Language & Mathematics 1

Everyday Language can create many difficulties in understanding word problems. Hence teachers need to be aware of them. There are some general issues and specific ones. Chapter 14.4 gives a comprehensive list of many such words.

We will deal with the general issues first.

Math & First Language

A child gets introduced to numbers through the first language that he hears at home, which is usually the mother-tongue. These early experiences build the brain pathways that make the mother-tongue the natural way to think about math.

Non-English learners do learn to think in English about math & other subjects. But our brain, goes back to its old ways when it comes to basics of math, like number names and counting. When someone is angry or scared, they might switch back. Neuroscience research is proving this.

This is one of the major difficulties faced by students, especially in the primary grades. Teachers need to be aware of this and if necessary adopt a dual-language mode when it comes to basic math ideas.

Specialized Math Vocabulary

Any society needs a set of commonly understood words for communication. Every learning discipline also needs a common vocabulary.

An abstract discipline like math needs a specialized vocabulary since each word has a specific meaning and needs to be used in a specific context.

And since math needs to be understood by many people outside the discipline of math, many words in the math vocabulary need to be borrowed from words which are already in use, albeit with a special meaning.

Math & Language

There seems to be a deeper connection at the cognitive level, between math & language abilities.

There seems to be consensus among scientists, however, that only humans mentally represent numbers precisely and with symbols, and that we need some kind of education to do so. This is potentially because many higher math skills, including arithmetic, depend on the use of language—a symbols-based system—where quantity-based judgments are pre-verbal.

It could also be because math needs categorizing a lot of abstract ideas and thinking about the relations between them. This needs "naming" of categories which in turn needs language.

Researchers opine that arithmetic is difficult to do if one does not have the language for it.

English & Math

Both English & Math are polysemantic languages, where words have different meanings depending on the context in which they are used.

English is a widely spoken language, which has borrowed words freely from other languages and has by necessity become very flexible.

Math, by necessity, had to use words which are "familiar". Hence it had to borrow words from different languages to describe it concepts & procedures.

This poses a lot of difficulties for students who are learning math through the medium of English. The issue becomes critical for students whose mastery of English is very weak.

Criticality of language

Language is a very critical part of any kind of learning.

1. Language helps us to connect our previous experiences with new learning and cast them into new structures in our mind. It is plays a vital part in “constructing” knowledge & abstract ideas.

2. It helps us to clearly explain our thought processes for others to understand. We understand ideas & concepts through introspecting and the process of discussing, arguing and defending our perspectives with others.

3. One of the most effective ways to understand abstract concepts is by collaborative discussions with other learners. A fluency in language & mastery of the necessary math vocabulary are critical requirements.

Hence a weakness in language skills will also affect math learning.

Language itself is abstract

Language used in daily interactions is a human invention. Its vocabulary and syntax are very abstract. Words have multiple meanings depending on the context. “Above” could refer to “position” or “value” depending on the context. Different speakers also have different accents. Except for those who are fluent in a language, decoding & understanding a language through listening, for a prolonged period of time is difficult. For children, hearing a teacher explain abstract concepts and procedures of Math in a language with which they are not very fluent, can become boring, leading to their loss of interest. Hence, as a rule, a teacher should not spend more than a quarter of the class time talking to children. In a Math class, most of the time should be spent by children in doing Math.

Ambiguity of Daily Language Vs Precision of Math Language

Ask students to carry out the following activity in the classroom.

1. This task will be carried out by a team of 2 students.

2. The teacher would give a sheet of paper to one of the students, with a very simple geometrical diagram drawn on it.

3. This student will stand facing the black board with his back to the class. He will hold the paper above his head so that the entire class can see the diagram.

4. The second student will be at the board. The second student cannot see the diagram.

5. The first student will have to explain the diagram orally and the second student will have to draw it on the blackboard.

6. The aim is to get the relative proportion of the diagram and its orientation correct. The exact dimensions are not important.

At the end of this exercise, students will hopefully realise the following

1. What is easy to understand visually, is very difficult to explain very clearly.

2. Even simple ideas will be very difficult to convey in a few words

3. The figure drawn on the board, many a time, will have no relation to the figure on the sheet.

4. The need for the many math words which are required to convey very precise instructions.

Now let us look at some specific ways in which language interferes with math learning.