Math and Science Popular With Students Until They Realize They're Hard

First time accepted submitter HonorPoncaCityDotCom writes "Khadeeja Safdar reports in the WSJ that researchers who surveyed 655 incoming college students found that while math and science majors drew the most interest initially, not many students finished with degrees in those subjects. Students who dropped out didn't do so because they discovered an unexpected amount of the work and because they were dissatisfied with their grades. "Students knew science was hard to begin with, but for a lot of them it turned out to be much worse than what they expected," says Todd R. Stinebrickner, one of the paper's authors. "What they didn't expect is that even if they work hard, they still won't do well." The authors add that the substantial overoptimism about completing a degree in science can be attributed largely to students beginning school with misperceptions about their ability to perform well academically in science. ""If more science graduates are desired, the findings suggest the importance of policies at younger ages that lead students to enter college better prepared (PDF) to study science.""

Comments

like anything else..

[houbou]

hard is merely the fact that often, the theories and equations taught are quite abstract. It is very important to have a solid grasp of concepts, but in the end, the material could be improved with visual and/or tangible results which have some values and/or association to the abstract concepts.

Re:like anything else..

[Rockoon]

Whats needed is good educators, like Richard Feynman was. What passes for "good educator" these days is pathetic.

Re:like anything else..

[ackthpt]

hard is merely the fact that often, the theories and equations taught are quite abstract. It is very important to have a solid grasp of concepts, but in the end, the material could be improved with visual and/or tangible results which have some values and/or association to the abstract concepts.

I've had dozens of college profs and the ones which stood out were the ones who were good listeners as well and perceptive of what students struggle over. Generally I found when I thought a course was 'hard' I knew 80% or more of the material or concepts, but I was struggling over one or two things which blocked conceptual understanding of things further on.

Subbing, as a TA once in a programming class I was perplexed how people couldn't wrap their heads around the idea of a Variable (think of it as a name on a bucket, into which I add or remove apples, yet they were still stumped).

Things do tend to be more 'hard' when the student spends more time listening to their nay-saying peers than their instructors. When you actually believe Math, Chemistry or Physics is 'hard' your belief is your own largest obstacle to learning.

Re:like anything else..

[ackthpt]

Whats needed is good educators, like Richard Feynman was. What passes for "good educator" these days is pathetic.

We could certainly do with a lot less people going around saying Math is hard. That's defeatist thinking. Math is easy!

Re:like anything else..

[Anonymous Coward]

No. Math is hard because it's like running long distances. Few people actually like running, or any kind of exercise. Many people do it for utilitarian reasons while hating it. Some people like it inherently, though. I had a gym teacher once who was addicted to running to the point that it was bad for his health.

Re:like anything else..

[fredprado]

Math is the most difficult subject known by humankind. Basic math is very easy, college math is reasonably easy, engineering school math is quite hard, mathematics graduation math is considerably harder, and math research is ridiculously hard.

Re:like anything else..

[expatriot]

Feynman was fantastic at inspiring people and giving them an intuition for physics with simple drawings.

Do you think he understood partial differential equations, functions in a complex space, matrix math, group theory? Sure he did. If he wrote some of that on a blackboard in a 60 minute talk, would the audience struggle to keep up?

I am still not sure I understand using 4x4 matrices to do transforms in three space. I can write the code though (slowly).

My wife (English and Drama) said the biggest party people were the liberal arts students because they did not need as much time to study. And when they were studying they mostly were reading.

A good educator can make learning calculus better than a poor one, but there it is still hard (well for me anyway).

Re: like anything else..

[Anonymous Coward]

I have a most wonderful proof of that assertion, but sadly the limited character set of the slashdot text editor will not allow me to present it!

Re:like anything else..

[khallow]

Well, there aren't many fields with well-defined problems that have solutions which can't be found without many human generations of effort. And many math problems are known to be intractable. For example, the Halting problem.

I mention that example because there is probably a Turing machine with input that can be fully described in modest time by a human, but which can't be determined to halt even using the entire resources of the known universe converted optimally into a computer and run for the rest of eternity.

Re:like anything else..

[slew]

Whats needed is good educators, like Richard Feynman was. What passes for "good educator" these days is pathetic.

I'm not so sure Richard Feynman would agree that he was a "good educator", although he was a great scientist. By many accounts, he mainly enjoyed teaching as an exercise to keep his own mind fresh and as an excuse to re-explore things that he knew very well and hopefully stumble upon a new way of looking at things. On his famous lecture series, he himself stated "I don’t think I did very well by the students" and by some accounts was generally depressed by average scores on the tests the year that he was teaching that class in introductory physics from which the lectures were recorded.

It's not to say that really smart folks can't benefit from learning what he could teach, but that even he would probably recognize that if the students aren't learning, you need to have some different approaches to teaching to truly be a good educator.

FWIW, Having sat through a couple of his lectures (right before he passed away), I can say you come out feeling that you know exactly what he's talking about until you actually put pen to paper and realize, he just made it seem so simple, not that you learned what you needed to learn (I apparently was NOT one of those gifted enough to get it on the first pass). Certainly it takes a great talent to make something so complicated seem so intuitive, but at the same time, that doesn't necessarily make a good education plan.

Re:like anything else..

[benf_2004]

I found the exact opposite to be true. I put forth minimal effort in high school (rarely studied, frequently daydreamed during classes, ignored lots of homework assignments) and graduated with honors. I tried to do the same thing when I started college and I was on academic probation after the first quarter. I learned then that I was actually going to have to put forth a reasonable amount of effort if I wanted to graduate.

Re:like anything else..

[Iniamyen]

Care to offer some evidence for that assertion?

Of course not! He was talking about math, not science!
I guess technically he needs to provide a proof.

Re:like anything else..

[onkelonkel]

In high school a very smart student can get honours marks with minimal effort. In high school an average student can get honours marks by working very hard.

In engineering school a very smart student needs to also work very hard just to get by. If you are diligent about doing all the problem assignments, hand in all the labs, study efficiently (in a small group really worked for me), be very strategic about obtaining all possible marks, you can do reasonably well. In engineering school an average student can't get by on hard work, because the workload is too high, and will likely fail.

Re:like anything else..

[grizdog]

The problem with math, if problem is the right word, is that it changes its character, and the kind of thinking that is required at each level is quite different. It helps to be painstaking, but that is true in many fields. The skills required in arithmetic, algebra, calculus, discrete math, linear algebra, and number theory are all quite different, and students who think they are good at math move to the next level and find something quite foraign and quite unpleasant.

Along with this is the problem of grade inflation in high schools. I spent most of my career as a college math professor, and I ran into students every year who thought they were good at math because they had gotten good grades in it, but when I handed out problem sets the first week which reviewed prerequisite material, they could not do them at all. Math is pretty standardized nationally - f you have completed Intermediate Algebra or Precalculus or Calculus 1, there is a standard collection of problems that the student ought to be able to solve - you can find them in any standard text. And since it was the first week, it wasn't because I was a bad teacher - they had barely been exposed to me. But even though their transcript said they had received an A or B in the course, they couldn't solve the problems at all. So suddenly they get to college and a subject that previously didn't require a lot of work, now requires a great deal of work. It happens all the time

Re:like anything else..

[Austerity Empowers]

Or because running long distances requires a constant amount of effort. You can't show up to a marathon 13 miles in, think it's over in less than 4, and expect to win anything or even get a sense of accomplishment.

Math and science build, it starts very early, and it keeps building up. By high school most people are already severely disadvantaged. By college, the game is over but for the most dedicated. I will give these people a little credit, I think they truly want in and see the value, but get lost in college material and pacing, and don't even understand how they went wrong, They end up with retarded cop-outs like "i'm dumb at math" or "science makes no sense", which sometimes become self-fulfilling prophecies. They have to be approached like a physical fitness program: you start out easy or you will hurt yourself, and you work up to the serious stuff. There's no cramming for it, you can't jump in and be awesome, it takes a long time.

Most of the other subjects covered in that article can be easily picked up to "beyond the average bear" levels by just reading some books for a few weeks. It's not a surprise then if you're looking for a piece of paper in 4 years and you do not already have some skill in STEM, you go for something easier.

Re:like anything else..

[UnknownSoldier]

> I am still not sure I understand using 4x4 matrices to do transforms in three space. I can write the code though (slowly).

That's just proof that you had a bad/crappy teacher. :-( Here is one explanation:

In 3D computer graphics we use a 4x4 matrix to conveniently and compactly represent _two_ things:
  a) orientation, and
  b) location (or position) within a single variable.

M = [ R 0 ]
    [ T 1 ]

Where:
    R = 3x3 orientation matrix, and
    T = 3-dimensional position vector.

To understand how this comes about let us start with something a little more basic: 2D Affine Transformations. Namely: Rotations, Translations, Scaling.

Given a point P = we can write it in matrix form as either [ x y ], or
[ x ]
[ y ]

How would we write the equation for a point that is rotated around the origin (or z-axis.)? We will eventually want to write a matrix equation where the matrix represents a change in orientation. That is by definition:

  x = R * cos(A), and
  y = R * sin(A)
x' = R * cos(A+B), and
y' = R * cos(A+B)

Where:
  R = radius of the angle,
  A = initial angle,
  B = the relative change in the angle,
  A+B = the absolute final angle

We don't always know R, so let us rewriting these in terms without R:
x' = R * cos(A+B)
  = R * {cos(A)*cos(B) - sin(A)*sin(B)}
  = {R*cos(A)} * cos(B) - {R*sin(A)} * sin(B)
  = x * cos(B) - y * sin(B)

Similarly we do the same for y.

Now, we would also like to write the equation for the Translation of a 2D point:
  x' = x + dx
  y' = y + dy

Likewise Scaling is pretty straightforward:
  x' = x * sx
  y' = y * sy

These 3 different operations require 3 different functions and order of operations! This sucks. It sure would be nice if we could unify these operations into one equation! We actually have two choices for how we could write/calculate this:

a) Pre-multiply the column vector (ignore the '.' it is whitespace due to /. being lame.)

[ x' ] = [ m p ] * [ x ]
[ y' ] . [ n q ] * [ y ]

b) Post-multiply the row vector

[ x' y' ] = [ x y ] * [ m p ]
                      [ n q ]

At the end of the day it doesn't matter which convention you pick just as long as you are consistent.

Since /. is lame and doesn't like an _informative_ MATH post I'm breaking it into two parts...

Re:like anything else..

[ebno-10db]

Engineers want to be physicists.
Physicists want to be mathematicians.
Mathematicians want to be God.
God is an engineer.

Re:like anything else..

[UnknownSoldier]

> I am still not sure I understand using 4x4 matrices to do transforms in three space. I can write the code though (slowly).

Part 2 since /. ecode formatting is still so gey I am including a bunch of whitespace filler text '.' to align things up in columns.

Now, expressing the Rotation equation in Matrix form. Remember we ended up with these two equations:
  x' = x * cos(B) - y * sin(B)
  y' = x * sin(B) + y*cos(B)

We can literally "transcode" them from algebraic form into matrix form without too much difficulty. We end up with this:

[ x' ] = [ cos(B) -sin(B) ] * [ x ]
[ y' ] . [ sin(B) .cos(B) ] . [ y ]

And expressing the Scaling in Matrix form:

. [ x' ] = [ sx 0 ] * [ x ]
  [ y' ] . [ 0 sy ] [ y ]

Likewise expressing the Translation in Matrix form:

x' = x + dx
y' = y + dy
x' = (x*m + y*p) + dx*1
y' = (x*n + y*q) + dy*1

The problem is that a 2x2 matrix form won't do! We need to extend the problem from 2D to 3D !

[ x' ] = [ m p dx ] * [ x ]
[ y' ] . [ n q dy ] . [ y ]
[ 0. ] . [ 0 0 1. ] . [ 1 ]

The exact same _principle_ is used for 3D. We extend a 3x3 matrix (orientation) to a 4x4 matrix so that it expresses BOTH a orientation AND translation.

[ x' y' z' w' ] = [ 4x4matrix ] * [ x y z 1 ]

Hope this helped!

Re:like anything else..

[Anonymous Coward]

The beauty of math is that once that that problem is solved, you are able to teach the concepts behing the solution to an average human mind without excesive difficulty.

Exactly..... wrong.
The beauty of math, is that once the problem is solved, you can teach any average idiot how to go through the motions and arrive at the correct the solution without understanding it.

Re:like anything else..

[TaoPhoenix]

Hmm, go a bit easy on the frustrated comments of people who might be looking at a change of major!

I'm right in line of all this. High School science was different. It's hard to say, but it was "fundamental" enough. If you grow up prowling around the pop-sci section of a bookstore, it's not delusional to think "well gee, maybe I'll study science". So I made it through Freshman year in college still kinda enthused.

Then over summer break I got hold of discard-copies of old versions of the textbooks and collapsed. The combination of Calculus and Organic Chem (and then beyond!) sunk me. Plus I suk at anything spatial involving curves. But the un-sung third point is that I didn't want to spend nine months in a lab recording tedious results and then produce one crispy little paper, and then do it all over again.

So I went back as a business major. I'm clever, but most of y'all here are brighter than this ol' humanities bird. But also it felt "Closer to the ground". Pay a bill in AP. Close a Monthly period. Post Stuff to a contract. "Stuff" gets "done" and it sticks.

This just in: Science is Hard

[Yergle143]

The Onion has reported on this ground breaking finding exhaustively.

Everyone Wins

[SuperCharlie]

Its the last 20 years of coddling and telling kids thay can do anything, handing out prizes to everyone, and boring the crap out of anyone with an extra IQ point above average that makes the mentality that well, of course you can dear, all you have to do is work hard and you can do anything.

Then you get a classroom full of people who expect a prize every time they do anything.

/ old grump rant..

Comment removed

[account_deleted]

Comment removed based on user account deletion

Math and Science are taught wrong!

[m00sh]

The main problem is that large parts of science and math are skills. But, they are taught as other subjects with a lecture and homework. You wouldn't learn swimming by listening to someone talk about it for an hour or learn to play the guitar by looking at someone playing it for an hour.

Seriously, there is even a saying among people that the best way to learn something is to teach it. Sitting in class and listening to lectures is the wrong way to learn something.

It's Impossible until it becomes Trivial...

[Gavin Scott]

In almost any skill that has to be learned, there's often a fairly rapid and abrupt transition from "I can't do that" to "I CAN do that and since I now know how to it's actually easy".

I think a lot of people get discouraged when they're unable to get through that transition on their own the first time they try it, and "I can't do that right" can be appear to be an impossible mountain to climb, even if you're not far from the top.

I think we need to be challenging kids from an early age to learn things that are "hard" so that they become intimately familiar with this progression from impossible to trivial. Too often I see kids these days try something that looks interesting to them a couple times and then decide "nah, that's too hard" and quit.

It's not specifically teaching perseverance, but more about learning to recognize that progress is almost never linear toward a goal and many times you won't recognize you've reached your goal until you're actually there.

Additionally, we ought to be able to get better at helping people fight through these places they get stuck, rather than just leaving them with a failing grade in a math class and a feeling that that they're not up to the task. Early recognition of students who are having difficulty and focused tutoring and other help getting through the hard parts to the point that they achieve their needed breakthrough.

I don't think any undergraduate subject should be so inherently difficult that anyone who can get into the university in the first place shouldn't be able to do well in it.

G.

Don't ignore the study itself

[yurtinus]

Make sure you include the requisite grain of salt. The blog is based on a study from over a decade ago - performed at a liberal arts college. Quickly perusing the school's website, I do not see a strong emphasis on STEM programs (I don't even see a B.S. offered, even the CS degree is a B.A.).

Not that I entirely disagree with the premise, but I think a study at a school with a broader academic base would provide more worthwhile results.

Re:dumb

[PRMan]

Having talked to East Asian co-workers, we came to the conclusion that while rote memorization was by far in favor of the Asians, solving unseen problems went to the Americans. They were constantly astounded at how easily we could solve problems that we had never heard of before and credited the American education system. So, I would say not dumb, just a different focus.

Why would I care about doing the lightning-speed mental arithmetic? I have a calculator for that.

Real-world examples, shaky foundations

[Cyrano de Maniac]

While my intuition tells me that high school grads are, on the whole, not as well prepared as they should be, there is certainly some improvement that could be done at the college level.

One problem I faced on the path to my EE degree was that in mathematics classes and some engineering classes (particularly electromagnetic fields, communication systems theory, and stochastic signal analysis -- which of course are some of the most math/calculus heavy of the EE curriculum), was that I lacked an intellectual model of what the mathematics was accomplishing. While concepts like derivatives and integrals made a degree of sense because they could be related to velocity, acceleration, position, area, and volume, when I got to the point I was dealing with eigen-this and eigen-that and hermetian-something-or-others I had lost any real-world connection, and my understanding suffered as a result.

The most frustrating and poignant instance of this was the first day of my linear algebra class, which I was taking only as a pre-req for CS class on GUIs, which only needed it to the extent that rotation, translation, and scaling using matrices was involved, and I already knew that much. Anyway, the mathematics professor walks in and announces "I do not care, even one little bit, what this material is used for in the real world. I am here to instruct you in mathematics alone." I looked around the room. In a class of about 25, I believe there were 20 science/engineering students, 4 math students, and one photography major (she was one of those brilliant types who took upper level classes in sciences, math, philosophy, or anything else just for fun). I was somewhat incredulous at the professor's utter disregard for his students' background, abilities, and interests. And just as I expected the course was utterly miserable and tedious, and then there were the bad days.

I contrast that with the math classes I took for Calculus II-IV, and Numerical Systems Analysis. The professors (thank heavens I avoided graduate students) who taught those classes were totally on top of the situation, and made it very clear what we were trying to accomplish with real world examples, or at least didn't veer too incredibly far from intuitive models. I think it helped that in Calc II-IV I had the same professor all through, and he was teaching a pilot course that integrated calculators into the material, so there was a lot of approachable material throughout. This was a stark contrast from the previously mentioned Linear Algebra as well as the Differential Equations I courses.

To this day I hate Linear Algebra and Differential Equations, and I'm 100% convinced it's due to the terrible instructors I dealt with. Which is a shame, because I loved mathematics in high school, and would go beyond my coursework to explore what I could on my own without much additional help from my (incredible) high school teacher, and I had a blast doing it. If I hadn't developed a strong interest in aeronautics and computers I most likely would have pursued a math degree.

The biggest problem I faced throughout my mathematics education, as well as many engineering classes, is that as the course would progress it was building taller and taller upon a shaky foundation. While my arithmetic was bedrock, my algebra was concrete, and my trigonometry was 2x4 construction, the rest was a lot less solid. Calculus felt a lot like building with Tinker-toys, and by the time I got to anything past that it was toothpicks stuck together with Sticky-Tack. As more and more material was piled on top, a lot of it kept slipping off because the stuff underneath it was crumbling. I would have benefited greatly from either better construction (i.e. better instruction), or a lot more hands-on experience with those shaky bits such that they were strongly reinforced.

I totally understand in a way...

[jo7hs2]

I started in college as a comp sci major. I already knew how to program in BASIC, C, and C++ with reasonable proficiency and was excited about the major. However, I had a string of lousy math teachers until high school and struggled with algebra. Oddly, I was always fine with trigonometry and statistics, and I never had issues with the logic part of programming (I'm an attorney now). I was drastically unprepared for college mathematics. Because comp sci majors weren't even allowed to take major-required coursework until they had various math prerequisites, I started behind. After I nearly failed a mid-term in math class I barely understood with a TA I literally could not comprehend, I dropped the class and the major. I retreated to my safe zone in history and eventually ended up in law school.

While I'm not disappointed with the way things worked out, since my hands give me trouble just with the typing I do for my job now, I do wonder how different my life could have been if one of my math teachers caught on that I was struggling before my senior year of high school. I finally had a good teacher that last year, and she pulled my aside after class and turned a D to an A, but it was too late by then. I just lacked the skills.

From my perspective, the biggest issue in math education, and really education in general, is grading with no follow up. If a student isn't getting it, failing them doesn't make them get it, and passing them with pity is even worse. This flaw in a lot of education was really hammered home to me in law school when a professor got frustrated her ENTIRE class failed an exam. If the whole class fails, it isn't the students...

Ironically, I always had amazing science teachers. They were always engaged and excited. I usually got good grades. But, one science teacher was the only teacher I ever had who picked up on the fact that I was being teased and then tried to do something about it. And, my aunt is a science teacher, so I may be biased.

My rambling point...they need to be catching the kids who are struggling in second to fifth grade. My math issues started with multiplication in elementary school. I was behind, and no one ever caught it because in our school system you could basically still pass if you didn't understand, provided you just got enough questions right and showed effort...and passing was all that mattered.

Great until you find out how hard it is

[PopeRatzo]

Funny, marriage is like that, too.