Mathematics as a Language (Speaking Mathematically)

David Pimm (1987)

Chpt1: Mathematics as a language


The author explores the nature of a metaphor ‘mathematics is a language’ in the first chapter from three perspectives: meaning, symbol and symbolized things, and syntax. Construction and structure of meaning in mathematics as a language, get students confused between mathematics English and everyday English. For instance, since the word “multiply” means increasing in number, the students wrongly answered to the question of 6.23 × 0.48 as around twelve. Additionally, according to the author, pupils face the confusion caused by focusing on the symbols themselves, rather than on the meaning of those symbols. One of the examples the author introduced here is when one teacher said, “Let n be a number”, the student said, “But n is a letter!”. The third point is syntax which regulates grammatical rules. The author points out that students’ confusions can be seen same as the English language, but he argues that many errors in algebra are happened because of the abstract symbol-manipulating manner in algebra.

Comment

Because I am an English language learner and learned the meaning of “multiply” in mathematics context earlier than in other contexts (e.g., increase in number), the story of “multiply” is interesting to me. While mathematics terminologies can be seen in mathematical contexts, many words in mathematics textbooks are used in everyday life in different contexts. The former one that students have to understand new vocabularies and the latter one that students need to distinguish by situations should be challenging for them including language learners.
  As I read this article, I wondered why we use English letters when we show algebraic expressions. Even for non-English native speakers, English letters are used in mathematics without a doubt. In the previous Japanese national curriculum, an academic subject of English (as a second language) starts in junior high school, and elementary school students learned just English alphabets. As far as I know, however, no Japanese student thinks up the idea that “But n is a letter!”. I believe that algebraic letters such as n or x might be close to a symbol rather than a letter for Japanese students (or non-English native speakers). In fact, mathematics textbooks in elementary level in Japan avoid using algebraic letters for unknown numbers, they use circles or a question mark (?) instead.