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I'm going to chime in from experience and say that your college algebra students are the bottom of the barrel in regards to math students. With that respects t
by wortiz 16y ago
I'm going to chime in from experience and say that your college algebra students are the bottom of the barrel in regards to math students. With that respects there can be many reasons why they are there: they didn't care about math, they never really understood math, and/or they never really tried to get math.
If you are judging the ability of finishing word problems in the textbook, I'm assuming for homework assignments, and they really don't understand the actual math I think your problem is probably that most are using a solutions manual or spending what would seem too much time solving the homework problems.
As for solving word problems or practical problems I believe that this is exactly what math should be for especially at the college algebra level. To be serious most students entering college who want or are going to pursue a degree in mathematics are going to start off closer to the calculus level and maybe trigonometry depending on underlying circumstances. What people in college algebra are going for is a degree where math has to be practical and the more diverse applications they see the better. To give a simple example take logarithms: if you were to teach logarithms on the sole basis of algebraic symbols and expressions when it comes time that these students need to apply logarithms to real world problems (like say compound interest) there is going to be a good chance that they didn't really comprehend logs when they were taught them and won't be able to use them properly.
Which brings me to another point for word problems: word problems exist because they make students think and relate math to the real world it is fundamental to learning for many students to apply mathematical concepts in a multitude of ways in order to actual grasp a concept and one of the easiest ways to do this is to place that concept into word problems.
- yequalsx 16y agoI strongly disagree with the notion that college algebra ought to be the place where one learns practical applications of mathematics. A valuable skill for any educated person is the ability to plod through minutia and make sense of it. Being able to be focused on the point at hand and not let distractions cloud judgment is a valuable skill. If one really understands the mechanics of logs then I think they will not freak out when presented with a formula involving logs. I'm all in favor of applications but isn't this the job of other subjects? The applications should be taught in the subjects that apply it. The goal of a mathematics class ought to be to understand mathematics. This lecture, http://www.youtube.com/watch?v=WwslBPj8GgI http://www.youtube.com/watch?v=WwslBPj8GgI is long but well worth watching. He provides strong evidence that students learn to solve word problems but haven't the slightest idea of what is really going on. They are memorizing steps. This happens at Harvard and the community college. I've given my students the standard word problems on travelling problems. They get the problems right. Then I ask them this simple problem and they universally get is wrong: You drive 1 mile at 40 mph and then the next mile drive 60 mph. What is your average speed? (Almost everyone says 50 mph.) We aren't teaching thinking skills. We are teaching memorization of problem types. Almost none of them is actually practical, correct, or useful. But why are we teaching travelling problems in a math class? I think it should be taught in physics.
- wortiz 16y agoTo answer your last question first I think traveling problems are taught in math because speed and time are easy for students to relate to, the same way that finding the height of a flagpole by its shadow problems are easy for students to visualize and relate to. As for average speed that is one of those concepts that really isn't that relatable and should probably require an introduction beforehand. As for the goal of a math class being that students should come out understanding math I completely agree but the beauty of math is that it is applicable everywhere and the goal of teaching a math class should be that students understand mathematics and where to apply it. I couldn't imagine being taught vector calculus without some mention of applications and examples, my professor catered more towards mathematics majors with an abundance of Tensor notation and proofs but he never failed to understand that many in his class learned well by physical and other practical examples such as magnetism or fluids and so on. Although I failed to watch your video I believe there is most likely a counterargument to word problems and what effect they have on students because if students really are solving word problems with the math they are learning the issue isn't that they don't understand what is going on but rather how to apply it to an actual math problem. Either that or the word problems do not incorporate well enough with the math that a student can grasp it quickly without knowing underlying ideas.
- yequalsx 16y agoThe experience of the professor at Harvard in the video contradicts your last paragraph. They know how to apply the math but they don't understand the problem. And the traveling problem I gave underscores this point. It's a very simple problem and almost no one gets it correct.