Wednesday, January 25, 2012

Teaching yourself mathematics

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Of all the subjects a student is likely to encounter after elementary school, mathematics is by far the easiest to teach yourself. With the appropriate attitude and assumptions, adequate motivation and a simple and easily mastered set of skills the majority of students can take themselves from pre-algebra through calculus [..].

[A]t some point all disciplines require the transition from passive to active and that transition can be challenging. In courses like high school history and science, the emphasis [is] on passively acquiring knowledge [..] By comparison, junior high students playing in an orchestra, writing short stories or solving math problems are almost entirely focused on processes and those processes are essentially the same as those engaged in by professional musicians, writers and mathematicians [..] Unlike music and writing, however, mathematics starts out as a convergent process [.. for any intro level course] say, differential equations, most math problems have only one solution and students are able to quickly and accurately check their work [..].

This unique position of mathematics allows for any number of easy and effective self-study techniques. One of the simplest is the approach that got me through a linear algebra section [ is this ..]

All you need is a textbook and a few sheets of scratch paper. You cover everything below the paragraph you're reading with the sheet of paper. When you get to an example, leave the solution covered and try the problem. After you've finished check your work. If you got it right you continue working your way through the section. If you got it wrong, you have a few choices. If you feel you basically understood the solution and see where you made your mistake, you might simply want to go on; if you're not quite sure about some of the steps in the solution, you should probably go back to the beginning of the section; if you're really lost, you should go back to the preceding section and/or the previous sections that introduced the concepts you're having trouble with.

Once you've worked through all the examples, start on the odd numbered problems and check your answers as you go. If you're feeling confident, you can skip to the difficult problems but if you make a mistake or get stuck you should probably go back to number 1.

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