To Solve a Problem - Part III Language

Writing well – for math class??? 

Yes, writing well is important for the expression of ideas.  This is not a deviation from the needs of math students.   Even math students need to express themselves using ours or any language.   Indeed, how can anything be achieved without something of a command of thought - though linguistic expression.     

Consider the article at  http://chronicle.com/article/10-Tips-on-How-to-Write-Less/124268/  It lists many ideas for students, professionals, and even parents on how to express their ideas by writing well. Included in this list are the importance of (1) the practice of writing, (2) the goals of writing, (3) the time required for proper and correct expression, (4) the profundity of written expression, and more.  These are not only tips, they are pathways and guidelines everyone needs to understand.  Specifically for students, one cannot simply pull an all-nighter, under pressure, to produce a masterpiece or to solve a difficult problem.  It usually doesn’t happen.   The works you have heard developed in hours, e.g. Voltaire’s Candide, are the exception.  Most of the preliminary efforts began much earlier and developed over days, week, months, or years.   Language is needed.  Do we have an internal language, incommunicable to others, though which we think and consider?  Most do not.

These are wonderful tips, and true. It is difficult to write well, and surely the constant practice of writing is one path toward the goal. One aspect of the current and massive blog writing, and I do mean massive, is that many folks are becoming better writers. It takes time to learn how to express one's views that others can relate to, in either the positive or negative – and of course ambivalence. And I don't mean simply using a spell checker.

For math students, it is important for them to learn how to think about a problem, how to expostulate what it is, how to express what they know or do not know, how to extirpate false paths, and finally how to suggest what its solution may be.  For most students, myself included, it is simply not possible to internalize the problem and then to spontaneously extemporize the solution.   The use of language is a deeply misunderstood and underestimated tool for students in expressing their ideas, and as well a gross misconception in teaching.  Even the teacher, K-12 and collegiate, often suffer from a diminished ability to communicate concepts, problems, and solutions, using proper language. 

Like it or not, we submit that language is one of the most important components in our understanding of problems, the development of how to solve them, and the communication of solutions to others.