Andrew Hacker inadvertently illustrates why you shouldn’t take advice on mathematics education from a social scientist who probably hasn’t taken a math course other than “Statistics for Social Scientists” since he struggled with math in high school seventy years ago:

Nor is it clear that the math we learn in the classroom has any relation to the quantitative reasoning we need on the job. John P. Smith III, an educational psychologist at Michigan State University who has studied math education, has found that “mathematical reasoning in workplaces differs markedly from the algorithms taught in school.” Even in jobs that rely on so-called STEM credentials — science, technology, engineering, math — considerable training occurs after hiring, including the kinds of computations that will be required. Toyota, for example, recently chose to locate a plant in a remote Mississippi county, even though its schools are far from stellar. It works with a nearby community college, which has tailored classes in “machine tool mathematics.”

I don’t honestly know what it’s like in the field of political science, Dr. Hacker’s actual area of expertise, but in science, technology, engineering, and math advanced skills are built on a foundation of basic skills. In engineering in particular differential equations are essential. They’re built on a foundation of calculus which is built on foundations of algebra, geometry, and trigonometry which are built on a foundation of arithmetic. Mechanics and dynamics are built on foundations of physics, geometry, and differential equations.

I was once kicked out of an undergraduate social sciences class for knowing too much math. I’ll repeat the whole story some other time. Back when I was in grad school I used to tutor social sciences grad students in statistics. I was dismayed at their lack of mathematical maturity and their complete lack of a feel for numbers. Essentially, whatever was spit out of the computer statistics package they were using was good enough for them. They had no idea what it all actually meant. If I’m judging my timeframe correctly, these were the scholars who were, at least, the contemporaries of the doctoral candidates that Dr. Hacker advised and who in all likelihood are heads of departments now, preparing for retirement. If you want an explanation for the sorry state of the social sciences, this is it.

I’ll go farther and hazard a guess that poli sci, like the other social sciences, is much more empirical and quantitative now than it was then and that Dr. Hacker would be hard put to earn a doctorate in his own field nowadays.

If you want to drop something out of the high school curriculum, drop high school social sciences courses. They’re worse than useless—they’re propaganda. They give no foundation in anything including an undergraduate or graduate degree in the social sciences.

I would replace them all with an epistemology class.

Essentially, whatever was spit out of the computer statistics package they were using was good enough for them.Calculators and computers should not be allowed in mathematics courses below the 4000 level.

PERIOD.“I don’t honestly know what it’s like in the field of political science, Dr. Hacker’s actual area of expertise.”

I do. Math, including but not limited to algebra, is important in most areas of political science.

“Calculators and computers should not be allowed in mathematics courses below the 4000 level. PERIOD.”

They do all of their homework and submit it on computers. (Son is basically a math major right now.)

Steve

I don’t mind that calculators and computers (is there a difference these days?) get used in science classes – that is, in fact, the proper place to use them. But it is antithetical to developing a feel for numbers and geometry to use them in mathematics classes. They absolutely should not be used before one is very far along. I saw people becoming very skilled with graphing calculators in the 1980s and 1990s and having no actual

feelfor what was actually happening with the equations. Developing understanding and intuition are far more important than being able to create fancy graphs or calculate things out tondecimal places.Make ’em all calculate 1/n for n = { 1, 2, 3, …, 1000} until they can start to see the patterns, sez I. It was good enough for Gauss, it should be good enough for all the other pikers that come along.

I have a good story about a dear friend, the finest mathematician I know. In his first college math course, ironically the course that the advanced freshmen took, his first assignment was to graph a half dozen different formulae. He drew the same graph six times and relabeled the axes. At the bottom of the page he wrote “I am not an artist”.

He drew the same graph six times and relabeled the axes. At the bottom of the page he wrote “I am not an artist”.But did he understand why the things should look different?

I remember a story one of my profs used to tell his students. He had a professor that drew the most perfect circles on blackboards free-handed – they were things of beauty. One day my prof walks into his prof’s office and finds the older man working at the blackboard, drawing one perfect circle after another, from very small circles to very large circles. “Why are you drawing all those circles? Your circles are perfect!”

“And how do you think I came to draw perfect circles?”

“… Oh.”

…

More seriously, it isn’t about drawing works of art, it is about developing feel. And shockingly most people develop feel by lots of practice. Having someone else do it for you (carbon or silicon based) isn’t going to help develop that intuition. If GAUSS could find benefit in practice surely everyone not named John von Neumann can as well. (Of course, Gauss practiced by coming up with new proofs for the Fundamental Theorem of Algebra and the like, but hey, HE WAS GAUSS!)

Most importantly, who the hell wants to converse with somebody who can’t do math?

Unfortunately, except for Breyer and about 8 congressmen, we are subject to a SCOTUS, POTUS and COTUS that are noticably lacking in math and science education and ability. No wonder we are destined to bust our budget, remain in a recession forever and get climate change all wrong

And hey, the little bastards should be happy we don’t make them construct a 65537-gon, and show their work. So shut up and graph you quadratic equations!

I think the other thing which has changed, and ftr i am mostly in agreement with Icepick, is the prevalence of computer science in many curricula. You have to be proficient with programming and modeling for most of the sciences.

Steve

Steve, I am fine with people learning programming and using programs and calculators IN THEIR SCIENCE CLASSES. That is proper and good. I’m not an actual Luddite. (Well, actually I am, but that’s another topic. Damn you, Skynet! Damn you, Eli Whitney!) I just oppose it most mathematics classes until one is rather far along. There’s stuff one should have at one’s mental fingertips.

It will be interesting to see how schools address this once my kids get a bit older. My memory of high school was that calculators were only used in physics classes and only for certain portions of tests.

I’ve been over at OTB, so didn’t know this essay had been posted. So with some repetitiveness.

I’m basically with icepick. And with Dave. For many professions the math per se is useless. It’s the feel, as icepick says. And Dave’s anecdote about the graphs is perfect. You have to have a feel for how real world systems work mathematically, even though you might not be able to write down or solve the equations. But you have to understand with a “feel” what the math tells you about how a real world event behaves.

As you all know, I’m an engineer, but my field, really physical chemistry, is math-light. It’s not astrophysics. The math is superficial, and in an engineering sense, once you get done applying various factors and such, the real math is bastardized. But still, you must have that basic feel for kinetics, how fluids flow, what happens in a chemical reactor. But hard core math? No need.

Finally, as I said at OTB, the elephant in the room is statistics. Statistics is something with which everyone should have a reasonable mastery, from housewife to engineer to politician. Statistics is a real world, every day event, and we, collectively as a nation, are woefully short on statistical savvy.

Give me a person with two courses in stats, vs Calculus II any day.

It isn’t shocking once you’ve gone through this. This is something I tell my son over and over and over. I tell him, “The best way to get a feel for this stuff is to do the problems.” Interestingly it is the same way in the martial arts. You can watch the instructor do a technique. You can even practice it a few times. But you wont really “know it” until you have done it thousands of times. Then it is part of you, and when you need it you’ll do it without thinking.

Agreed. Totally agree. Not having a good base for mathematics means that your models will likely be…bad.

And can sometimes be counter-intuitive.

I did 1,000 uchikomi a day, six days a week, for decades. It becomes part of the fiber of your being. It’s not even “feel” any more than breathing is.

@Steve Verdon

… This is something I tell my son over and over and over. …

You are not speaking his language. Tell him it is like getting a new video game. At first, it is too hard, and he cannot do it. Two days later he has advanced to level 14, and when asked about the difficulty, the response is that it is not that hard.

Heh. I guess we have a couple martial arts guys.

As the resident golfer, the same thing applies. I bet it applies to almost all high end physical activities. Do it until its natural.

Then focus on the result. Tell yor mind where to go. The mechanics of getting there will just happen. They just will.

It isn’t shocking once you’ve gone through this.“Shockingly” was purely sardonic.

I bet it applies to almost all high end physical activities.Drop the “physical” and you’ve got it precisely.

Be the club, Drew. Be the club.

Icepick

That’s fair. Physical or otherwise. I suspect your reference is Caddie Shack, but I only watched it once, many years ago. Don’t remember.

The real importance is……you work hard, you perfect something, you will probably wind up with something that makes you uniquely capable, or at least in the competitive game. Woudth that the left understand that.

Tasty,

Shockingly, my son isn’t into video games…Hell I’m into them more than he is….maybe a swimming metaphor…..

The Caddie Shack reference is, I think, “see the ball, be the ball…”

Took my son to see that about a year ago at the Egyptian…gotta love revival theaters….

I taught for years. I taught judo for one year while I was still in high school, four years of college, two years of grad school, one year after grad school. I taught self defense for three years in college, two years of grad school. That’s part of how I put myself through school. I’ve studied judo, kendo, shorin ryu style karate, taekwondo, and a bit of aikido. Also Western fencing.

I suspect your reference is Caddie Shack, but I only watched it once, many years ago.Maybe, but I don’t know! I’ve never seen that movie. What I’m referencing is a desk-top computer golf game from – oh, probably twenty years or so ago. It came with WIntel machines back in the day. It was a pretty good time-waster. And “Be the club!” was one of the things the computer golfer would say after a shot.

Steve V, are you in Maryland? Are you referencing the Egyptian down at the Arundel Mills Mall?

I have to admit that I’m more shocked by the implicit assertion that Toyota moved its Corolla plant from Fremont California to Tupelo Mississippi in disregard of the educational attainment of prospective machinists. There are two or three leaps of faith in the in logic there.

Ice,

Nope, I live outside Los Angeles and was referencing the historical landmark, Mann’s Egyptian Theater, no part of the American Cinmatique. They show relatively recent as well as classic movies. Just took my son to see 2001 A Space Odyssey at the Aero then later Citizen Kane at the same theater. The latter was interesting is that they had Henry Jaglom speak after the showing, he was a good friend of Welles and worked with him up to the time of his death.

Right now they are doing their spaghetti westerns, but not sure we’ll get a chance to see many since we are rather busy the next few weekends. 🙁

Dave

Please, if I offend you in public………..don’t bring it all out! ; )

Poor graduates! They´re not capable of anything practical after they finish university. I think everything would be much easier, if they were showed how to use the knowledge gained while studying. Maybe by combining of theoretical and practical subjects. Are there any universities or colleges that offer something like that ?

An example of what you’re talking about might be Northwestern University’s engineering co-op program. For their first two years co-op students follow the same schedule as non co-op students. Thereafter co-op students do two quarters in school followed by two quarters at work (at NU there are four academic quarters in a calendar year). Co-op students graduate in five years rather than four but they graduate with a year’s work experience and, usually, a full-time job offer.

@Andy

I would replace them all with an epistemology class.

I would include several logic classes.

Predicate logic is practically algebra. Venn diagrams and truth tables are logic based. Types of curves (exponential, linear, etc.) for growth or decay are important. A lot of higher math is applicable also, but it could be simplified.

A rational argument requires epistemology and logic. Unfortunately, many “rational” arguments have neither. Rational should be replaced with emotional.