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Mathematics

# Overview

Do birds know how to count, Ma’am?

This question by a child of class 8 triggered my thoughts on ‘number sense’. This led to an interesting class session which I wish to share here with the fellow teachers.

The basic perspective: From relative to absolute number

It was amazing for me to know that even birds have a number sense.  Not just birds or fishes but all other primates have it in a certain sense. They can’t count as such. A pigeon can’t tell 49 from 50. But they perceive changes in the number of things in a collection. The number of young that the mother animal has, if changed, will be noticed by all mammals and most birds. Many birds have a good number sense. If a nest contains four eggs, one can safely be taken, but when two are removed, the bird generally deserts.

Similarly, in the insect world, the ‘solitary wasp’ seems to have the best number sense. The mother wasp lays her eggs in individual cells and provides each egg with a certain number of live caterpillars on which the young feed when hatched. Some species of wasp always provide five, others twelve, and others as high as twenty-four caterpillars per cell. The solitary wasp of the genus Eumenus, will put five caterpillars in the cell if it is going to be a male (the male is smaller) and ten caterpillars in a female’s cell. This ability seems to be instinctive and not learned since the wasp’s behaviour is connected with a basic life function.

The number sense, for most animals and even infants, a fortiori the animal brain, is seen not in their ability to count, but a general sense to recognize that something has changed in a given collection. Small children around fourteen months of age will almost always notice something that is missing from a group that he or she is familiar with. The same age child can usually reassemble objects that have been separated into one group again. But the child’s ability to perceive numerical differences in the people or objects around him or her are very limited when the number goes beyond three or four.

A rudimentary number sense, not greater in scope than that possessed by most primates, was the nucleus from which the number concept grew. Yet the transition from relative numbers to absolute is not difficult. It is necessaryonly   to create model collections, each typifying a possible collection. Anthropologists have discovered that primitive societies find such models in their immediate environment. For example, the wings of a bird symbolizes the number two; clover-leaves means three, the legs of an animal represents four and the fingers on one’s own hand denotes five. Researchers have also found the evidence of the origin of number words in many primitive languages. Of course, once the number word has been created and adopted, it becomes as good a model as the object it originally represented.

Interestingly, however, there are primitive languages which have words for every colour of the rainbow but have no word for colour; there are others which have all number words but no word for number. But it is ‘counting’ that consolidated the concrete. Thus, the heterogeneous notion of plurality transformed into the homogeneous abstract number concept. This is just the beginning of the fascinating tale of numbers starting with counting.

What our students get in the classrooms is a whole set of diverse notions of various kinds of numbers.

Here is an attempt to create a lesson on ‘Real Number System’to unfold the various kinds of numbers and ways to classify them for students of class VIII. Click on the link to see the lesson on Real Number System: https://drive.google.com/file/d/1ReXfxovwYXXjfgJAlRPbr8icYwte8kRs/view