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Writing was developed by the Sumerians approximately 5,000 years ago. At the same time, the Sumerians developed some written notation for mathematics. Writing and mathematics are brain toolsthey are powerful aids to the human mind. The abilities to use both written language and mathematics are so useful to people that these are "basics" in our formal educational system. Students study and practice the "three Rs" year after year in K12 education and even on into higher education as they work to develop contemporary and more advanced knowledge and skills (expertise) in these areas. Our math education system pays some attention to the idea that math is a language. For example, many math teachers have their students do journaling on the math learning experiences and their math use experiences. Some math teachers make use of cooperative learningan environment that encourages students to communicate mathematical ideas. Some math assessment instruments require that students explain what it is they are doing as they solve the math problems in the assessment. There has been a great deal of research on the teaching and learning of reading and writing in one's first (natural) language. In addition, there has been a great deal of research on the learning of a second language. It seems likely that some of the research findings and practical implementations of these findings would be applicable to teaching and learning of mathematics. In the early days of computer programming, there was quite a bit of research done how to identify people who might be good at computer programming. It turned out that music ability and math ability correlated well with computer programming ability. This is interesting from the point of view that in some sense music is a language, and computer programming requires learning programming languages and then solving problems using the languages. ======================================= The following article provides some research on the value of directly teaching language skills in various disciplines, including math:
The following email from Garry Taylor is a valuable resource in exploring mathematics as a language.
ReferencesMusic as a language. Quoting Howard Gardner:
English as a Second or Other Language (ESOL) Research on Learning Computer Programming and Software EngineeringMathematics as a LanguageCrannell, Annalisa. Writing in
Mathematics [Online]. Accessed 1/26/02:
http://www.fandm.edu/Departments/Mathematics/ Crannell gives writing assignments in the calculus classes she teaches at a university level. Her Website includes a 1994 booklet A Guide to Writing in Mathematics Classes. Quoting from the first part of that booklet:For most of your life so far, the only kind of writing you've done in math classes has been on homeworks and tests, and for most of your life you've explained your work to people that know more mathematics than you do (that is, to your teachers). But soon, this will change. Language and the Learning of Mathematics [Online]. Accessed 1/26/02: http://www.mathematicallycorrect.com/allen4.htm. A speech delivered at the NCTM Annual Meeting Chicago, April 1988 by Frank B. Allen, Emeritus Professor of Mathematics Elmhurst College. Quoting from the paper: This brings me to my major thesis that natural language, gradually expanded to include symbolism and logic, is the key to both the learning of mathematics and its effective application to problem situations. And above all, the use of appropriate language is the key to making mathematics intelligible. Indeed, in a very real sense, mathematics is a language. Proficiency in this language can be acquired only by long and carefully supervised experience in using it in situations involving argument and proof. Mathematics as a Language [Online]. Accessed 1/26/02: http://www.cuttheknot.com/language/. Quoting from the Website: However, the language of Mathematics does not consist of formulas alone. The definitions and terms are verbalized often acquiring a meaning different from the customary one. Many students are inclined to hold this against mathematics. For example, one may wonder whether 0 is a number. As the argument goes, it is not, because when one says, I watched a number of movies, one does not mean 0 as a possibility. 1 is an unlikely candidate either. But do not forget that ambiguities exist in plain English (the number's number is one of them) and in other sciences as well. A a matter of fact, mathematical language is by far more accurate than any other one may think of. Do not forget also that every science and a human activity field has its own lingo and a word usage in many instances much different from that one may be more comfortable with. The Language of Mathematics [Online]. Accessed 1/26/02: http://www.math.montana.edu/~umsfwest/. This Website is based on a book by Warren Esty and a course at Montana State University by the same name. The first quote given below is from the Website, and the second is from the Warren Esty book.Jointly with Anne Teppo, Warren Esty published an article in the Mathematics Teacher (Nov. 1992, 616618) entitled "Grade assignment based on progressive improvement" which was reprinted in the NCTM's Emphasis on Assessment. and posted on the web by the Eisenhower National Clearinghouse for Mathematics and Science Education. In a language course, you can expect continual improvement. This article discusses why grading should not be based on averages of unitexam scores and how a course like "The Language of Mathematics" can be graded. The Language of Mathematics [Online]. Accessed 1/26/02: http://www.chemistrycoach.com/language.htm. This Website contains a number of quotations that relate to the topic of mathematics as a language. Here are two examples:Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say. Bertrand Russell, (18721970) The Scientific Outlook, 1931.
