Math Educations: What's Wrong, and How to Fix it

College Majors Engineering Majors
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<p>I read this article: College</a> Remedial Math Increasing: Are Advanced Math Classes Helping or Hurting?</p>

<p>....and it got me thinking about problems in math education. What are your thoughts? Is it basically down to calculators ruining everything? Teachers unions? Is it just an American problem?</p>

<p>I think a few things wrong with it are that people aren't being taught <em>how</em> to think mathematically, and they aren't being taught how to visualize graphs. I didn't really learn how to think properly about algebra and functions until I studied computer programming. Then it all clicked.</p>

<p>My Chinese math professor from a few quarters ago said that learning how to put everything in "y=expression" terms was keeping us from seeing how to "read" an equation properly and see how its graph would look. We're not taught how to "see" Ax + By = C, or that B/A is the slope of the normal line.</p>

<p>I also think certain concepts are introduced way too late. They wait until pre-calc or calc to introduce the limit concept, vectors, threespace, etc.</p>

<p>Obviously not everybody is going to be a STEM major, but what makes a lot of STEM majors drop out is that they weren't prepared for the math, not lack of interest or ability.</p>

<p>I also think I'm alone in that I love word problems in math class. Where I differ from math textbook-writers is that I prefer more real-world problems where you can clearly see the mathematical concepts of the problem, i.e. rates of changes (sliding ladder, distance between trains), science concepts (acceleration, velocity, distance, work, etc.). I think people hate word problems because they aren't taught how to break them down and solve them.</p>

<p>Could a large part of the problem be that most people learn math in grade school and high school from people who, in college, took multivariable calc as the very highest level of math they went to, and with little application (that is, they didn't take many science or engineering classes to make use of what they were learning)? Is it like learning table manners from a person who's never socialized?</p>

<p>Are calculators over-blamed?</p>

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<p>[Salman</a> Khan Talk at the MIT Club of Northern California | Khan Academy](<a href=“Khan Academy”>Khan Academy)</p>

<p>Food for thought if you have some free time.</p>

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<p>I think the problem is that it is too boring. Math classes up to collegiate level really are very mechanical and dull. </p>

<p>You could make classes much more interesting and require more creativity, but that also makes them an awful lot harder. Would the increase in ‘interestingness’ outweigh the spike in difficulty, and would students do better in math? My guess: no. Even math that requires creativity is still pretty dull to most people. To me, it seems like not much can be done about it.</p>

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<p>I think that they are necessary for elementary math classes–which primarily are training for day-to-day use for math. Problems involving money and geometry (areas & such) come up in real life, so it is useful to have ‘real-life application’ questions.</p>

<p>Outside of that, though, word problems seem silly. Why should you have to wade through a bunch of contrived crap to arrive at a math problem? I admit that some math concepts are better illustrated by appealing to real-life things, but from what I remember from grade/high schools, word problems really weren’t like this at all. I also don’t agree that physics belongs in math classes.</p>

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<p>GASP!!! And why not? Why, if Newton or Gauss were here, they’d wash your keyboard out with soap!</p>

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<p>I don’t know, in my experience, physics in math classes isn’t done that well. Usually the professor will define some physical thing mathematically and then do a bunch of problems with it. You really don’t get why that physical quantity is important, and you usually don’t pick up any intuition about the physics. It just becomes window dressing for the math problem.</p>

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<p>It all comes down to teaching. Some people just can’t teach, but we need them anyway because we already have a shortage. Any solutions would have to be put on hold while we get more competent teachers to carry them out.</p>

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<p>you<em>of</em>eh:</p>

<p>Thank you for posting that video, I’ve used Khanacademy.com for the past year and was really impressed with his take on how to fix education.</p>

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<p>"Quote:
I also don’t agree that physics belongs in math classes.</p>

<p>GASP!!! And why not? Why, if Newton or Gauss were here, they’d wash your keyboard out with soap! "</p>

<p>Too tired to actually figure out the actual quote system…</p>

<p>Why would you think that? Sure you need math for physics, but you absolutely do not need physics for math… so why would you teach physics problems in a math class? I never did understand why…</p>

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<p>Because then it’s not just mindless number crunching. To some people, it gives mathematics more meaning when they see how it can be applied in the real world (and I would guess that most people have no idea how useful math can be to describe natural phenomenon).</p>

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<p>First, teachers are human, and they are unique as human beings. You may not like the approach your teachers teach in class, but the reality is that someone else may like it and are grateful for your teachers’ approaches. </p>

<p>Secondly, I am an immigrant, and I have been educated by Americans since 7th grade. I concluded that I spent 4 years doing basic math (algebra and geometry). So dull, so repetitive. So I agree that we are not pushing the math curriculum harder enough.</p>

<p>I never liked math until college, because many of my professors are capable of bringing the subjects lively and applicable. We know the importances of calculus. We learned surfaces and how to integrate them, and why we need to do these integrations. The fact is, we love these higher-level math just because they are more advance. </p>

<p>The only problem with our math education here in United States is that we spent a few years repeating ourselves, just like doing global history and U.S. history twice in junior high and high school. What if we leave two semesters free for students to explore technical skills and interests, once we eliminate these repetitions?</p>

<p>I am not suggesting that we don’t care about late-starting students. I, myself, is one. So I always seek helps from teachers and my sister back in the days. Now I don’t, because everything makes sense. When I need help, I go on the web for information, or just keep doing problems over and over. </p>

<p>However, the problem lies in the brain development. When we were younger, we didn’t have all these brain cells and knowledges. Do we? How much can we accelerated?</p>

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<p>But students are struggling to learn the basics! Why make it harder? It’s not like needing to know more math is more useful for most people. Hell, you can practice medicine or law without needing to know much more than arithmetic and elementary algebra.</p>

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<p>Oh, I see. Well I agree with you there, math teachers and textbooks are lousy at teaching physics (yes, I know it ain’t their job, but come on, physics and math have a symbiotic relationship and it’s foolish to ignore it). Things like work, moments, torque, and centers of mass are taught very badly in calculus textbooks. I just wait for them to come up in physics so I can learn it for realz.</p>

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<p>If math wasn’t taught with applications, it would still just be arithmetic. Why bother with geometry and trig? Circles, squares, and triangles are all things from the real world, not pure math, right? Save 'em for the “shapes” class. Who cares about the slope of a line or the area under the curve? Save that for the “graphs” class, it ain’t math.</p>

<p>I’m sure somebody was saying that once upon a time…</p>

<p>:-P</p>

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<p>huh?</p>

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<p>No it isn’t foolish to ignore it. Bringing up a bunch of physics terminology in the middle of a math lecture and not explaining the physics well only muddles things. Why teach something if you can’t teach it well?</p>

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If you read my first paragraph, I stated that some people are grateful for the today’s approach, having 4 years learning the same thing. I do too. I slowed down, and learned the basic again. </p>

<p>But, I think majority, even those who are struggling, find repetition boring. In fact, if you can’t pass your junior high state exam (say it’s a requirement to graduate from junior high), then you haven’t meet the requirement to enter high school. If you do, and you still can’t comprehend the materials (forgetting stuff is fine) then it means the education, in fact, the exam itself has a problem. </p>

<p>However, I see the good side of this current American education (I know back in the days, I mean BACK IN THE DAYS, the American education was very tough at students). The good side is that students can enjoy their students lives. In Asian and European countries, however, students are hostages of books and exams. I am glad I received the American education here because I gain more academic knowledge from people-people relation, than I do from reading books.</p>

<p>But if you ask me what is wrong with the math education, then I say, stop doing things over and over.</p>

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<p>IMO, the problem stems from a lack of emphasis on proofs and the importance of Algebra and Trig at higher grade levels. It seems as if once you’ve had arithmetic drilled into your psyche in grade school all the other concepts are optional. At higher grade levels there seemed to be less attention paid on understanding and more on knowing what is needed for the test. It’s like spending 5 hours teaching a kid how to dribble a basketball but only 10 minutes on how to shoot the ball. If Algebra and Trig were thought at an “Algebra for Dummies” pace as i think Math scores would likely improve.</p>

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<p>In my case electronic calculators were not the problem, they were the solution to my problems with math. I hated math in high school and did very poorly in it. It was just so tedious that I could not concentrate on the concepts. When I went to college in 1973 I had to take a math class and I purchased a TI SR-10 for $100 (which was a lot of money for a college student in 1973) and had to wait a week until it was in stock. As crude as the SR-10 is compared to present calculators it utterly changed my life. Suddenly, all the tedium seemed to disappear from my math classes and I got the highest grade in my class. I began to really love math and physics and astronomy. Every time a new more capable calculator came out I bought it. </p>

<p>I went from a student who could not pass Algebra II in high school to doing three semesters of Calculus for math, science and engineering majors, linear algebra and differential equations in college. I took Physics through Quantum Mechanics and relativity, advanced E&M, solid state physics, astro-physics and geo-physics. I ended by getting a BS in Astronomy. I went on to medical school where I invented and received a patent for a more efficient type of Positron Emission Tomography (PET) imager. If it was not for that TI SR-10 I am sure I would still be hopelessly innumerate.</p>

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<p>Wow, great story Lemaitre1 and congrats!</p>

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<p>I think the problem lies in focusing too much on drilling, and too little time on problem solving and mathematical reasoning. For most, studying entails memorizing methods to solve extremely specific problems. A “tricky” question that applies the same exact concept causes much frustration and is usually left blank. This combined with the tedium of memorization of concepts is a turn off.</p>