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Math is, generally, poorly taught (Engineering student's perspective) 
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#1
Dec1311, 01:23 AM

P: 145

[I'm more concerned with how mathematics is taught in university in this topic]
I'm a junior Mechanical Engineer and have taken Differential & Integral Calculus, Multivariable Calculus, Differential Equations, and Linear Algebra. Just from these classes and talking with a variety of peers in STEM majors, it's pretty clear to me how poorly mathematics is introduced and driven into us. At least for the nonmathematics major. Just because we're engineers or scientists doesn't mean the mathematical theory shouldn't be expounded upon. I'm not necessarily talking about proofs (which engineers and scientists usually DO hate), but more about the consequences of some theorems, how a theorem came into conception and what it enabled, what it actually means versus being just some formula, etc. My Linear Algebra instructor took the route of skipping formal proofs and instead tried to get us to understand the subject and theory itself rather than just solving rote, systematic problems (though we did do some of that, of course). By elaborating on concepts in class, he took our thinking to a deeper level and my interest piqued, and thus I strove to do better in the class and get a better understanding, which ultimately led to a very satisfying Math class that I haven't been able to have in forever. Just because I didn't major in Mathematics doesn't mean I don't appreciate math. My only gripe is that he would seldom relate the many applicable concepts to engineering or the sciences, such as bases or eigenvectors. Differential Equations was by far the worst. I learned the methods. I learned how to use integration factors, Fourier series, Laplace transforms to solve different problems. But did I learn why I did what I did? Did I ever learn what a Wronskian truly meant? Or that the the conception of the Fourier Series enabled the heat equation to be solved because it turned complicated oscillations into sines and cosines? Or what the hell "s" was in a Laplace transform? NO. This shouldn't be optional for the curious student; it's pivotal in understanding why a certain method is used and why it's used the way it is. If you understand that, you have a much better chance of retaining that knowledge, a deeper grasping of the theory, and possibly an ability to apply it creatively to unknown territory. I can now say I have a firm grasping of intro Linear Algebra, while I can't say the same for Differential Equations. A lot of my friends who took the same LA professor will say the same. DE was a worthless class because it consisted of crunching out Godgiven methods without a good theoretical understanding. So in essence, this is an engineering student's plea to anyone who sets up Math curricula for engineers/scientists or teaches it: TEACH US THE THEORY. Get us to appreciate it. Get us to understand it from an abstract, qualitative perspective rather than just part of the problemsolving drudgery. That doesn't necessarily mean make us do a formal mathematical proof, but rather make us see mathematics in a meaningful light. [sorry, I may have rambled a bit. Just trying to get people to understand what is wrong with mathematics in university today.] 


#2
Dec1311, 05:15 PM

P: 717

I agree that some professors in mathematics could do a better job of teaching proofs and intuition handinhand, but the traditional method in math is to show the proof and make the student grapple for the intuition on their own. To compound this, the math curriculum for engineers is designed to pack as many disjointed tools into as short a time as possible so that you can get on with building things. No wonder engineers don't want to see any proofs. Could it be improved? Most definitely. It comes down to good teaching skills, though, and those are in short supply in any field... 


#3
Dec1311, 09:38 PM

P: 107

Mathematics courses that neglect theory can cover more topics and focus on computation and applications. Most science and engineering students will never need to know what a supremum is, but they'll need to know how to tackle a variety of problems.
I think that schools should offer two flavors of mathematics courses: computational and theoretical. Then students who only care about the tools can take the computational version and students who are interested in the development can take the theoretical version. 


#4
Dec1411, 09:45 PM

P: 1,296

Math is, generally, poorly taught (Engineering student's perspective)
I am teetering on the edge of giving up on being a math prof (currently, I'm a PhD student, struggling to possibly graduate this year), chiefly due to student complaints (which are a dealbreaker because the powers that be in math departments get so panicked about them). When I started on my path towards being a mathematician, I liked the idea of teaching because I just thought of it as, "explaining math". When I found out that it was not about explaining math, but more to do with putting on an act to prove to the lower level students think you are good enough for them, the whole career has lost its appeal for me. The question is whether I can learn how to put on this act for the lower level students, and whether the upper level teaching and research is worth putting up with it for.
Anyway, my greatest fear if I do decide to continue in academia is that I will present things conceptually and intuitively and the students will just PREFER to just plug and chug because that is what they are used to. Then, to avoid their dreaded complaints, I would have to do the ultimate sellout, dumb things down, and make it all cookbook. Essentially, when I taught trig/precalc, that is exactly what happened to me. Maybe this fear is unjustified. But I have heard some math profs express this sentiment about teaching linear algebrathat the students just want cookbook. I hope it's not true. So, instead, I'm thinking about just finding whatever job outside academia I can get that pays the bills and leaves me with plenty of free time, so I can create the best math website on the web, and then most of the unmotivated, unintuitive, conceptually shallow math woes will be solved for everyone once and for all. Just look it up on my website. Give me 5 years, and we'll see if I can't make it happen. Whether or not I go for academia, this is one of my life goals, and a much greater contribution to mathematics than what would come through researching new topics. 


#5
Dec1411, 10:52 PM

P: 6,863

Websites, and youtube are also good for this. Just don't expect any of this to be counted toward tenure review. On the other hand, I've found that sometimes doing stuff like this is necessary to just keep sane. On the other hand, we really can't expect our students to do things that are not in their career interests out of pure academic curiosity if we ourselves aren't willing to do the same thing. 


#6
Dec1511, 12:56 AM

P: 717

I agree with twofish that the strange beast that Calc I,II,III, ODEs and LA have become is directly driven by the getitdonequickly mentality. You have to be a pretty patient teacher to deal with 120 disinterested students. That doesn't stop a teacher from at least trying to convey some of the context of what is going on. For profs, upperlevel courses are much more attractive to teach because most of the students actually want to be there.
This, of course, is only useful for those who aren't interested in plugnchug. Also, students still need facetoface courses with researchlevel professors, especially as they get further along their education. That said, I speculate that, for nonprofessional degrees, there will come a point where the debt load becomes so high for a degree, and free information of high quality becomes ubiquitous enough, that something is going to break. I hope that the traditional university model doesn't melt down too much, as there is a lot to lose. 


#7
Dec1611, 06:46 PM

P: 145

The core problem is that educators believe, when choosing quantity over quality, all those techniques and methods STICK.
What good is learning 20 different ways to tackle an ODE if you easily forget them right after you take the final exam? That's the point I'm trying to make. A conceptual approach yields greater retention and a better ability to apply those techniques to various problems. There were two LA professors teaching the semester I took it; my professor took the more conceptual approach while the other one chose to cover more topics with less focus on the theory. In the end, her students couldn't tackle the problems as well as we could. Plugandchugeducation only works so long as you have tests and quizzes and homeworks to keep it fresh in your mind. Once that incentive is gone, how are you going to plugandchug data that you have no idea what to do with? That's what a conceptual approach corrects, to a certain extent of course. Too much theory, I believe, can be bad for such engineers and scientists, but if the educator can find a happy medium between elaboration and sparsity, students will benefit most. The issue now is that it's weighed much more heavily on the side of sparsity than theory. 


#8
Dec2111, 11:16 AM

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If you think math is poorly taught, try some physics classes. When I was a student the math dept had the most brilliant and most skillful and dynamic lecturers teaching the math class I was in, but the physics dept had the oldest, poorest most boring lecturer in the world teaching the physics class. Objections ran so high that they had to actually replace him with someone good after the first term. By then I had quit caring or trying.
Of course I was in the super honors math class and the regular physics class. Against all logic they often put the best teachers in the honors class instead if the other way around as they should. But you might try taking an honors math class. 


#9
Dec2111, 11:39 AM

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P: 15,201

However, as a counterpoint, the absolute worst math course I have ever taken delved way too much into theory. The class was on optimal control theory. The instructor was a pure mathematician. He balked at the light treatment in the text on uniqueness and existence. Light treatment, my eye. The book spent 60 pages on uniqueness and existence. Most texts on optimal control theory spend at most 1020 or so. Some, much, much less (paraphrasing): "Sometimes there is no solution, optimal or suboptimal. Sometimes there are multiple optimal solutions. Sometimes there is just one optimal solution. Live with it." This was one of the most theoretical texts on optimal control theory I have ever come across, and yet it was too light for him. We spent a good 2/3 of the class on those 60 pages on uniqueness and existence. We never did learn control theory, let alone optimal control. 


#10
Dec2111, 12:39 PM

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sometimes you need to remind the professor that while he is primarily interested in why the solution exists, that you are more interested in how to use it once that is established.



#11
Dec2111, 12:53 PM

P: 1,084

What I mean to say is that I not want this style of teaching. That course, or lackthereof, gave me a terrible foundation for quantum mechanics which still haunts me to this day. I wish you had a really naive outlook and thought that you could change the world, because it would at least change a class. 


#12
Dec2111, 07:36 PM

P: 1,296

I know many students don't like the cookbook approach. But there are a lot of students who just want the piece of paper and don't really care about learning. 


#13
Dec2111, 10:17 PM

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look on my website and you will find several free linear algebra books. i spent years writing them. but will you read any of them? sighhh...



#14
Dec2111, 11:20 PM

P: 1,296




#15
Dec2111, 11:53 PM

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from "change the world" to "have some fans" is a little adjustment.



#16
Dec2211, 12:40 AM

P: 661

To the OP, I'm an EE major and I had the exact same experience just last semester. I took a combined Linear Algebra and Differential Equations class and it made me hate math for a short time. The beginning of the semester seemed really cool then the plug and chug began and never stopped. My linear algebra experience consisted of 2 weeks of lectures and two problem sets that occurred early in the semester. We learned how to calculate RREF, vector spaces, determinants, eigenstuff, basis, span, Wronskians, and Jacobians in that 2 weeks. About 2 months in, I grew extremely frustrated with the way the class was taught and spent a lot of time on my own trying to learn what it all meant. It's sad to say but the things I learned on my own felt like I discovered their true meaning, but really I just made some sense of the concepts my professors brushed under the rug. I'm not one to make excuses but because my frustration grew so great and I had to venture out a lot just to learn the concepts, my grade slightly suffered. I'm very confident though that I now have a far better understanding than the vast majority of what my classmates learned from that class. The self learning was a very worthwhile experience but I still feel cheated on what I could have learned if they approached the subject differently. 


#17
Dec2211, 12:53 AM

P: 1,306

I agree, I want to to know the theory! And I want to know the big picture of things and the context of what I'm learning in the grander scheme.



#18
Dec2211, 12:53 AM

P: 1,296

If I can affect just one person's life significantly with my work, I think that will justify it. 


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