Speaking Mathematically :  A Class 2 teacher was explaining the concept of place value to his students, using the number eleven. He started by saying "One and one make eleven." Some of the children, who had till now learnt that one and one actually make two, were thoroughly confused. Why did this confusion arise? Could it be because of the language used?

Clearly, language is needed for conveying mathematical notions to children. Also, language itself is something that children are trying to master. Hence, in learning mathematics, children have to cope with trying to understand language as well as mathematics. And therefore, when you find that a child is not able to understand a particular mathematical concept, it may just be due to confusion created by the language used for explaining the concept.

E1) Give some examples, from your experiences, of confusion arising in a child's understanding of mathematical concepts because of language interference.

Sometimes children coming from certain backgrounds may not be familiar with some words that are used in the textbooks and by the teachers. For example, not knowing the meanings of terms such as 'shorter', 'wide', 'same', 'different', 'few', 'as many as', 'equal to', 'each', etc., can obstruct their understanding of mathematics. Another source of confusion is when many different words express the same mathematical concept. For example, 'equals', 'makes' and 'is the same as' are all represented by the sign '='.

Even older children often have to face this kind of problem. This is because the language used in conveying mathematical ideas at any level places heavy demands on the children's ability to comprehend language. Getting children to talk about the mathematics that they are doing helps them to tackle this problem, and to learn the language of mathematics.

At another level, children can be confused by the grammatical complexity and sentence length of a word problem. For example, the question "What number between 25 and 30 cannot be divided exactly by 2 or 3?" is indeed complex.

Wouldn't a child find it easier to understand if it were reworded as "Look for a number between 25 and 30. You cannot divide this number exactly by 2 or by 3.

What is the number?"?

Doing the following exercise may give you some more insight into the importance of using language that a child is familiar with.

E2) Identify the different ways in which you can explain the following mathematical problem to a Class 2 child and to a Class 4 child.  Why is one-fourth less than one-half?

Observe the language you use.

And finally, a point to keep in mind about the learning environment, that holds for any of us, child or adult.