Language & Mathematics 3

Math is a discipline which has developed to solve problems faced by our cultures. Hence many words used in math have been borrowed from our daily language. A lot of words have also been specifically invented only for communicating mathematical ideas. The mix of these vocabularies can create a lot of confusion for students.

Value –Loaded Vocabulary

The day-to-day meaning of many math words is value loaded causing some confusion. Odd, improper, irrational, imaginary, complex & borrow are some examples. Teachers need to emphasize that these are just names “invented” by mathematicians and have no other connotations. They do not reflect any property or behaviour of numbers.

Math-Specific Vocabulary

Mathematics has many words which are mostly used only in the Math classroom. Some examples are Transcendental, Obtuse, Scalene, Isosceles, Reflex etc. Students listen to these words only in the Math classroom which could be about 3 hours in a week. It takes a long time for students to internalise the sound of the words as well as their meaning. Just repeating these words once or twice and expecting students to remember them is futile.

Teachers should put up such words on a chart in the classroom while and after the relevant topic is being taught. They should also refer to them and make students use them frequently in the right context, until the students have internalised them.

Words which have different meanings within Math

There are a few words which have different meanings in math itself with finely differentiated meanings.

For example the word negative have several interpretations. In the sense of a verb is it used as "minus". It also qualifies negative numbers, a term which is quite different from the word minus. It could also mean the quadrant of a cartesian plane where x & y values are negative.

The term "put together" could mean the life situation leading to addition or the procedure of addition itself.

Pre-Arithmetic Words

Almost all cultures had names at least for smaller numbers, before the decimal number system was universally adopted. Almost all languages also have different names for smaller numbers like Pair, Couple, Brace, Twin, Both, Dozen etc. These words are still in use.

Confusing Homophones

Many words are homophones with different meanings in daily language & math. Some examples are whole & hole, for & four, principal & principle, lesson & lessen, ate & eight, one & won, too & two etc.

A teacher found out that her children thought only 0, 4, 6, 8 and 9 to be whole numbers. She later realised that they were confusing “hole” with “whole”!

Homonyms With Different Meanings

Many words are spelt the same way but used with different meanings in the math class and in daily life. Some examples are even (equally shareable, level), mean (behaviour, statistical term), table (format, furniture).

Vocabulary With Subject-Dependent Meanings

These words are a subset of homonyms with different meanings. In these cases, the same word is used with a completely different meaning in another school subject. Some examples are Balance, Left, Right, Rest, Principal, Interest, square (shape, power raised to) etc. Both the subject teachers need to be aware of the possible confusion caused by these words.

The Solution

There are two solutions to take care of problems like these.

One is to first introduce the math aspect of any topic using manipulatives, visuals & role play. A topic like fractions can be introduced in terms of visuals sharing a square sandwich and let the students describe the various ideas in their own words. Once the concepts are clear, the "mathematical" vocabulary can be introduced.

Simultaneously, the teacher should check the prior knowledge & vocabulary levels of students and ensure that the multiple meanings are made clear, as and when they occur in the topic. For example, while introducing the idea of a whole & a part, it should be pointed out that there is a word "hole" which sounds like whole and that both of them have different meanings depending on the context in which they are used.

The math teacher needs to be a language teacher as well!

Chapter 14.4 gives a list of words which can be difficult for students to understand. It is a tentative list. Many more words can be added to this list.