The readability of mathematical english

Abstract

Ma1 hematical english (ME) is a hybrid language. It is composed of ordinary englisli (OE) comingled with various brand. of highly stylized formal symbol systems. The mix of these two kinds of language varies greatly from elementary school texts to books written for graduate studelits. The OE component often is laced with iesidue from formal symbol systems. For example, phrases such as "if and only if, if . . then, A or B" are direct translations lrom the sentential calculus and their precisll technical meanings must be compreheiided and applied to the text in which they :tre embedded. Moreover, nouns that name mathematical objects are used in sentences that are OE sentences in other respects For example "The root of a linear eqzintron containing one variable is a single numbcr." The italicized nouns must be processed by the reader in a quite different way from nontechnical nouns in order to acliiel e comprehension. Additionally, spe-cia1 s;\ mbols such as2, + ,z p (i) log, p ) etc. introduce a tremendous compacting of information compared to OE text. Perhaps these illustrations help to suggest tllat M E and OE exhibit different characteribtics and consequently may require different skills on the part of readers to achier e acceptable levels of reading comprehciision. Similarly, the application of readal)ility formulas devised for use with OE nlay be inappropriate for measuring ME pissages. 4 n i=lThe following paragraphs include some ways in which ME and OE are likely to differ. Letter, word, and syntactical redundancies are likely to differ. Perhaps it seems obvious that ME should be less redundant than OE in an information theoretic sense, due to the compactness of mathematical symbolism. Preliminary experimentation with junior high school mathematics and social studies textbooks casts some doubt on this assumption. The stereotypic sequences of symbols extant in certain types of ME passages may account for these preliminary results. Perhaps t,he restricted linguistic structure within the formal language component of M E improves the predictability of its symbol sequences. In the following sample passage both these ingredients are evident. 3~2 8 6 4 = (3x2000) + (3x800) + (3x60) = 6000 + 2400 + 180 + 12 = 8592 + (3x4)

Characterizing Reading Comprehension of Mathematical Texts

“…However, literature only dealing with the symbolic language of mathematics was not included since the main purpose was to examine more general aspects of mathematical texts. A time period of 35 years is included in the references, from Kane (1968) to Adams (2003), and different levels in the educational system are included, from younger children (Shuard and Rothery, 1984) to university students (Defence, 1994). However, no claim is made that the survey has covered all relevant literature.…”

The Cloze Procedure as a Measure of Mathematical English

“…It has been argued that readability formulas devised for ordinary English prose are not appropriate for use with mathematical material (Kane, 1968(Kane, , 1970. It has been argued that readability formulas devised for ordinary English prose are not appropriate for use with mathematical material (Kane, 1968(Kane, , 1970.…”

Language Factors In Learning Mathematics

“…The most popular are the Dale-Chall formula, the Spache formula, and the Cloze technique. Kane (1968Kane ( , 1970 has given detailed reasons why readability formulas for ordinary English prose are usually inappropriate for use with mathematics materials. According to Kane, ordinary English and mathematical English differ in that: (1) letter, word, and syntactical redundancies are different; (2) in contrast to ordinary English, in mathematical English the names of mathematical objects usually have a single denotation; (3) adjectives are more important in mathematical English than in ordinary English; (4) the grammar and syntax of mathematical English are less flexible than in ordinary English.…”