meep (meep) wrote,
meep
meep

"Hey, we've got a NEW idea for teaching math!!!"

And, of course, it's the same bad idea for teaching math that has been ruining U.S. math education since Tom Lehrer wrote "New Math" -- let's make it less boring! More relevant!



(that one just confused the hell out of students and parents)

WSJ: THE MOVEMENT TO MODERNIZE MATH CLASS

with the sub hed: "‘Freakonomics’ co-author Steven Levitt and other reformers are pushing for more equitable curriculum that better equips students for a data-driven world"

You know what would be a more equitable curriculum? Actually teaching the kids how to deal with numbers via stuff like Kumon and Khan Academy: that is DO DRILLS. DO LOTS OF PROBLEMS BY HAND.

Okay, that's before I've even read the piece, but I had an extremely good idea of what was going to be there, given more than twenty years of my bitching about this very thing.

Here we go:


Steven Levitt, like many parents, has spent countless evenings helping his kids with their math homework. Increasingly, his four teenagers' work on quadratic equations and imaginary zeros has felt like an exercise in futility.

"They'll never use it again," says Dr. Levitt.

It's an odd thing for someone like Dr. Levitt to say, given his career as an economist at the University of Chicago and his work as co-author of the book "Freakonomics." But learning math is different from understanding data. He and others contend that the way math is taught in schools is outdated and impractical in preparing students for today's data-driven world.



I actually have no problem with dropping quadratic equations and even complex numbers in high school. I am very pro-dropping calculus (and you will see why later in this post...if you haven't already heard this one before from me).

Dr. Levitt's proposal is simple: Condense three years of high-school math -- typically Algebra I in ninth grade, Geometry in 10th grade and Algebra II in junior year -- to two years. Then, devote the freed up time to more relevant learning, such as data science or financial literacy.


So. This is dumb. Why not drop all of that shit for those specific grades, and do the stats/finance/probability in 9th grade? Algebra can wait. Hell, I would give them personal finance in 9th grade. They should have personal finance in middle school and elementary school, too, but baby steps, y'all.


Policy makers are beginning to imagine what a modernized math curriculum could look like -- one that would acknowledge the prevalence of computers and the importance of data literacy, broaden the pathways to college acceptance, and prepare students for real-life issues, such as understanding the amortization of a mortgage, evaluating the impact of waste on the environment or deciphering infection rates of Covid-19.


So.... I used to teach a class like that in NYU, and the math was not all that complicated. I did stuff like teach Benford's Law (yes, really), inflation-adjusting dollar amounts to try to determine the best movie box office take of all time, dimensional analysis, proportions, and that sort of thing. Excepting Benford's Law (which had been new to me), all the math involved, I knew before I entered high school.

But I have objections to this, because I have a very good idea where the math education falls apart, and it's not in high school. It starts in elementary school.

Conrad Wolfram's vision is at the extreme end of math reform: His idea is to eliminate hand calculations from the curriculum. Mr. Wolfram, the co-founder of Wolfram Research Europe, the mathematical lab behind the specialized search engine Wolfram Alpha, has campaigned for over a decade to overhaul the way mathematics are taught. Mr. Wolfram, author of "The Math Fix: An Education Blueprint for the AI Age," says the fundamental problem with today's math curriculum is that it doesn't acknowledge that computers exist.
Oh Conrad Wolfram, brother of Stephen Wolfram, who is really best known as the creator of Mathematica.... mmmm.

I have heard this bullshit before, and I wrote about it before, twenty years ago.

From August 2000, my tirade on the use of calculators (and Maple/Mathematica) in teaching math


Much has been made of the use of calculators and computers in math, and they are indeed very useful, powerful, and even necessary tools in modern math research. However, I feel that the focus of the use of these tools has been misplaced. Too often they are seen as something that can remove the tedium from math, as opposed to tools that remove tedious calculations
that one understands very well and can do by hand one's self.

People claim that many students are turned off by math early on due to excessive rote memorization of addition tables, multiplication tables, and the like. Math is about recognizing patterns, not simply arithmetic, they enthusiastically proclaim, and let us use calculators to cut through the tedium of practicing long division and graphing lines.

I would agree with them -- mathematics has very little to do with arithmetic and has everything to do with finding patterns and relations and using these things to solve problems. Indeed, I rarely do long division by hand, or even integrate by hand anymore. However, I do not agree with the reasons as to why students are getting turned off from math.

They get turned off because they do not understand it.


By all means, why not argue that music students need not learn how to play any instruments, read music, practice scales, and any number of other things. Hell, why teach students to read regular language anymore -- don't we have code that can automatically transform text into audible input? Why learn foreign languages? We've got google translate! Why learn how to write text? Or even type? We can do voice-to-text!

If you start thinking through why students actually do need to learn how to read text, be able to print letters and numbers, then you might be able to understand why students also need to understand how to do long division, which is generally about the step where math starts falling apart for students. And, obviously, long division is at elementary school level.

Fractions and long division are the first huge cognitive steps in math, and many people never get over it. Math class is hard for most people. Even if it's not hard in elementary school, many people run into trouble in algebra or geometry, as the abstraction begins to step up.

Reading is actually hard, too, but people do acknowledge (at least, for now) that as hard as reading is for many students, they've actually got to learn how to do it. Same for learning to print letters. Maybe they don't acknowledge the need for cursive script, but at least printing is required, and many students have huge issues with that.

But when we run into problems with understanding arithmetic, they think calculators should be broken out.

They do not understand it because they don't have enough practice with basic problems and are rushed onto harder problems that are grounded in one's knowledge of what multiplication or division means. They haven't dirtied their hands in the earth of numbers, so when they're asked to tend a 10-acre field of word problems, they become flummoxed.
.....
No, I didn't really enjoy memorizing my times tables or solving very similar linear equations or taking countless derivatives or proving continuity through delta-epsilon proofs. But I did them, knowing that I was developing my mathematical intuition and making my life in math that much more smooth for years to come.

Why am I allowed now to use the computer programs that I disallow my students? Because I already know how to do these and through my experience, know what answers to expect. Technology nowadays allows the taking of a derivative, minimization of a function, numerical and symbolic integration, plotting of a complicated function, and much more difficult mathematical tasks with little effort on the part of the user of the technology. However, students often get incorrect answers, mainly because
they are asking the wrong questions.


This still pertains -- I've seen stuff on machine learning/AI coming from actuaries that has appalled me as I realize they didn't truly understand how certain systems work and more importantly, where they break. I have been appalled that I had to point out that some of these models would simply be disallowed by regulators, and the regulators would be right (though not necessarily for the reason they think.) So far, we haven't had huge problems in the U.S. insurance realm, but such shortfalls occurred in the UK ... about 20 years ago, come to think of it.

[and don't get me started on CDOs and the Great Credit Meltdown of 2008]

[the problem, per se, wasn't the math]

Back to the WSJ piece:

Math curriculum has remained largely unchanged since the 1950s, when Russia beat the U.S. to space. After the Sputnik satellite took off in 1957, U.S. math curriculum was revamped to churn out a workforce fluent in the kind of high-level calculations needed to help military and space endeavors.

Besides what some see as its arcane demands, the current curriculum leads to inequities, according to research from Dr. Boaler. Some schools place students into different tracks as early as middle school, putting those who show early promise on the fast path to calculus, a desired course for admission into four-year elite colleges, and filtering out those who struggle.

I agree, calculus should be disallowed in high school.

The prominence of calculus in the college admissions process is another issue. Many colleges view calculus as a signal that a student is a high achiever. Not all high schools offer calculus, putting students without access to high-level math classes at a disadvantage when applying to college.


I'll be extremely blunt here: the vast majority of college students are not at selective colleges. When you discover how many people actually have college degrees by age group, calculus is not the problem. Just getting past pretty basic math is. Trying to pretend that these "alternative paths" will get anybody into a difficult degree program is stupid.

An Urban Institute analysis of data from the Department of Education covering 2013 to 2014 found that 20% of Black students attended high schools that didn't offer calculus, compared with 13% of white students.

So, they're saying that 80% of Black students do attend high schools that offer calculus. How many of the students in such schools (of whatever race) ended up taking and passing calculus in high school?

For what it's worth, I'm not joking about disallowing calculus classes in high school. Having taught calculus to college students who had had calculus in high school (and they got decent grades in it), I came across all sorts of math deficiencies among the students -- understanding the equation of a line, or knowing the extremely simple formula for the area of a circle, for starters.

It was clear to me that these were not bad math students, but that there were bad incentives for the schools to push as many students as possible into calculus by senior year of high school. It was a status thing. The AP/Achievement Exams had exposed these students' lack of ability to actually do calculus, which is why they were in my class. Some objected to having to take a class again in something they knew well -- which, when I had no experience, I thought might be correct. Then I got their first tests graded and discovered what the problem was. They had holes throughout their math skills, not only in calculus. But no, none of the students in my calculus class actually knew calculus. I had to try to get them to unlearn some of the "voodoo math" they had picked up in high school, which was meaningless manipulation of symbols for many of them.

That was far from the worst issue I ran into in teaching in college, though.

I taught the "here's the last math class you'll ever take in your life!" at NYU, and I knew the students hated me. They hated the subject, and I didn't blame them. They had been cheated in the K-12 years. We see the indignant op-eds and letters-to-the-editor when people graduate high school and can't read, but we get excuses when they can't add fractions.

Skeptics contend that having computers do all the calculating would deny students the ability to understand the basics of math. Mr. Wolfram and Dr. Boaler say that basic arithmetic is important and should be learned. "What we don't need is to make them memorize the times tables," says Dr. Boaler.


Bullshit, we do. Not only that, we should teach students how to make change in their heads, about counting coins (you will absolutely get interest in money-related items), etc.

There are all sorts of patterns in numbers, and there are ways of making times tables, etc., somewhat engaging. But the main thing is that yes, memorization is good. The students will never get any unconscious mastery of numbers unless you let them get some conscious mastery and that yes, this stuff is going to be work for most of them. Suck it up and do the work.

When I was a kid, I used to think like these "education reformers" did, as math came very easily to me and I had been given much more interesting math stuff to think about by the likes of Martin Gardner and Raymond Smullyan. I had fun teaching myself programming, and I had always focused on numerical code, not coding for games or graphics. When I came across Maple and Mathematica, I was so happy -- even when I had to learn how to force the systems to do trig substitutions properly, it still cut out a lot of tedium in my math-related work.

But once I started teaching math, I changed my mind -- a lot. I realized all the work I had put in as a kid, and how that made certain things much easier for me. Students' glaring holes in skill and knowledge were hard to ignore. I came across Kumon, and the concept that one needs to have mastery of a particular skill before moving onto the next incremental step made lots more sense to me.

That's the true reform that needs to be made - not whatever high school classes, but that in elementary school students need to proceed at their own pace for putting down the basics, and they shouldn't be pushed to the next step until they demonstrate mastery in the earlier step. Yes, students will be all over the place in their progress, but so what. Figure out a way to make that work rather than this same bullshit reform they keep coming up with, in different words.

Whether it was New Math, or Common Core, or whatever, it generally was to try to get away from the "boring stuff" of actually having to do calculation by hand, and do it a lot, which was boring for the teachers as well as the students. Let's do the interesting stuff! they cried, ignoring that they could do both the boring stuff and the interesting stuff in parallel.

I mean, I was doing the interesting stuff at home, and the boring stuff at school (with regards to math, at least), but one could carve out some fun math stuff time in school, I'm sure. Just remember that the tedious stuff also needs to be done, and is a bit more important in being able to do even more fun stuff later.

Mr. Wolfram thinks that without a curriculum makeover, math as it is currently taught runs the risk of becoming as obscure as Latin.


Way to pick something that isn't obscure at all, doofus. Latin is extremely well-studied, has loads of connections to European languages, lends entire words into English, and is still used in medical and legal terminology. Evidently, Latin is still compulsory in secondary education in some countries.

Anyway, I am sure the WSJ is getting all sorts of smartass letters to the editor, and will not be needing my contribution at this time.

The only plus I see is that, given this isn't a new concept at all in math education reform, the amount of damage they can do (even in California) will be limited. If it gets calculus out of high school, I will be pleased. (I don't see that happening, though)

And Kumon will thank them for the revenue boost as they get another crop of parents who want to make sure their kids actually know how to deal with numbers.
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