Math Is Hard

Math is hard, that's why some of us become biologists :p

Math is hard

I have a shirt to that effect, but I figure I'm entitled - I've got a degree in the subject.

...'course I was a shitty student, so maybe not...

My first thought echoes a lot of the comments in that thread: Can we even find enough teachers who understand math to do that?

Ending math in grade ten for people who don't expect to need anything beyond arithmetic and basic geometry seems quite reasonable to me. No sense pushing people through stuff they aren't interested in and never expect to use. Keeping those people in class will just drag down performance and lead to dumbed-down courses, anyway.

And you know, there are quite a few things you can do without any more math than that. A college major in English, say, or History shouldn't require anything more. (Some colleges will, of course, since they have breadth requirements or other artificial roadblocks.)

Sorry it's a pdf - but here is a link to Lockhart's Lament. If you haven't read it, you may find it interesting (although long).

http://www.maa.org/devlin/devlin_03_08.html

Oh math, four years in H.S.

1) Algebra
2) Algebra/Trig
3) Geometry
4) Pre-Cal

Then college:
1) Linear Systems
2) College Algebra
3) Calculus

I don't ever really want to see another math class. The problem is I'm very haptic, to the point where if I don't see an immediate application for it, I don't give a crap.

Which explains why I've been delving into calculus again, seems it's used quite a bit in RF electronics.

Ending math in grade ten for people who don't expect to need anything beyond arithmetic and basic geometry seems quite reasonable to me. No sense pushing people through stuff they aren't interested in and never expect to use. Keeping those people in class will just drag down performance and lead to dumbed-down courses, anyway.

why stop at math? What about Literature, history, geography, foreign languages, etc. Most of that has been pretty useless for my day to day life.

I always found it amusing that my university required everyone to pass a real, honest to goodness, college level writing class, but didn't care if people were only working at a 10th grade level when it came to math or science.

Life is hard, so what?

> "...seems it's used quite a bit in RF electronics."

LOL! Life is full of calculus and imaginary numbers. I can't think of a single solitary example where both don't apply. Sure, you can simplify things to where you don't need them but that doesn't mean they aren't there.

Life is hard, so what?

> "...seems it's used quite a bit in RF electronics."

LOL! Life is full of calculus and imaginary numbers. I can't think of a single solitary example where both don't apply. Sure, you can simplify things to where you don't need them but that doesn't mean they aren't there.

Zeroth, Lockhart is mostly right. High School Math is not really Math, it's a cruel parody of Mathematics.

First, I've taught High School Math on and off for 4 years as a substitute, "permasub", and student teacher. Much more, if you count 5 semesters as University Math professor, where both Algebra 1 and Algebra 2 were de facto Remedial High School Math. Hence I speak from experience as a Math teacher, and not merely from the grotesque dumbed-down College of Education system which attempts to make credentialed teacheras from the students emerging from the utterly failed secondary schools.

Second, I bear the twin burden of being a professional Mathematician (unlike ANY of the Department Chairpersons in any of the departments where I ever taught), and a professional Scientist. In the prior case, I know how foundationally flawed is the California State curriculum in Math. In the latter case, I know what Math would actually be useful for students majoring in Astronomy (I've also been an Astronomy professor), Biology, Chemistry, Economics, Geology, Physics, and similar subjects. Why do I have to teach Scientific Notation in EVERY course that I teach? Why don't students already know it?

Third, the curricula in secondary school, college, and university (except the elite ones), seem to neglect the faft that the 20th Century had a second half, and that we are well into the 21st Century. There is significant Math from the past 60 years, at least SOME of which should have trickled down to High School by now. A little noncommutative stuff (good for Quantum Mechanics, too; Quaternions were in curricula at start of 20th century, then were dropped)? A little Topology (Manifolds useful in Relativity, at least)? A little Chaos Theory (which I consider coequal to Relativity and Quantum Mechnics in importance)? A little real Computer Science (as opposed to the Computer Literacy and brainwashing in applications the school bought at a discount)?

I have not given up. I still intend to be the best Math Teacher that I can be, having started the job officially in 1973. I still intend to reform the system, even if it means earning an Ed.D. so that clueless "Educators" will be persuaded that my experience is at last of significance to their theory and practice.

@Johan Larson

By that argument you don't need four years of anything in high school. High school biology has never been of any particular use to me. We spend a full quarter memorizing the organs in a fetal pig. European history is another thing I've had remarkably little use for as an adult.

That is also demanding that kids know at pretty young age what they are interested in and what the real world requirements for it are. You would also have to have decent counselors. Mine thought typing (old school how to use a typewriter in the early 90s)would be more useful to me that calc. I have never in my life typed anything more than a form or a label on a typewriter, but calc came in handy for econometrics.

Although I'm not at a liberal arts college, math and the natural sciences are generally included in definitions of "the liberal arts" and most academics claim to hold the "liberal arts" in high esteem. Despite that, I've always felt like we scientists are second-class citizens in the liberal arts. People in other disciplines will admit without shame to being ignorant about math and science, but as you said in the post you linked to, academics will look at you funny if you don't know much about art or philosophy. Moreover, while every school is different, I find that at most schools GE requirements tend to be heavier on humanities and social science than mathematics and natural sciences. And science majors are always being told that we need to be more well-rounded. There's an implicit endorsement of the idea that knowing a lot about natural science and math is less "academic" than knowing a lot about humanities and social science.

Meanwhile, the health professions and engineering disciplines that we often collaborate with in our research endeavors are specifically excluded from definitions of liberal arts for being grubby, practical, vocational things. Sure, you can find collaborations between natural sciences and other liberal arts disciplines (especially in teaching) but there's no denying that a natural scientist is still more likely to have a collaborator in an engineering school or medical school than in the humanities or social sciences.

So, nobody really needs to know about our stuff, and our collaborators are grubby and unworthy. Why, pray tell, are we included in definitions of the lofty "liberal arts"?

As an outside observer (termed "Exterrestrial_intelligence" by your species) it is amusing that humans would treat mathematics as "liberal arts" as if this is something only related to your species. I'm sorry but for every truely intelligent life in the universe we've found eons ago that it is the only universal language based upon which your observed universe is "built" (if you will), and the level of mastery of this language is how your species will be judged by other intelligent life forms. Many of us would care less about what kind of combination of piano keys within a narrow frequency band (limited by your hearing ability) will stimulute your sense of pleasure. Same applies to your so called "arts" (as in painting) that relies on your limited vision (200-700nm electromatic wavelengh to be a little more precise).

I'm sorry if you find this universal language is "hard" - it is understandable given your current level of poor average intelligence (to quote your own measuring stick "average IQ of 100").

Finally, I find it easier to communicate with you using one of your own languages instead of a more universal language, say a binary language which only a handful of you can translate.

For the college-bound and particularly those going in to technical fields, 4 years of math is, of course, better than 2. On the other hand, one of my largest complaints about public school curricula is that we try to cram everybody into more or less the same mold, regardless of their interests, abilities, and goals.

I, for example, wish I had learned more math in high school. If I had gotten an introduction to linear algebra, matrix arithmetic, and differential equations, it would have been advantageous in college. I learned these things anyway, but why couldn't I have gotten the basic out of the way sooner?

At the same time, the groundskeeper at my apartment complex, for example, would have been better served to spend less of his time in high school learning how to solve quadratic equations, and more time learning how to choose a retirement fund, identify a good loan or credit card rate, how to interpret our absurdly complicated tax code. For that matter, he also would have been better served to spend less time learning how to compose a 4 paragraph essay and the time line of European history, and more time learning why it important to vote, and why we have the separation of church and state (not just the fact that we do, but why its important). He should also have spent less time learning the facts of science and more time learning what science is and why its a good and important thing.

Just to be clear, I'm not knocking people who don't go to college or enter technical fields. Not everybody is or should be an academic, and that doesn't make them dumb or less valuable in any way. My basic complaint is this: by trying to shoehorn every student into the same curriculum, we ultimately force that curriculum to be too basic for the college-bound, and not practical enough for the average person.

Even worse, we end up with a lot of people who are left without much practical understanding of how the world works. Maybe there wouldn't be so many anti-vaxers if we taught people how medical science works and why they should trust it. Maybe we'd have less people voting based on a candidates piety if they understood why the separation of church and state is better for both church and state. Maybe this home loan crisis could have been averted if people understood enough basic personal finance to realize they were agreeing to a horrifically bad loan.

So before we start pushing for more math, maybe we should push for more curriculum options in general. Let me take more math and less shop class, and let those who prefer it take more personal finance and less pre-calculus.

There's no particular reason to force people to take pre-calc or HS geometry (proofs) if they're not going to like it and be good at it and go on to higher math. But you could do worse than make people take stats in order to graduate. Statistics, and the ability to manipulate data in a spreadsheet, and the ability to think about randomness, is *important*.

A lot of what Tercel, and Harlan say rings true. There is true math, with to me resembles mental gymnastics (proofs) for its own sake. Then there is basic problem solving, which should be useful for nearly everyone, so for instance they can determine if that offered loan is NOT a good deal. And of course there is statistics. A lot of people pursuing non-math subjects, such as psychology, social science, political science, or business, may discover later on to their horror, that a good understanding of math is basic to these fields as well. I am reminded of two fields -geology, and biology, which are gradually (or not so gradually) being taken over by math and physics types. This trend is likely to spread to other fields as well.

First, a disclaimer: I teach HS math (Geometry and AP Calculus).

Geometry proofs aren't really mental gymnastics for their own sake. A good proof requires you to understand all the given information, and then to justify (with appropriate rigor) each conclusion you draw on your way to finalizing the proof. An algebraic derivation requires the same kind of thinking, as does the computation of the surface area of a weird shape. I tell students who ask (and many do) that they may never have to prove two angles congruent (or explain the Franco-Prussian War or analyze Raskolnikov's motives). But they will almost certainly have to present reasoned, fact-based arguments to support what they say.

Or they will believe everything talk radio tells them.

Ending math in grade ten for people who don't expect to need anything beyond arithmetic and basic geometry seems quite reasonable to me.

tl #7 has already quite properly jumped all over you for this statement, but let me add to his comment: Just because you don't expect to need something is not a good reason for not learning it. Just as an example: No pilot ever expects to need to know how to safely ditch a plane in water. Nonetheless this training is required for commercial pilots, just in case--and the pilots of that US Airways jet last January suddenly found that they needed that skill. While I can't point to an example where knowing trigonometry or calculus made a life-or-death difference, there are times when these skills come in handy. For instance, construction is one of those jobs for which most people think you don't need that much education, but if you are building or repairing a pitched roof, knowing enough trig to be able to figure out how long to make the beams and rafters strikes me as a good idea.

Bailing out of math after tenth grade doesn't just rule out science and engineering majors. Economics makes heavy use of calculus. I had an "aha!" moment in my high school economics class when I realized that "marginal X" is just another way of saying "take the derivative of X".

With reference to Jonathan Vos Post's comment (#10), here's a further take on the 'cruel parody'.

http://jedidiah.stuff.gen.nz/wp/?page_id=10

How hard to educators try to make Math easier?

I only scanned the comments, so perhaps I missed this: maybe the students who do well go on to take the extra two years. I'm not sure the correlation here is the cause & effect that is being proposed

"We have anecdotal evidence that suggests that students who actually take math for all four years of high school do better in math here than those who don't."

1) Is anecdotal evidence actually useful in setting policy? It may be useful in guiding research and collecting data, but we'd need more than anecdotal evidence to make a major change in educational policy.

2) Is this forwards or backwards? There is also anecdotal evidence that people who run marathons are healthier than people who don't. Should we drive everyone to run full 20 plus mile races in hopes of improving public health?

Re Tercel: "For that matter, he also would have been better served to spend less time learning how to compose a 4 paragraph essay and the time line of European history, and more time learning why it important to vote, and why we have the separation of church and state (not just the fact that we do, but why its important)."

You can't understand why it is important to vote and why we have separation of church and state without understanding European history. Of course, just learning the timeline is not particularly useful without also learning the important trends and persistent conflicts, such as the rise of democracy and the secularization of society. Math isn't the only subject poorly taught. History is taught poorly as well, though generally for different reasons.

A lot of people pursuing non-math subjects, such as psychology, social science, political science, or business, may discover later on to their horror, that a good understanding of math is basic to these fields as well. [Emphasis mine]

This is another problem with math education. From essentially day one, students are taught that Math is Hard and Boring, and only Really Smart People can get it. Even in university, this is the case, despite the fact that math is an academic discipline just like philosophy, biology or law. I can't remember a single math lesson in grade school that I found interesting, and I slept though most of grade nine math. Now I'm finishing a Master's in applied mathematics, so obviously something happened along the way to get me interested. It definitely didn't come during elementary school. Maybe if elementary school teachers took more of an interest in math and science (not just memorizing times tables and doing useless, repetitive tasks), people would dig it, providing a possible solution to the problem of high school math. Why are there more years of history classes than high school classes in some cases? Because history's interesting. If math were taught as something more than x and y's on the blackboard, maybe students would find it interesting too. As a side effect, we might just see higher aptitude in problem solving, statistical and logical reasoning.

JMG said something with which I agree.

When I start with a new batch of students, whether as substituite or at start of a semester, I ask: "Do you think that this subject [Math, Science] is only for the smart kids?"

Many students vocally say that they do think so.

"Wrong!" I reply. "This is too important to leave to just the smart kids. Or to the professionals in the field. Let alone to the politicians and 'educators' who make policy, and set the rules you have to obey. You CAN do this stuff, understand it, master it, and enjoy it." And then I explain how, together, we shall meet those objectives.