Math and Science Popular With Students Until They Realize They're Hard 580
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.""
Comment removed (Score:5, Interesting)
Math and Science are taught wrong! (Score:5, Interesting)
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.
Re:like anything else.. (Score:3, Interesting)
Re:dumb (Score:5, Interesting)
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.
Re:like anything else.. (Score:5, Interesting)
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.
Real-world examples, shaky foundations (Score:5, Interesting)
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.
Re:like anything else.. (Score:5, Interesting)
> 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:
And expressing the Scaling in Matrix form:
Likewise expressing the Translation in Matrix form:
The problem is that a 2x2 matrix form won't do! We need to extend the problem from 2D to 3D !
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.
Hope this helped!
Feynman on sticking it out (Score:3, Interesting)
Feynman had a wonderful statement in his precursor lectures that I found inspiring. I don't have it on hand but I think it should be taught to all incoming university students. So here it is paraphrased:
Upshot: it's worth the struggle. Stick it out.
Also, from the books Feynman was disappointed in the quality of the solutions to the physics exercises that his lecture series students could perform (understatement). So let's not just assume he was the world's greatest educator :)
500 students (Score:4, Interesting)
My pre-calculus course at a major research university had nearly 500 students. Lab/section consisted of an underpaid graduate student with poor English. I'm all for the US attracting top minds from other countries and we should fund it, but not with undergraduate tuition. That class brought in over a $1 million for that department. At 500-$1,000/credit, you can afford private one-on-one tutoring sessions at $40-$50 every day for the entire quarter. The only difference is that "student aid" (aka taxes in the form of debt) won't pay for a tutoring! On top of that, the professor also told us to expect devoting 50-100% more time than the normal credit/hour ratio.
I dropped the class and took it (in two quarters instead of one) at the local community college, where I had a class of 25. If you were lucky enough to be an honors student in HS (yes, lucky enough to have a normal childhood and good teachers) and you get on the honors track in college, you will be rewarded with small class sizes, a smaller selection of higher quality professors, scholarships, and projects instead of rote memorization.
So yes, if you give us poor grades on top of a shitload of homework and a terrible education we will be very unhappy.
Re:like anything else.. (Score:5, Interesting)
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.