Woke Math?
I’m not going to bury the lede here. Seattle public schools is proposing to incorporate more ethnic studies into it’s mathematics curriculum.
Most of what they are proposing is pretty standard math history. Basic knowledge that disabuses the student of the idea that old, dead white guys from Europe were the be all, end all of mathematical knowledge and development. Truly, if it hadn’t been for Gutenberg, I suspect that Europe would not have claimed so much of the development of mathematical knowledge. Europe had a way to mass disseminate knowledge, and a cultural and political will to do so, and since the US descends from those traditions, that is what we learn.
But that doesn’t mean the Middle East, and Asia, had nothing to contribute, or that they stopped developing mathematics after 1400 AD. 1
There are even some very good points in the proposal about how suppressing mathematical literacy was right up there reading literacy when it came to keeping power concentrated in the hands of the elite. Or one of my favorite topics, the fact that there are multiple paths to take to reach a mathematically sound result, and students should not be punished for taking the road less traveled.
Still, I worry. We are not very good at teaching mathematics. Some teachers are rock stars, but the quality is woefully inconsistent, even within a given school 2. But taking on topics that are emotionally, socially, and politically charged while still sucking at teaching the topic that is actually at the heart of the class?
That gives me pause.
Maybe if we still didn’t have parents, and teachers, and pundits, out there talking about how some kids just aren’t good at math 3, and we had programs that focused as hard on math literacy as they do on reading literacy. I mean, so much of the problems we have with kids learning math is emotional, in that we have kids not believing that they can learn it. And not because they have a well known disability, but because the adults in their life have basically conditioned them to believe they can not learn it, simply because they did not grasp some things straight away. I mean, think about reading. If a kid struggles with learning to read, and people notice4, they toss extra resources at the kid. Even kids with disabilities are taught to read. If you are dyslexic, somebody will probably be willing to get you over that reading hurdle. Are you an adult who can’t read? Someone will step up and help you learn. Even the blind are taught to read. I can not think of a single disability that stops us from trying to teach a kid to read.
But math, we give up on pretty damn quick. And teaching a bunch of Social Science on top of that doesn’t strike me as something that is going to help much. Especially social science topics that some people just really like to get up on their soapbox about.
Maybe I’ll be proven wrong, and the district will develop very clear and concise curricula. But my quick skimming of the proposed topics this morning struck me as being filled with a lot of social science word salad. It’s going to need a lot more development, and Seattle Public Schools is not a district that fills me with confidence.
Luckily, Bug isn’t in that district.
- For fun, how many mathematical concepts were simultaneously developed in the far corners of the world, but no one knew for decades because of how slow information traveled.
- Lest people try to pretend that it’s all about funding, it’s not; even really good schools can have crappy math teachers. Good schools just have parents that can tutor their kids, or pay for tutors
- Ever notice how we don’t have people talking about how some kids just aren’t good at reading, or at social studies, but math…
- And care. Kids still fall through the cracks because no one cared enough…
Honestly, I don’t remember history being part of math when I went to high school in 1994-1998. It was all about learning how to use the equations. The little of the history I know is mainly from self-reading.
But I still think too many people think STEM STEM STEM is a cure-all for everything and this is a grave mistake. To be fair, it is far from an American mistake. It is a pretty universal one.Report
As our societies become more technical and advanced, mathematical and scientific literacy is just as important as reading literacy. I think a lot of the focus on STEM is from the realization that we have greatly lagged behind in this.
Let me put it this way, the fact that I have a strong math and science literacy grants me a much larger advantage in society than simple reading literacy does.Report
Margaret Thatcher was chatting with Ronald Reagan at some major event and she related a story about being asked what a young person should study to be successful. She told Reagan that she’d said “study math”, because no matter what happens, people who are good at math will always have a leg up.Report
“I think a lot of the focus on STEM ”
The focus on STEM is “We don’t know what to do about jobs, so we’re going to pretend STEM is the answer because it sounds very Silicon Valley. Who is against scientists and engineers, amiright?”
I mean first off, I know scientists — as in actual STEM degrees. Quite a few make less than teachers, and struggle to find jobs. Turns out there’s not as many science jobs out there as you’d think. I know engineers — the market’s pretty variable on them. Some do well, some end up never using their degree. But I can say that at least half the people that try for an engineering degree shouldn’t be there and won’t make it. Quadruply so for chem es.
STEM is shouted like “everyone should learn to code” — it’s not actually a solution, and is pretty idiotic once you think about it. STEM jobs aren’t limitless, many — most people — are a poor fit for a STEM job, and that’s assuming they can actually get through the degree.
STEM is pissing into the winds of increasing automation and pretending it’s a solution, because words are easy and everyone feels better when you believe all the people out of work are lazy morons who got basket weaving degrees in college.Report
I think it depends on what a person means by ‘STEM education’.
If “STEM education” translates to, “A four year degree in a traditional STEM field”, then I agree with you. We can not degree ourselves into prosperity.
But if you take a wider view, there is a lot more good that STEM can do as our societies become more technical.
A modern welder, for instance, has to have a fair understanding of chemistry and physics (metallurgy, heat transfer, structural mechanics, etc.). All of the other skilled trades likewise demand more and more STEM knowledge in order to continue to be relevant and useful.
Even the basics of computer coding can help other, non-STEM fields. Knowing how to construct basic scripts can save even lawyers a lot of time doing research.
STEM isn’t just about training scientists, it’s also about keeping the lower skill workers from being unemployable. And that all starts with Math.
If you never learn the basic math, you will be less and less employable.Report
When I began my career in 1981 the elderly architect I worked for used a slide rule to calculate floor heights, areas, and occupant loads. Our developer clients used paper spreadsheets and manual adding machines to calculate rates of return.
We used pocket calculators in the 80s to do that stuff.
Today no one does that stuff- the software does it for you.
Isn’t the entire point of automation to do the dull tedious math, and let you focus on making decisions about creative and managerial things?
Its literally the advertising pitch they use!Report
First rule of calculators: GIGO
Second rule of calculators: You are the final error checking of the calculator.
If I didn’t learn the numerical methods and the underlying physics of the stuff I do, how can I be sure that the calculator/computer is producing a sound answer? How can I be sure I didn’t make a mistake in the inputs? Or the assumptions?
Understanding math allows you to spot errors when they occur. If each of your columns can support 5.5 tons, and you have 20 columns, and your loading calculator says you can support 1100 tons, knowing the math instantly tells you that you dropped a decimal point in your inputs.
But if you can’t do the basic math, and you just trust the calculator…Report
Hee hee.
I recognize a Dad Lecture when I hear one.
Seriously, while you are correct, the “operator input error” problem is precisely the thing software engineers work at eliminating.
So for example, when I ask my software for the area of a floor, I don’t need to “input” anything at all; I just trace a line around my building;
There is in development now, software that needs even less- you just input the parameters of a building and it designs the columns and beams by itself because beam and column design is very, very, algorithmic.
I guess the question is, is math something that users want to eliminate from their life? Are they willing to pay for it?
If so, an algorithm to do just that will be produced. (That whole “market signals thingy).Report
Sure, right up until you leave Roark’s behind. Then the algorithms need human help.
The point should not be, “We need people to do the exact same thing, over an over again, until the end of time”.
The point needs to be, “We need people to constantly push the boundaries past what we know how to do real well, and to further that endeavor, we will make the simple stuff easy”
You can’t stand on the shoulders of giants, if you have to constantly rebuild the shoulders.Report
The most important app in the world would be unit testing for Excel spreadsheets, if only anyone would use it.Report
So, important math problems come at me every day, but they are disguised as not math problems at all. Because people want my money.
For instance, the last time I bought a car, they tried to sell me the extended warranty. I said, politely, “No thank you”. The sales manager (they had booted me to him by them) said, “Well, why not?”
I hate it when sales people don’t take my no for an answer, so I said, “Because I can do math.” He gave me a blank look.
I said, “An extended warranty is a kind of insurance. Like all insurance, it’s a bet, with odds. In order for an insurer to make a profit, the odds have to be in their favor. I have no objection to people making a profit, but if I can afford the risk myself, I prefer to carry the risk myself, since it will, on average, cost me less. So, I don’t want the extended warranty.”
Life is full of math problems pretending to be “exclusive offers”. Notice I didn’t do any calculation at all in making that decision. Spreadsheets, calculators, computers were irrelevant. What was relevant was the concept of expected value, and that it is beneficial to use it to drive decision making.
But expected value is a mathematical concept.Report
+1Report
I had a fun math problem a few weeks ago. It was called “Is X dollars for Y windows a good deal”.
It wasn’t hard to figure out the per-window cost, even with the fun “This is the price, but here’s the deal, and here’s more deal!” obfuscation.
The real problem was determining “How much should it cost to replace a window”. The answer “About a thousand less per window than they wanted to charge”.
Now I only knew that because I spent literally hours digging around before and after their sales pitch.
Sadly, math class really can’t help with that besides deriving unit pricing. I really don’t know how much a window costs, or how much work lies in replacing it. They don’t need replacement often. I know how much it costs to replace an alternator on a car, though.Report
Aha! You are the reason that all the rest of us get daily phone calls asking about our cars’ extended warranty. It all makes sense now.Report
STEM isn’t just about training scientists, it’s also about keeping the lower skill workers from being unemployable. And that all starts with Math.
Last week I was visiting in-laws in rural Kansas. One of them is a now-retired union electrician who keeps in touch with the union. Rural industrial-scale electricians often wind up having to fabricate structural bits. I was pleased when he told me that the parts of the union’s apprentice program dealing with fabrication is now less about hand tooling and more about building models with computer software and letting the six-axis CRC machine do the actual cutting.Report
CRC? or CNC?
Still, I like to hear that the trade Union’s push that kind of stuff.Report
CNC. Stupid fingers.Report
Like Saul, I don’t remember any math history as being part of my high school or middle school education. I don’t even remember the teachers telling us much about the real world applications of algebra, trigonometry, pre-calculus, and calculus. That would have been helpful and make the entire thing less abstract.Report
As I said, we suck at teaching math.
I think the Seattle proposals have a lot of good stuff in there. Learning more about the history and application of mathematics is a net good. It will allow the topic to be more engaging.
But I also see a lot of stuff that is much better suited to a upper level high school social studies class.Report
I really don’t know where it’s best applied.
I’m afraid that the good stuff won’t make it into Seattle classrooms, but heartened that the bad stuff won’t either. My perception (which is admittedly based on second and third hand information much more than direct experience) is that this stuff is a mix of well-intentioned attempts to improve things that don’t take the many constraints on teaching into account, and a full employment program for ed majors.
As to the underlying question, it’s hard to say. I’ve had a long-time interest in history of mathematics which has been almost entirely satisfied by self-teaching, but I also think that in a lot of cases the historical context has deepened my understanding and appreciation of the math itself.Report
Teaching math history could be fun.
“About three seconds after the initial cosmic expansion kicked off, the “Big Bang”, the first numbers formed. These early numbers were all positive integers and only included few primes, and the only mathematical operations that condensed out at these early stages were addition, subtraction, and oddly, the traveling salesman problem. Then…”Report
My recollection is that textbooks sometimes had sidebars where they might talk about Archimedes or Newton or whatever, but it was very peripheral.
My suspicion is that this Seattle thing is an extension of the idea that every class is to include reading and writing. I don’t know how current this idea is, but it was definitely the hot trend in education for a while. It may be due to return to the top of the Hot New Educational Trend cycle. So you saw kids in P.E. writing papers about P.E. stuff, with pretty much everyone involved appreciating the absurdity. So if math class has to include this stuff, math history is an obvious route to go. Given that, making it more than Dead White Guys is all to the good.Report
I’m not even talking about the history. I’m talking about what do you use these equations for in modern life. There was no lesson on the real world applications for math or applied mathematics at all.Report
Because math pedagogy is created by mathematicians.Report
Math history is rarely explicit. It is more implicit – it’s in the names of techniques. It’s in the sidebars in the books, the references to Greeks like Pythagoras and Euclid, to Germans like Gauss and Euler. The 7 bridges of Konigsberg problem is often seen in high-school or even earlier. These all have embedded references to Europe and Europeans (and to males). There’s nothing wrong with this per se, but a student who is not European (or male) might easily get the idea that “this has nothing to do with me”.
Which we know to be false, right? We know that algebra, and our number system was developed by non-Europeans, by Arabs and Indians. We know that certain women have had a big impact on mathematics, physics, and computing. So let’s take care to ensure that the students know that, too.
I get Oscar’s concern for how well this is executed. Will this result in less mathematics being taught and more history, geography and literature, this time in math class? We’ll have to see.
I want to leave one note, which seems related. I have seen research that demonstrates that if a quarter-long math/physics class (at the college level) begins with the instructor having all the students write a paragraph on one trait that is admirable in a person – any trait at all, not necessarily related to STEM – it erases half of any racial or gender gap in performance for that class. This is not a small effect.Report
That last note is very interesting…Report
Here it is: http://blogs.discovermagazine.com/notrocketscience/2010/11/25/15-minute-writing-exercise-closes-the-gender-gap-in-university-level-physics/
I am happy to shout this to the heavens.Report
That’s awesome!Report
Sorry to be a downer, but it doesn’t replicate (along with many of the other stereotype threat alleviation studies).
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3587853/Report
That is a super interesting paper, and I intend to digest it more. Thanks for bringing it to my attention. I note something from the abstract:
So. This only studied gender, and you realize of course, that the link I offered above was about race, not gender?
But they say they noted no acheivement gap. Which means they aren’t going to see the intervention do much, how could it? And yet they don’t say they find “no” stereotype threat endorsement, but rather that they find “little” stereotype threat endorsement.
Soooooo, that really doesn’t look definitive to me. Many researchers have found validation of the concept of stereotype threat. Some of that research doesn’t replicate, and that is a substantive issues.
At the same time, I read a piece by one of the scientists who failed to replicate ST, and it was clear that he didn’t understand it, and left out critical elements. So of course it didn’t replicate.Report
Gender is the decriptor in your link html and I looked at the study as well which also referenced gender. Maybe you linked to the wrong one?
I’m happy to be corrected if there are any positive replications (send a link!) but if you do a google search on stereotype threat replication, it’s not very pretty.
https://www.google.com/search?q=stereotype+threat+replicationReport
“a student who is not European (or male) might easily get the idea that ‘this has nothing to do with me'”
I might be the wrong person to comment on this, but how would a person think “math has nothing to do with me”? Do I lack the experience of 7, or live in a world without circles? Math is universal in a way that language, culture, and even science isn’t. I mean, I can imagine a situation without race, or even without carbon, but not without mathematical principles. (Even non-Euclidean principles are something.) And I personally never knew anyone named Euclid, so I never associated the word with a person of any particular group.Report
How did you come to understand how deeply math was embedded in everything you know and do?Report
Word problems :^)Report
Another of my math education hobby horses…
I truly did not learn how to do a word problem until college.Report
As an okay but never good math student who nevertheless got really interested and even excited once I took trig and calculus….I hated word problems.
I suspect they were created in order to get students to learn that math applies in everyday life, or to get the student to apply their skills/knowledge to a situation that wasn’t just a “solve for x” proposition. Still…they were so artificial as to be unrealistic. And the teachers (in my experience) usually had some very formulaic approach she (almost always a she, in my experience) forced us to use. (That goes to your point above about not looking into multiple ways to get the same result.)Report
Still…they were so artificial as to be unrealistic.
Yes, but. They can’t require any domain-specific knowledge beyond what students can be expected to have encountered. They have to be simple enough that they can be worked by hand* in a reasonable amount of time.** Those are really significant constraints.
* What to teach in a calculus class is facing a serious problem. Much of Calc I time, for example, is given over to teaching students how to do differentiation and integration by hand. Thing is, Mathematica and other symbolic math tools are better at that than you or I will ever be. Are we wasting the students’ time?
** When I teach math in a classroom, one piece of advice that I give to students goes something like this (example drawn from calculus). If you’ve set up the integral for the problem, and it rapidly explodes into some unmanageable mess of complicated algebraic manipulations, you’ve made a mistake. No instructor wants to grade problems like that.Report
Rooting around in my memories here, but it was my brilliant college algebra teacher (an economist by training, not a mathematician) who taught me how to work word problems. And what he did is reflective on Gabriel’s complaint – he ran through a number of different approaches to getting all the pieces of the problem together, so if method A, B, & C didn’t gel in your brain, perhaps D would.
He did this for all of the topics he covered, always taking the time to explore multiple approaches to the solution, and telling us to use the one that we are most comfortable with.
Re: Calc 1 – My teacher there (also not a mathematician, he was a biologist) had us all working in small teams on large, real world problem sets. Every other Friday he’s hand out a packet with a complex problem described and broken down into chunks. And over the two weeks, he’d tie the lectures to the chunks, so by class time on the coming Friday, you should have the packet completed and the problem solved.
And no, he did not expect us to do complex integration or derivatives by hand. It was mostly understanding how and when to use integration and derivatives, and when you could do a hand analysis using one of the common forms, and when you should probably put it in Mathematica.
I compare those two community college teachers with my Calc 2 & 3 professors at the University, and honestly the CC did a better job.Report
Thanks, Oscar and Michael, for this discussion.
Michael: What you say makes sense. Also, I probably am a little too harsh on my teachers. I’ve taught, too (but history, not math), and I realize that those things that annoy the students are often there for a reason.Report
I don’t have any strong memories of not knowing that. Maybe it hit when I first understood the commutative property of multiplication, that X * Y = Y * X. Which is still pretty cool, if I think about it. There’s a power in the statement “for all values of X and Y”. There’s a certainty in that, but also a recklessness in saying that there are no conditions in which my statement could ever be incorrect. X stacks of Y things are always going to equal Y stacks of X things, no matter what the things are. If I recall correctly, the addition and subtraction tables were boring to me, but by the time we got to multiplication and division i was hooked.Report
One of my perennial complaints about math pedagogy is that the curricula is/was (IMHO) designed by mathematicians in order to identify and cultivate other mathematicians. Especially past, oh, say 8th grade.Report
I’ll disagree. The “standard” curriculum from freshman year in high school through sophomore year in college is designed to identify and provide a foundation for engineers (with that term used broadly). For the students they think have potential to be mathematicians, the curricula start to diverge in college. I was in the latter group. We got invited to take honors calculus in college, which not only went faster, but was taught differently — we got the beginnings of real analysis. Differential equations was split into “Diff E for engineers” and “Diff E for math majors”. I couldn’t take the engineers’ class for credit towards my math degree. We were given opportunities to see how broad a field “math” was, with so many things that weren’t real and complex numbers and functions.
At a fundamental level, if they (we?) were trying to cultivate mathematicians, discrete math wouldn’t be ignored in the “standard” curriculum.Report
It’s less the topics covered and more the rigidity in the pedagogy.
As I mention elsewhere, math usually has multiple ways to solve a given problem, but rarely are students encouraged to explore those alternate pathways (at least, we weren’t in my schools). If the ‘acceptable’ path doesn’t gel in a students brain, then they get stuck. In my experience, the path that is usually ‘acceptable’ in math texts and answer guides is the one the mathematicians tend to prefer.
Hence, the kids who ‘get math’ in high school are the ones whose brains gel around those solution pathways.Report
There are long- and well-known fundamental conflicts in and around math education. One of them is whether to deviate from the methods that the student must have mastered for the class two semesters ahead. (If there’s a class in it, there’s always a more advanced class, or seminar, two semesters ahead. Students may or may not be going that far, which is a source of conflict.)Report
Again, it’s not the topics that are a problem, it’s the pedagogy. Does the teacher/curricula allow for students to explore the alternate pathways for thinking about and solving a problem?
And if so, does the course demand that students show proficiency in each pathway?
Going back to my College Algebra teacher, he demonstrated (whenever possible) multiple paths to the solution, and then told us to use whatever method we felt most comfortable using. We were not required to use any specific one, and we only had to show enough of our work so that he could follow the logic used.
The stress level in that class was non-existent, and it opened mathematics up to me.
As for the topics covered, if it’s a class that is required by the state for graduation, it should not include any topics that are foundational for advanced work unless that advanced work is also part of the state requirement. Schools have elective math classes for students who want to go further, and that is where such topics belong.Report
I hear you. Now go win the argument with today’s high school accreditation people, who say that Algebra I, II, geometry, and pre-calc must provide the student with the skill set to start calculus and analytic geometry.
As an aside, the community college system here makes all incoming students take a math placement test. A surprising number who thought they were going to jump right into calculus find themselves placed in “remedial” classes.
I’m old, so went to high school in a place and time where the math program was split, with one side labeled college prep and one labeled practical.Report
Oh, yea, don’t even get me started on how we’ve structured our HS system to be all college prep, all the time.
I mean, isn’t that what CCs are for?
My college education was not lessened because I did my first year at a CC. People need to really stop insisting that kids should leave a public HS completely ready for University. Send your kid to a prep school if you want that.Report
“As I mention elsewhere, math usually has multiple ways to solve a given problem, but rarely are students encouraged to explore those alternate pathways (”
It’s called Common Core, and the complaints about it are insane.
I mean just google Common Core math, and you find angry parents upset that their children are either doing math “wrong” or “weird” or are being deducted points for not doing it “the right way” and screamingly furious about it.
The biggest hump in math education is the introduction of algebra, because children switch from “memorize these tables, memorize this algorithm” to “Here’s a problem and here’s some tools, have fun” and you go from “Do X to solve Y” to “If you want to solve Y, you have tools A-G, so start poking the problem with your toolkit” with literally zero preparation.
A method of approaching math (memorization and algorithms) drilled into their heads for 6 to 8 years is suddenly tossed away, and replaced with “It’s all totally different now” and suddenly a giant chunk of the kids flounder and decide they’re “not good at math”.
So the solution is to take the toolbox approach and start it from the beginning. Sure, memorization and rote algorithms (like long division and multiplication by hand) have their place and are taught. But kids are also taught other methods (given their age, they’re mostly the sort of ‘mental math’ the ‘good at math’ kids work out — trying to multiply or add or divide by tens when possible, etc) and of course required to USE those other methods, so as not to rely on the crutch of a single approach.
Which again, has infuriated parents, who don’t understand why their kid is getting marked down for not using the correct method to solve a problem, because “why isn’t the normal way good enough” because they don’t understand the whole point of math is “Math is an infinitely varied set of tools, and teaching kids there’s “one way to do math” handicaps the crap out of them once they’re out of the kiddie pool. And also your kids will be able to estimate tips in their head, determine whether answers are roughly correct without doing the work by hand, and a whole bunch of stuff that the average American associates with ‘being good at math’ so why are you so angry we’re actually teaching them to be good at math exactly like you want, which means we have to teach them BETTER than we taught you.”Report
Overall, I agree with you here. With one quibble:
If a single approach is a crutch, it’s a bad approach to teach.
That said, most people will gel onto one approach, and be able to use one or two others well enough. Requiring that kids use every method available is just asking for trouble when the kid hits a method that just won’t click at all.Report
“Requiring that kids use every method available is just asking for trouble when the kid hits a method that just won’t click at all.”
The level we’re talking about here is elementary school. These are not complex methods, nor are you at the sort of math wherein individual methods and approaches matter.
Asking a student to demonstrate, say, subtracting one number from another using both the basic subtraction algorithm and the ‘nearest tens’ method is not something that is blocking the child.
And honestly, how can someone tell what method works best for them if they don’t at least try all of them?
I mean I loathe integration by parts, but sometimes that’s the only tool for the job.Report
I’m only just now encountering the elementary level stuff (Bug is in 2nd grade), but I have tutored the occasional HS kid, and that is where I saw an insistence on being able to use each approach to solve problems.
Like I said before, expose kids to every method. Have them try it in class.
Don’t make it part of their grade.Report
“Don’t make it part of their grade.”
It depends on what you mean. If they are being tested and graded on “can you apply method X” then yes, make it part of their grade.
If they are being tested on “can you solve this problem” then no, don’t make it part of their grade to use a specific method.
But again, you need to teach various methods, because unless you have a full math toolbox you can’t be sure you’re applying the right tool — and if you’re not exposed to all methods then you can’t tell which ones you prefer.
And if you’re being taught a method, you really have to be tested on the method to make sure you understand the method. So yes, that should be graded.
“Don’t make learning a method part of their grade” — so Cal 2 teachers shouldn’t grade students on applying integration by parts because some students dislike that method? They shouldn’t give problems that require integration by parts and ask students to demonstrate understanding over that method?Report
Honestly, no, not if it trips up the students and the problem can be adequately solved by another method.
Listen, I don’t grok math, even derivatives and integrals, the way a lot of people do. I have to come to understanding from a different direction. It’s frustrating as hell at times, and I do numerical analysis for a living.
Once I have understanding, once my brain finds something to gel around, then I can start figuring out how to use the other approaches. But if a teacher is demanding that I master method X (which I don’t get) and prove mastery via an exam, before I have found a way to grasp things…
Well, there is a reason I aced (literally got an A) in Calc 1 and an F in Calc 2.
Yes, different methods have different utility towards solving different kinds of problems, so eventually a student will have to acquire some proficiency with all of them if they want to keep advancing in mathematics. But to demand that as each method is taught is to leave students behind.
As I said elsewhere in these threads, both my College Algebra and my Calc 1 teacher managed to demonstrate multiple approaches to solving the problems and then let the students figure out which works best for them at the start. As a student works more and more problems, they start figuring out the other methods, mostly out of necessity (because problem X is a lot easier to solve using method A, rather than the preferred method C, but since you can think about it in terms of method C, you can start to understand how A works).Report
The history of math is deeply fascinating. Fascinated things inspire curiosity. Curiosity inspires learning. I’d be unsurprised if teaching math techniques along with their history didn’t help students learn.Report
Yes.
My worry is that instead of it being an interesting lesson, it’ll be an emotional sermon, and getting kids emotions ramped up while trying to teach math…
I can imagine ways to do such things well. I can also imagine people doing it horribly.Report
I can’t.
There are correct and incorrect answers in math. Worrying about ethics, history, and feelings is a waste of time in terms of finding the correct answer. Their introduction is at best a distraction.
The solution to “not enough math” is “more math”.Report
Again, it depends on how it is presented. I’ve taken physics and chemistry classes where the history behind experiments and discoveries was discussed as an introduction to the topic (sure, you can cover Maxwell’s Demon without talking about who Maxwell was and why he had a demon, but it’s more engaging to cover that).
Now, if math classes do stupid crap, like talking about how the quadratic equation is inherently sexist/racist/terrorist, that is going to be less than helpful.
However, if a math teacher opens up a section on Algebra with something like:
And just to drive things home, find some examples from history that show how data was manipulated to push something that was later shown to be false, sprinkle them throughout the class where appropriate, just to keep the kids engaged.
It really all comes down to what topics are expected to be covered, how much time the school demands teachers spend on those topics, and if the school insists that the topics be presented in specific ways that do not really further the learning in mathematics.Report
I agree that math and scientific literacy is important. Wasn’t trying to deny that. Here is what I think is troubling:
1. When politicians and pundits talk about STEM, STEM, STEM, they are not really talking about Science and Math most of the time. They really mean technology and engineering specifically stuff that can turn into investment and job creation. Do they want PhDs that can work for pharma or BP? Sure. Do they want an astronomer that explores the universe? Probably not. A more honest version would be Technology (in the Silicon Valley, WeWork is a “tech” company sense and engineering if it accompanies. Or some other engineering.)
2. Despite some odes, radical underfunding of the arts and humanities in school’s still continue.
3. Some tech, really “tech” is imploding. WeWork is a good example but I suspect more will follow because a lot of Tech 2.0 companies are far from profitable. This might be more dire than the 2000 tech bubble and the 2007-2008 fiscal crisis in results to the economy. What of all the “learn to code?” then.Report
This is off the OP topic, but tech isn’t imploding as such. Rather, the current tech fad is busy imploding thanks to the current fad being mined for every idea. And such mining is, frankly, common and unsurprising. Usually when a new vein is opened up, people will mine the hell out of it, both hoping to get rich by extracting everything they can, and hoping to find a branching vein they can develop.
This has been the pattern since the first stick was fashioned into a club. We just get to see it happening in less than a decade, rather than across generations.
If I get a chance to write another post about Boeing, we can have a discussion about the dangers of pushing tech too fast in the pursuit of short term profits.Report
“Rather, the current tech fad is busy imploding thanks to the current fad being mined for every idea.”
That’s good news for bitcoin. I kid. Seriously, in that vein — people need to stop trying to make blockchain happen. Cool idea, I get it. But if it’s ever useful for anything, it won’t be a currency, your current trading setup, or whatever idea you slapped “blockchain” on to appeal to moron investors with more cash than common sense.Report
What makes you believe point 1? And what would it matter if politicians really mean TE when they say STEM?Report
Because that means politicians only want STEM that directly produces profit. Any STEM that is more focused on pure research isn’t really what they want.Report
As JS said, the general idea is that STEM will be about economic growth and solid middle class or above jobs. How did WeWork get so overhyped? They are not doing anything new. IDW does the same thing, has been around forever, has more customers, makes a profit, etc. But IDW was only given a valuation at 2 billion, not 50 billion because they did not call themselves as a tech company and as far as I know do not have an app.
So politicians want FB or WeWork or Uber, a unicorn company and lots of well paid employees. They do not want an astronomer researching black holes.Report
If I said that politicians want an astronomer researching black holes, how would you refute it?
Does that question make sense? I can get why politicians would prioritize education in fields which are more likely to result in national benefit, and I guess that some might prioritize economic growth over any other type of benefit, and those same politicians might consider engineering and technology to be a stronger driver of economic growth than science and math, but it seems like a lot of assumptions for you to reach that conclusion with confidence. I don’t see any signs that they’re talking about T and E over (pardon me) S and M, and I don’t see any signs that they’re funding the former over the latter. That leaves me with neither theory nor evidence for your position. So why are you asserting it?Report
However, whatever they actually want, I suspect the likely result won’t be PhD’s, but a bunch of people with BS’s that work entry level jobs in those industries–sometimes in a lab, sometimes in administrative assistant positions–and earn maybe a little more than minimum wage. I don’t mean that as an insult to those jobs. I’ve never worked in a lab, but if there’s a job in one, even if it’s just the proverbial “cleaning test tubes,” then it’s probably a job that needs to be done.* And I know being an administrative assistant is important and requires a lot of skill. However, I don’t like the idea of creating yet another hurdle for such jobs, or making empty promises of the sort that humanities and social science educators are wont to make.
Its a tragedy that all person’s must bemoan.
*I feel inconsiderate saying “cleaning test tubes.” It sounds a little like “flipping burger,s” an expression I find condescending to people who actually flip burgers.Report
My first position at the Lazy B Airplane Ranch was, quite frankly, beneath the skills a person with an MS – Engineering should be doing. My primary task was to basically write the simple (but highly repetitive) scripts that would be used to analyze the internal loads of a given airframe FEA model. This required exactly zero engineering skills, but the Union said it was a job that an engineer had to do.
By the end of my first month, I had the whole thing scripted such that I’d get a load set and have the analysis scripts generated and ready in less that 5 minutes. Then I’d spend half an hour filling out a Word template that describes the analysis to be done (based upon the load information I’d gotten) and email all of it to the next person in the chain. I didn’t actually get to do the analysis, only senior engineers could do that.
Then I’d surf the web, or beg the senior engineers for something else to do. After 6 months, I was already looking for a different job in the company (which took 18 months to find and land).Report
There are departments in the STEM field that have weed-out courses.
Strangely enough, I think all of the STEM departments have weed-out courses.
What we need are STEM degrees without weed-out courses.
This way STEM degrees will be available to more people.Report
No, what we need are colleges who do not hold the weeder course against you.
For example. At UW-Madison, the main STEM weeder course is Calculus 2. It is a 5 credit course (normal classes are 3 credits). It’s 300 kids being taught by single prof with a handful of TAs. It is a pre-requistie course for damn near all higher level STEM classes. If you fail it, you get a big, fat, 5 credit F on your transcript and you are locked out of those next classes. Lots of STEM hopefuls are done right there.
What we should have is the weeder course being Pass/Fail and maybe 1 (or no) credit. It should be tough, and if you fail, it stings, but not a ton. You can’t advance, but you aren’t staring at a GPA that is now wholly in the toilet. You can rally and try again next semester. If you fail on round three, then perhaps STEM isn’t for you, but you still aren’t working to overcome a huge F.Report
A more important change might be to get the students to understand calculus down in their bones, and there are approaches that do this by having them spend more time examining what happens with little rectangles, or what happens to to equations like f(x)^y – f(x + d))^y as d gets very small. Basically, letting the derive some of the rules for themselves by seeing what’s happening on their pocket calculator. And only after they grasp a concept do they need to learn the shorthand scribbling to describe it.
It would take longer, but the premise is that weed-out courses shouldn’t be used as weed-out courses, they should be used as courses that teach really fundamental and important things that bright college students needs to learn, giving students the confidence that they can understand the complicated mathematics of physics and engineering and the organic chemistry of medicine, pharmacy, and chemical engineering because they have learned it.
As it stands, I fear that a great instructor whose students were all passing the weed-out courses would be called on the carpet for failing to weed people out.Report
Or this.Report
In sort of reverse order…
Your last paragraph is a theory of grading thing. There are two possible uses for grades. One is to sort the students. The other is to test mastery of concepts and/or skills. Consider a test question that every student gets right. For the first purpose, it’s useless. For the second, it’s a fine result. Weed-out classes at an undergraduate level are almost always in the second group.
The second paragraph runs into a problem that’s been skimmed over in this subthread — Calc II is often the weed-out course for people whose major is over in another department. The engineering college wants their students run through calculus, a semester of differential equations and a semester of linear algebra as quickly as possible. (This is also the basic situation that drives the 300-seat lecture plus TAs with questionable teaching skills model in so many math departments.)
Just observations on the first paragraph, reasonable people can disagree. Most Calc I instructors do the graphing calculator thing for motivation. We (putting myself in with the theoretical mathematicians for a bit) threw that all out and rebuilt calculus based on set theory and formal limits in 1820-1850 for reasons. For the math majors going forward, it’s much more important to realize that differentiation and integration are operators that act on functions and yield functions. Given the wildly different practical approaches, the fundamental theory of the calculus looks like a miracle: differentiation and integration are inverses of each other (plus or minus a constant). One of the points I try to spend a bit of time on when teaching is that notation is critically important. Ie, it’s not “scribbles”. Britain refused to give up Newton’s notation and was a non-entity in analysis for a century before the Royal Society finally admitted defeat and adopted Leibnitz’s notation.Report
George, I hadn’t read your comment before posting my own just below, but I really like it.
For the record (and as a tangent), calculus (and trig) got me interested in math. I never moved beyond calculus, but from those courses, which I took in high school, I benefited in a way that’s hard to describe. I’m not in a STEM field and probably could never have done well in one, and I probably “use” my calculus knowledge only when it comes to encountering things I don’t know (when I’m compelled, every so often, to think about rates of change), but taking calculus trained my mind in a way that it wouldn’t have been trained before. (I don’t know if I’m making sense.)Report
A couple of problems that will have to be solved are how to make this work with full-time and/or suitable progress definitions. Nine hours of other classes plus 5-hour Calc II is a full-time load most places; nine hours plus 1-hour Calc II probably isn’t. Being classified as “part time” may have unexpected consequences. None of that’s impossible, it just makes it more complicated.Report
Yep, it can work. But first you need the colleges to actually want to do away with weeder courses. But they actually don’t, because they are seen as a way to test the students mettle, and commitment.
We don’t want any poseurs taking up valuable space in the higher level STEM classes.Report
Being in humanities, I never really encountered weeder courses. I had heard of them, too, and they struck me as unethical. One reason is the one you state here.
The other reason: I believe that when a student undertakes to take a course (and pays the fee for that course), the school ought to undertake to help that student succeed. Weeder courses seem predicated on making a large number of students fail, or do poorly.
I need to qualify my claim to have never encountered weeder courses. As a TA in many, many history courses, some professors adopted a strict curve, so that only 10% could get A’s, 20-25% could get B’s, and on down the line. I hated TA’ing for those courses because it meant I couldn’t, in good faith, wish all my students good luck on their exams, because if they all did well, that would put me in the tough position of giving some of them lower grades.Report
I believe that when a student undertakes to take a course (and pays the fee for that course), the school ought to undertake to help that student succeed. Weeder courses seem predicated on making a large number of students fail, or do poorly.
After sleeping on this discussion, I have more to say.
Oscar uses Calc II as an example of a weed-out class. And it probably is — for the engineering college. Every spring semester, hundreds of engineering students troop over to the math dept and take Calc II. It chases many of them away from engineering, even many who pass the course, hence “weed-out”.
The math dept does not teach it as a weed-out class, they teach it like every other low level math class. Where I was an undergraduate, the math dept paid for (among other assistance) a math counselor in every one of the large dorm complexes, and two in the student union, five nights a week, who would help with anything up through Calc III. I was a counselor for two semesters — we worked hard to get people through. Granted that the classroom environment — the 300-seat lectures, inexperienced TAs, etc — is less than ideal, but no dept gets to size its faculty based on teaching low-level classes for “outside” students.
I took — once — a class that was taught as a weed-out class. The prof was told, “Make it as difficult as possible without leaving yourself open to reversal by the dean.” The textbook was bad. The prof’s lectures didn’t follow the text. That class was never used as part of the prof’s performance review. Not the same thing.Report
Agreed there is a difference.
Also, campus politics play a huge part in how such things are taught.
At my campus, the engineering college would have much, much, much preferred to teach their own math classes, especially Calc 2.
Why?
Because most students who went to Madison for engineering had already taken the equivalent of Calc 1 at a local CC, or as an AP course in HS. So Calc 2 was literally their first math class in college, and they got tossed into the deep end with a 300 person lecture, crappy math TAs, etc. The math department taught Calc 2 as a direct extension of their Calc 1 offering, which meant the class included lots of assumptions regarding who was taking the class (future mathematicians) and what they knew. They would also tack on stupid crap like professor refusing to allow calculators or notes during exams, and demanding that every problem be solved using a specific methodology. Lots of engineering/physics/chemistry hopefuls just hit that their first semester and got weeded out*.
How Calc 2 was taught was (according to the profs I had talked to) was a serious bone of contention amongst the other STEM departments. Those departments had their own weeding classes, and didn’t really want the math department doing it for them.
However, the math department, whenever the other colleges applied pressure, would go on about how it needed to teach all the math classes (basically to justify their importance on campus). So what would happen is, for example, the engineering college would offer help for students in the college taking Calc 2, time in certain lower level engineering classes would be spent going over Calc 2 topics in more detail, in case students hadn’t mastered that in Calc 2, and no one worried too much what your grade in Calc 2 was, as long as it was enough to pass.
*I failed it my first attempt. When I started looking to retake it, because I am a stubborn bastard, I did some research on the profs who taught it, and then rearranged my entire course schedule so I could take it with the one professor who refused to play those games.Report
My issues — as someone with a CS degree after being chased out of another science degree — is simply that the “prerequisites” between math and science did not always line up well.
It was rather difficult trying to apply techniques I’d literally learned Monday in Cal 2 to a physics problem on Wednesday. It was even worse when I was trying to apply them on a Wednesday but would learn them in a week.
Basic mechanics problems in physics was a lot easier for me than EM work, because I’d finished Cal 1 before taking basic mechanics — so the mathematical work was all stuff I had, theoretically, mastered and had not forgotten. A brief refresher on a few things was all it took.
I took EM while taking Cal 2, and I was struggling with integration concepts and tools while trying to apply them, which meant I was struggling to apply mathematical concepts I hadn’t really fully understood to EM concepts I was in the middle of trying to learn.
On the other end, I recall certain things in Cal 3 that I never applied until about three semesters later. I’d never really understood the point of that particular concept in Cal 3, until I saw it applied in another course. Which required a significant refresher on the concept, because I’d memorized and forgotten it — never having really understood it’s utility as a mathematical concept.
Trying to shoehorn in foundational math close to, but before, it’s required to be applied in other courses, without letting too much of a gap between teaching concept and application, all within a 4 year degree plan spread over numerous possible degrees is…difficult to manage, I’d assume.
I know for my MS I had to basically reteach myself half of a stats course I’d take about 5 years prior, during my undergraduate — I had a few years between BS and MS — because I suddenly needed to do some fairly simple statistics to demonstrate something, but had literally forgotten how to do it — but luckily remember the basics enough to find it. You know, what standard deviations meant and the difference between mean and mode, and how that could actually demonstrate what I thought was going on in the results.Report
I have a (very old) degree with a math/CS double major. Even then, I didn’t understand the infatuation with Calc II, which was a required class for the CS major. Yes, you had to have it if you were going to take Numerical Analysis II, but that wasn’t a required CS course. The year I took Numerical Analysis III it was approximation of functions, and Calc I and II were an inadequate preparation. As we approached the end of free add-drop, the class shrank rapidly to people who had the first semester of Real Analysis under their belt.
Many people’s interests in CS would have been much better served by taking more discrete math instead.Report
Doesn’t this get a little *tiring* for students to never have a respite from critical race theory? From having your differences and the suffering of your ancestors brought up? To be your own person? From having the social chasms we’re supposed to solve by busing and quotas reinforced by authority figures?
Have they driven away everybody who has an interest beyond this stuff.Report
I’m a person who, in answer to the question “Who are your people?”, has been known to blurt out w/o thinking, “The applied mathematicians.” We have nasty, ugly problems with gender and race. I am pleased that my undergraduate advisor recognized that, became head of the math department at that school, and has made it well-known as a place where female mathematicians will be treated fairly. I will certainly admit that I wouldn’t have been able to fight that battle for so long.Report
Check your privilege!
I kid, I kid. I’m optimistic that the fad will pass, just like it has before. If not I guess I’ll have to reconsider Catholic or Montessori school, which I never thought I’d do. Even with the former I could be pretty confident the religious mumbo jumbo is limited to 45 minutes a day and doesnt infest the academic subjects, assuming it hasn’t changed much since I was a kid any way.Report
Like I said to Veronica upthread, I can imagine ways where such topics are presented in a way that engages students.
Like explaining how, much like literacy, controlling who could and could not master mathematics was, and still is, a way to keep the masses in check. I would even make the argument that a lot of the methods of math instruction I was subjected to were designed to cultivate the minds of people who had brains wired to understand math a specific way.
There is an elitism not in math itself, but in who is and is not cultivated to learn it. Understanding that is important.
I worry, instead, that the message will be that mathematics as a discipline is somehow the problem.Report
Great post. 5 out of 5.
how some kids just aren’t good at math
Yep. I’ve had 4 of those and counting. One was mis-taught how to count to 100. The next wasn’t taught the number 14. There have been various other mishaps, EACH of the girls has dropped the ball at least once.
The solution in each case was to step in. Spend hours with them teaching them it. I’ve gone as far as holding them back a grade.
They WILL learn math, and lots of it. “Toss extra resources at the kid” is exactly correct.
If you are dyslexic…
I am, and I can tell you that while there is an equiv to that for math, what I normally see is some-failure followed by “not enough extra resources”. Math builds on itself, the point where you give up is the point where you’re done. If that’s in middle school then that’s a problem.
being filled with a lot of social science word salad
:Sigh:. If memory serves the guy who invented the “zero” was Arabic, but bothering to care about that is very much off topic. I think where they’re coming from is if you stress the diversity to the history of math then “everyone” will “feel included”. The problem is math doesn’t care about feelings, or skin color, or anything other than math.
Math has right answers, and wrong answers, and I don’t care what my kids “feel” about math. They WILL learn it and be good at it even if I have to spend an hour or two a day with them on it. Focusing on diversity rather than learning is a serious mistake, math is hard enough by itself without adding distractions.Report
“One was mis-taught how to count to 100. The next wasn’t taught the number 14. ”
It is pretty awesome that you caught that when no one else did. We often measure grand accomplishments by medals and tokens, but the small interactions like these save people from a very dysfunctional future. I hope you celebrate the small victories with a substantial self acknowledgment.Report
I think the historical bits are valuable. History weaves into math just as it does into science. You can certainly learn the topics without the history, but the history most certainly enriches the experience, and can be valuable for drawing in the students who are more interested in those topics. Got a girl who hates computers? Have you told her about Ada Lovelace?
There is also a value, as I say to LTL_FTC, in understand how the knowledge of mathematics is tied into power dynamics (just like literacy is), and that students who don’t master math are giving power to those who do (see Dr. Jay’s comment above about expected value). It’s also important to understand that how math is taught ties into the control of power. If math is taught only one way, and that way just happens to be a pedagogy that works real well for white males of a certain social upbringing…
And all of this can be taught alongside math in a manner that is constructive and empowering, or it can be a lesson in sermons and emotional lectures that inflame, more than empower. I don’t trust Seattle PS to manage that difference well.Report
That is the theory. In practice my expectation is if we “broaden” a math teacher’s job to “woke math” we’ll end up with less math and less learning. As you put it “sermons and emotional lectures that inflame”.
This kind of reasoning also becomes something we’re supposed to avoid if we’d change the description from “white males” to “people of color”. Expecting someone to “learn differently” because of the color of their skin color is nonsense.
“Social upbringing” as a stand in for resources, culture, parents, etc makes some sense, but teaching less math and more history is seriously unproven as a way to have more math.Report
Like you, Oscar, I have mixed feelings about the proposal (and I spent all of 50 seconds or so skimming the article you linked to, so obviously I’m an expert 🙂 ).
I suspect that in practical terms, these reforms will amount to, “did you know that the Chinese/Arabs came up with the concept of zero?” Or, “be sure to read this encyclopedia entry about this female mathematician.” Maybe the students can get the right question at Jeopardy!, but otherwise the takeaway will be something like LTL FTC seems to be criticizing (if I read him/her right): a ritualistic shibboleth that comes to sound like preaching.
I’m not against teaching the history of math or science. But I agree with your comment upthread that maybe the topic should be reserved for social studies. (Not necessarily upper division social studies. Some of this stuff should be included at beginner levels.) The reason I say that is that history is as much about critical analysis and even argumentation as it is about learning tidbits of trivia or “how it really happened,” to quote one famous’ish historian. There’s conflict and questions of power. There’s dispute about causation. All of that would get lost in a math course that first and foremost needs to teach math. (I suspect math also has its own intra-disciplinary questions and cutting-edge elements. Maybe some of those resemble history in terms of argumentation and conflict and disagreement. If so, maybe those need to be or could be explored earlier on in math courses.)
Finally, and kind of off topic but in my opinion not really, the issue of raising ethnic and historical awareness in math courses in its own way resembles disputes over creationism and intelligent design in science courses. I’m one of those who believes things like creationism and intelligent design need to be discussed and explored in secondary education….along with other world views and in a course that’s not called “science.” Maybe a comparative religion course or a course on competing world views. As much as I believe what passes for science is often (maybe inherently) a power play, I think students should learn it unvarnished from creationist inspired controversies. But I still think ideally those controversies should be engaged outside a science curriculum. The “We Shall Be All” mentality of the STEM’ish instructors I had in middle school and high school needs to be critiqued. But the skills need to be learned, too.Report
Yes and no.
The proponents of Creationism’s problem is that Science has a MUCH better claim on the Truth than their religious texts do. Their solution is to claim their “truth” (small “t” there) is every bit as valid as Science, even from a scientific standpoint. This is trying to include concepts that are provably wrong as “science”.
The proponents of “ethnic awareness” in math courses are engaged in social engineering. There aren’t enough engineers of type X, ergo the solution to go “rah, rah, math was invented by your ancestors”. They’re trying to expand the “cultural ownership” of math to include underserved groups. That’s not trying to teach anti-scientific concepts as science, but it’s not the job of the math department to teach history/ethics.
The job of the math teacher has never been to teach about dead-white-guys so “expanding that” to dead-non-white-gals/guys is unlikely to be helpful.Report
I see your distinction, and it makes sense.
I should have added in my comment that even for the courses on different world views that I advocate, I don’t hold a lot of hope that they’d work well in practice. (But that’s a different tangent from what you’re talking about, which, again, makes sense to me.)Report
As a mathematician and other things, I am interested in the question of , “Why, given that China, India, Greece, and assorted Middle Eastern cultures made fundamental advances in mathematics that didn’t take root in western Europe for more than a thousand years, did the great leaps into modern mathematics happen in Europe? Why are Chinese and Indian mathematicians today expanding in analysis, algebra, and assorted other math fields from a base that developed in Europe, rather than China and India?”
But I agree that these are probably not questions that belong in the math department.Report
Those who can’t teach math, surely must be able to teach a little history? Amirite?
I don’t think kids absorb values through ancient history in the manner assumed, and if it’s approached as another perfunctory box check it will be treated as such. Teach them that Pythagoras got so upset with Hippasus’ discovery of irrational numbers that he drowned him. Maybe not true, but relatable and memorable.
Seattle is a segregated city where parents striving to be in the ascendant class don’t want their kids to be in school with those that they fear will drag down their education and locate in neighborhoods accordingly. Ancient history won’t change how kids see parents and society acting today. Reinstating busing would be more effective.Report
During my long and circuitous under grad career (eventually got BA in Anthropology & minor in Art History and a few credits shy of a geology minor) strangely my math credits were the ones that did not transfer so after taking algebra at two different institutions when I then had to take a general math course for a third time thank god I found a math for non-majors course, the History and Philosophy of Math, that changed my whole relationship with mathematics. That course, plus having to take statistics multiple times when I switched majors, convinces me we need to change our approaches in teaching math and we probably should make everyone take statistics in High School.Report
I am one of those weirdos that thinks unless you’ve had a semester of calculus and a semester of discrete math, you can’t actually understand probability and statistics. Probably indicates that there’s something wrong with me.Report
Depends on how deeply you feel a person should understand something in order for them to ‘understand’ it.
If we just want to arm kids with the tools to avoid being snowed by stats, they don’t need a deep understanding, just enough to help trigger skepticism.
Researchers in fields like, say, psychology, should probably have a much deeper understanding of P&S if they want to keep playing with the tools in order to bolster their claims of significance.Report
Saul has good questions about the belief by many policy makers that STEM equals jobs. The belief seems to be based on a pair of true statements: “Significant population and job growth is largely occurring in metro areas. Every large-ish metro area that is experiencing significant job growth has significant STEM job growth.” From this they jump to “more STEM graduates equals more jobs.” The causal linkages are… skimpy.
I’ll always be a STEM guy, although with other interests as well. I assert that there’s no simple straight-line path that explains the success of STEM in the “coastal elite” cities (a term that irritates me since the group includes Austin and Denver and increasingly Salt Lake City, but that’s a topic for another day). The closest that I’ve seen to a path looks like universities (or large businesses) that beget startups that beget startup support businesses all of which beget a generally well-educated workforce that attracts lots of different companies (many of which are, at best, STEM-tangent). Feedback loops abound.
With a different industry, Detroit looked a lot like that — auto assembly that led to startup parts suppliers that led to all kinds of service businesses that led to… When the assembly plants moved away, the whole chain largely collapsed (Oakland County to the north of Detroit is still the largest collection of auto and auto parts design engineers in the world). Universities tend not to move.
Just STEM graduates will never be enough, though.Report
The best jobs require going to college. Ergo sending everyone to college means everyone can have the best jobs.Report