grade schooler) but how do you make it though school without knowing the basics of percentages?
Are your referring to Eureka Math? (What is usually incorrectly called "Common Core")
New Math is from the 1950s-1970s and almost entirely abandonesld except for some gifted/enrichment programs.
Wikipedia says:
> Topics introduced in the New Math include set theory, modular arithmetic, algebraic inequalities, bases other than 10, matrices, symbolic logic, Boolean algebra, and abstract algebra.
Eureka/Engage is a very watered down version of that (but still decent.)
Are your referring to Eureka Math? (What is usually incorrectly called "Common Core")
Eureka Math is produced by Great Minds. Until 2015, they were called Common Core Inc. In fact they predated the Common Core Standard, and were sufficiently influential in the creation of the standard that the standard was effectively named after them.
Therefore calling it Common Core IS historically correct. Furthermore I have a strong distaste for their attempt to rebrand themselves to distance themselves from the failures that they were instrumental in creating in the first place.
i had forgotten just how impressionable kids can be, especially when they really want to be. i "argued" with my buddy's oldest (a 5th grader) about "1 + 1 = 10". after a few rounds of nuh-uh, yes-huh, i gave a very rough explanation and ending with "in binary". until a few days later, buddy asks me to not be so cavalier with the challenging of the maths. apparently, his daughter had challenged her teacher with 1+1=10, and after a brief back and forth, she stipulated "in binary" to her teacher. the teacher being very young and not familiar with binary, sent the poor kid to the principal's office.
This. The complaint from parents seemed to universally be that they didn't understand the "new math". The conclusion they reached was that there was something wrong with the method, rather than the more obvious conclusion that they should have taken a bit of time to learn and understand it.
Right, I watched like a ten minute YouTube video when my nephew’s parents were complaining about it and found it not difficult at all to comprehend. I didn’t exactly struggle with the old math either though, but so many people did that it is clear there is room for improvement.
Maybe it is as you say. I don't have kids in school, so it was all a big nothing burger to me written off as a bunch of Karens needing something complain about for whatever purpose it serves them.
Common Core: "Common core math is a set of national educational standards that push kids to think of math equations differently. With common core math, kids begin questioning the relevance of each equation. Instead of just solving an equation for its sake, common core math makes children deliberate the reason behind the equation."
oooooh, scary. making kids think. me thinks that's the issue.
That's the theory, maybe. I have kids in school. In practice it seems more like simply rote memorization of multiple techniques to solve a problem. It's especially hard when a child figures out his own way, but is graded/marked on doing it the specific way(s) a homework or test question demands.
this is actually something i had to endure as well specifically from knowing these tricks and being well practiced in "doing it in my head". i had to be retrained to show my work. each new teacher would assume i was some how cheating on the homework by just writing the answers. that may be harsh, but that's the way it was always received. if they weren't going to give me the benefit of the doubt, why should i for them?
the thing that convinced me to switch to elaborately showing my work was partial credit. in the competitive tests, if you didn't know the correct answer, you'd look at the next 3 questions to see if you could answer them. a skipped answer was counted as wrong, and points deducted. since the test increased in difficulty as you progressed, you'd have to consider how many questions you were skipping and if it was better to just stop.
in classes, even if the answer was incorrect, if you showed your work you could receive partial credit. if it was clear you were using the right steps to get there but forgot to carry a one or skipped a step somewhere else but it was clear that the basic understanding on how to solve the problem was close, you could avoid a big goose egg for that question. IIRC, the AP exams were like that as well. more about showing understanding of the process than just the correct answer is what they were trying to achieve.
That's a lot easier than the method I was taught. The "old" way always resulted in me trying to carry state in my head, which doesn't work well for ADHD-limited memory.
Lehrer is talking about "new math" from 60 years ago. (it consisted of talking about set theory, union and intersection, also mentioning commutative and distributive princicples, i.e. mentioning some things that are not super necessary for arithmetic but which you will encounter later if you pursue mathematics further. In this way you would hopefully be more effective in contributing to the arms and space races and defeating communism.) https://en.wikipedia.org/wiki/New_Math
In high school, I participated in an event called Number Sense. 10 minutes to answer up to 80 questions. Catch was no scratch paper, no errant marks, no erasing, no modifications for anything. If you tried to turn a 7 into a 9, it was marked wrong. squares and roots were common. 3 digit numbers multiplied by 3 digit numbers. lots of things that once you knew the shortcuts made it very possible to do this.