January 17, 1934 in The Nursery World
The Teaching of Number
“X. Y. Z.” writes: - “How soon do you think I ought to begin to teach my little boy of three, who seems to be quite ordinarily intelligent, to count? I heard of a boy not much older who was doing little sums with his governess. Do you think this is a good thing, and if so, how should I teach him?”
The question of the age at which we should begin to introduce arithmetical ideas to young children is really bound up with the question of howwe should do it. Everything does depend upon how we go about it.
In the first place, all those who have been studying little children to see how they do learn to use arithmetical notions are agreed that formal lessons are quite useless in the early years. Indeed, they are worse than useless because they teach the child that arithmetic is dull and dreary; and once that emotional attitude towards the subject has been set up it is extremely difficult to change. It has been found that more children get held up in their understanding if number from emotional reasons than happens with any other subject of the school curriculum. Fear and boredom are the two biggest factors in backwardness in arithmetic among school children. It is easy to make minor mistakes of presentation in showing the chid how to add or subtract or divide, but these do not matter in comparison with the fundamental mistake of associating arithmetic with a notion of duty or boredom or anxiety. It is very difficult for even the best teaching later on to break down such an attitude once it has been built up. The very first essential is, therefore, to make sure that from the very beginning our methods are such as to let the child feel the natural interest of number relations between things, and to discover their practical value in his own active interest and pursuits.
Fortunately this is also much the easiest way to go about the problem, if only we grown-up can rid ourselves of the notion that children oughtto be able to count and add at a certain age, and recognise the real fact that if he is given a chance, the child loves to count and add and divide when these processes have some real meaning to him for the normal activities of his age. For this reason, all the number work of children in the home, indeed, even in the early years at school, say, seven or eight years at the very least, ought to be incidental to practical pursuits. Miss Margaret Drummond has made a very interesting comparative study of young children who had regular formal lessons in counting and adding and subtracting at school, and of children who have never been given any formal instruction in number, but whose parents have responded to the child’s natural interest in number by using incidental opportunities in games and handicrafts. She has found that the latter are quite as well advanced as the former at the age of six or seven, and quite as ready for the more formal work that is useful at his school age. Such games as, “One, two, Buckle my Shoe,” building towers of two or three or more blocks and counting the number of blocks that can be balanced on one another, playing games of shopping or helping mother in her real shopping, spending pocket money, playing card games and dominoes, reckoning up the days of the month on the calendar, the number of days before and since important events like a birthday or Christmas treat, laying the table with the correct number of plates and spoons and forks, and so on, are but examples of the endless opportunities which ordinary life provides for stimulating the child’s interest in number in a way that he can understand and use for himself. Miss Drummond is definitely of the opinion that to introduce formal work too early, so far from developing the child’s natural interest, actually inhibits it by creating the wrong attitude.
Other workers in education who have been studying the development of older children have come to the conclusion that the same applies even in the later school ages. It is only when the various arithmetical processes are linked up with the child’s interests in making and doing as well as in his concern to understand the general world around him, shopping and journeying, etc., that the child can come to ay deeper understanding of arithmetical notions and facility in using them. One of the most interesting recent developments in the teaching of arithmetic is the fruit of the work of the Decroly schools on the Continent. In these schools the child is introduced to number through measuring and weighing. They measure and weigh things they have collected themselves, chestnuts, acorns, apples, fir cones and beans, using these to weigh against each other and only later on coming to the conventional units of weight a volume. For example, when they have been growing beans in water and have noticed that as the roots and stalks sprout, the water grows less and less each day because the plant drinks it, they measure how much it has drunk in a certain length of time with a medicine glass that records drops of water and find that twenty-five drops is also just a thimbleful. From this they go on to the ordinary measures of volume. A great deal can be learnt of weight and measures in connection with cooking, gardening, shopping and so on. In general, it is found that arithmetical teaching that is connected with real situations is far more valuable and secure as a foundation. The various formal material such as the Montessori apparatus is valuable as a means of clarifying the child’s ideas, but it is not a substitute for the practical working out of number in real situations.
In number teaching in general an important principle is to make haste slowly, and it is beginning to be thought that many of the abstract processes that are now taught to children of eight to ten years would be better postponed to twelve or thirteen when the child was really ready to grasp them for their own sake.
There is thus no reason why you should not play simple number games with your little boy connected with his everyday life. But I should not yet for some time try to introduce any formal material or to make any demand that he ought to learn to count and add.
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