email@example.com (Herman Rubin) writes: > >This is exactly what is wrong with the teaching of mathematics, and the >engineers even contribute to the problem.
And physics, and math departments as well.
>One does not need the theory >as taught in theoretical, but one needs the concepts which at this time >are unlikely to be taught elsewhere, to do anything other than plug and >chug. But the engineering departments want their students to be able to >compute derivatives and integrals, and to solve differential equations, >without knowing what these are, and they want them NOW.
That is the conflict. Of course, they only really need them "now" for intro classes in physics where they should start to get some of the practice and application. Having seen this from several sides as a student and teacher, my instinct is to separate the two. All of the 'arithmetic' parts of calculus and simple differential eqns needed for intro physics and engineering classes can be taught at the rote level (where most students learn it anyway) in a semester. Include lots of graphing exercises and applied problems. It would not hurt to have a guest lecture from another department on what parts of this course will be used for the next 3 years by its majors.
>Furthermore, >they want them taught to students who have not been taught any of the >more basic concepts of mathematics, but merely manipulation.
This is why the 'new math' abstract approach used in calculus runs into trouble. You have to teach (maybe for the first time) what a function is while trying to cover what they need to know at a very practical level. The second semester can start over from scratch, with the "why", beginning with what a function is, the proofs, numerical methods, and more sophisticated applications and methods that follow from those proofs. That would be the stage where other tools (symbolic and numerical) should be introduced as well.
>Correct application of mathematics consists in formulating the problem >as a mathematical problem, then using the power of mathematics, and >finally translating the answer back. The one applying the mathematics >needs to understand the two translation processes, which means knowing >the concepts. Mathematicians can only help with the middle part, ...
They can help with the other parts as well, but only if they are broadly trained and moderately aware of what uses are made of the tool they teach. Spending a few days in each other's classrooms teaching might be enlightening.
>My colleagues and I have argued about this, and I take the position that >one cannot hope to use what one does not even know the existence of, and >a few of the properties.
-- James A. Carr <firstname.lastname@example.org> | Commercial e-mail is _NOT_ http://www.scri.fsu.edu/~jac/ | desired to this or any address Supercomputer Computations Res. Inst. | that resolves to my account Florida State, Tallahassee FL 32306 | for any reason at any time.