Pedagogical Anthropology, Maria Montessori [online e book reader TXT] 📗

(a+b+c+d)/(1+1+1+1)

When comparative figures are given, as, for example, those recorded by Quetélét for the stature, the diameters of the head, etc., such figures are always mean averages.

Such averages may be more or less general. We might, for example, obtain a mean average of the stature of Italians, and this would be more general than the mean stature for a single region of Italy, and this again more general than the mean stature for a city, or for some specified social class, etc.

It is interesting to know how the mean will be affected, according to the number of individuals examined, because it is obvious that the mean stature of Italians cannot be based upon measurements of all Italians, but upon a larger or smaller number of individuals. Now, if we take various different numbers of individuals, shall we obtain different mean statures? And if so, what number of subjects must we have at our disposal in order to obtain a constant medial figure, and hence the one that represents the real mean average? It has been determined that a relatively small number will suffice to give the mean, if the measurements are taken with uniform method and from the same class of subjects (sex, age, race, etc.); for the cranium, 25 subjects are sufficient, and for the stature, 100 subjects.

This method furnishes us with an abstract number, insofar as it does not correspond to any real individual, but it serves to give us the synthetic idea of an entirety. In anthropology we need this sort of fundamental synthesis before proceeding to individual analysis for the purpose of interpreting a specified person.

Now, it is evident that the figures representing the mean stature for each region in Italy give us a basis for judging of the distribution of this important datum, while an accumulation of a hundred thousand individual figures would lead to nothing more profitable than confusion and weariness.

The following table, however, is quite clear and instructive:

MEAN STATURE IN ITALY

(According to Departments)

Yet the interpretation of such a table is not simple; it is necessary to read the numbers, to remember them in their reciprocal relation; and it demands effort and time to acquire a clear and synthetic idea of the distribution in Italy of this one datum, stature.

On the other hand, we must lose as little time and spare our forces as far as possible. The value of positive methodology lies in the extent to which it accomplishes these two subjects.

Geographical charts serve the purpose of this desired simplification. Let us take an outline map of Italy, divide it into regions, and colour these different regions darker or lighter, in proportion as the stature is higher or lower.

The gradations and shadings in colour will tell us at a single glance, and without any fatigue on our part, what the table of figures reveals at the cost of a very perceptible effort. Little squares must be added on the margin of the chart, corresponding to the gradations in colour, and opposite them the figures which they respectively indicate—after the fashion in which the scale of reduction is given in every geographical map. In this way we may study these charts, and their examination is pleasant and interesting, while it successfully associates the two ideas of an "anthropometric datum" and of a "region," a result which a series of figures, pure and simple, could not achieve.

We have seen Livi's charts of Italy, both for stature and for the cephalic index. Analogous charts may be constructed for all the different data, for example, the colour of the hair, the shape of the nose, the facial index, etc. In the same manner we may proceed to a still more analytical distribution of anthropometric data among the different provinces of a single region. For example, I myself prepared charts of this sort for the stature, the cephalic index and the pigmentation of the population of Latium.

Sometimes we want to see in one single, comprehensive glance, the progress of some anthropological datum; for instance, in its development through different ages. Quétélet's series of figures for growth in stature, in weight, in the diameters of the head, the cranial circumference, etc., offer when read the same difficulty as the similar tables of distribution according to regions. On the contrary, we get a synthetic, sweeping glance in diagrams, such as the one which shows the growth of stature in the two sexes. The method of constructing such diagrams is very simple, and is widely employed. When we wish to represent in physics certain phenomena and laws; or in hygiene, the progress of mortality through successive years, etc., we make use of the method of diagrams.

Let us draw two fundamental lines meeting in a right angle at A (Fig. 151): AS is known as the axis of the abscissæ; AO, the axis of the ordinates. We divide each of these lines into equal parts. Let us assume that the divisions of AS represent the years of age, and those of AO the measurements of stature in centimetres; and since the new-born child has an average height of 50 cm., we may place 50 as the initial figure. From the figure O (age) and from 50 cm. (measure), we erect perpendiculars meeting at a, where we mark the point. At the age of one year the average stature is about 70 cm., accordingly we erect perpendiculars from 1 (age) and from 70 (measure), obtaining the point c. Since the stature at two years is about 80 cm. the same procedure gives us the point e. Since the stature at the age of three is about 86 cm., I erect the perpendicular from a level slightly higher than half-way between 80 and 90, obtaining the point i; and so on, for the rest. Meanwhile we begin to be able to see at a glance that the stature increases greatly in the first year and that thereafter the intensity of its growth steadily diminishes.