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To 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 fi
by wortiz 16y ago
To 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.
- wortiz 16y agoThen perhaps you and him are assigning the wrong word problems or not giving proper introductions to said word problems.
- yequalsx 16y agoPerhaps you should watch the video and then you would realize that your characterization of this professor and me is wrong.
- argv_empty 16y agoIf all students are taught to do is "memorization of problem types" (to borrow GP's term), then they will only be able to handle actual problems that match one of the necessarily finite set of types of problems they have memorized. A different selection of problem types to memorize will not provide general coverage -- that requires learning to construct a solution to a new type of problem.
- nitrogen 16y agoNowhere in the thread has it been demonstrated that it would be impossible to design a word problem that does require the construction of a solution. One of the problems I had with my dif. eq. class was that the grad student teaching the class just focused on "tank problems" and other "x problems" sets. So I see why story problems alone are not helpful. But, if they're judiciously used to encourage the understanding of abstract mathematical concepts, I think they are invaluable.