# Language and Writing

## Practicing Precision: Lessons from Mathematical Language and Writing

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## OBJECTIVES

I feel that it really helps a teacher of mathematics to view mathematics writing (such as word problems) as a student sees it: as a mysterious foreign language. Mathematics writing is unique, with its combination of words and symbols and special, compact style, and inner city children are often terribly disadvantaged when it comes to communications skills in almost all areas. This is particularly devastating in learning mathematics where every word must be precisely read (or written) and understood. Students need experience in dealing with math topics in more than one form; for example, some math writing is all writing, but other math, like equations, is all symbols. Students must become adept at “translating” from words to symbols as they search for meaning and solution. Additionally, reading mathematics equations has a unique directionality, quite different and frustrating for a newcomer to mathematics. For example, correctly reading this illustrated equation must follow the direction of the arrows:

(figure available in print form)

One main objective of this unit is to help students feel confident around mathematical language and writing style. A measure of achieving this objective can be sought in your students’ increasingly improved attitude and involvement in accepting the challenge of understanding word problems. This has to be a first step in developing the confidence to attempt to find the proper function necessary to solve the problem.

Another unique feature of mathematics as a foreign language is its vocabulary. Some words are special to mathematics, some are borrowed from ordinary usage, and some are familiar words with new and different meanings. Another objective of this project will be to help students increase their mathematics vocabulary and develop a more discriminating attitude toward the contextual use of words. Mathematical vocabulary’s departure from ordinary usage can be | illustrated in the following example | ||||||||

word | ordinary meaning | mathematical meaning | |||||||

prime | to prime a pump | a prime number has | |||||||

itself and one as | |||||||||

factors | |||||||||

power | God has great power | two raised to the | third power |

word | concept |

negative | a loss, a penalty, losing ground |

positive | a gain, a reward, a raise, an increase |

volume | the contents, the fullness |

set | a collection of items, a pair |

What is ten percent of three hundred?

? = 10 % x 300

Putting the translated symbol or numeral directly under the corresponding written item is essential for the success of this type of exercise, as precision is one of the main goals of this type of learning. This involves identifying that “is” means equals and “of” means times. Also demanded is the correct recognition of an unknown (?) which could be replaced with a variable symbol (x, y, etc.). Proper transcription of words for numbers to numerals is essential for answering of course; not surprisingly, many of our students cannot reliably write the numerical equivalent of numbers in words, especially decimals, mixed numbers, and fractions.

More reading must be an objective of learning to love and appreciate mathematics language also. Recreational reading which has high mathematics content is not hard to find. Understanding ERA s in baseball and gleaning the statistical information from surveys are two ordinary avenues for practice.

Increasing interest and motivation is an important aim also. Students must be led to feel excited and successful in understanding something new. Almost all of my students have strong competitive urges, once drawn out of themselves long enough to become involved. Activities involving mini computation races, logic word puzzles and other such exercises are really helpful in this area and will be discussed in more detail below.

Our students in the lowest math learning groups have a negative mindset against any kind of printed material given to them in class. We must break that mindset by requiring our students to read and begin practice in writing by requiring them to take at least some notes in class.