Slike strani
PDF
ePub

second report (1901) of M. Billiet, the following conclusions are given: "(1) The simultaneous teaching of plane and solid geometry saves time. (2) The new method restores the agreement between the various subjects in the mathematical program and those of theoretical and practical teaching with which it is connected. (3) It appeals to intelligence more than to memory. (4) It accustoms the pupils to think for themselves... "From the above we see at least what is being claimed for the new method.

It appears that Méray's method has received official recognition in France. In L'Enseignement Mathématique,' the editor quotes from a circular written by Professor C. Bourlet of the Lycée St. Louis, addressed to his colleagues. M. Bourlet says that in August, 1904, the French Association for the Advancement of Science voted in favor of the adoption of Méray's method. This was transmitted to the Minister of Education. As a result, "the instructions annexed to the new decree of July, 1905, invites, among other things, the teachers to follow a method entirely new in geometry. . . "It is that with joy," writes M. Bourlet, "that I have undertaken the delicate task of rewriting the 'Nouveaux éléments de géométrie,' so as to conform to the program, to the instructors, to the ideas of M. Méray, and to the necessities of our teaching."

[ocr errors]

For two reasons this new movement in France seems to be of a permanent nature. First, it has already been tried, apparently with success, in many of the schools. Secondly, it has received ministerial sanction. It is to be noted, however, that the lycées have not made use of Méray's text. Undoubtedly the problem of preparing for the higher examinations has influenced the teachers in these schools. It remains to be seen if the new book to be prepared by M. Bourlet will find a place in the lycées.

ITALY

Before 1848, the classics reigned supreme in Italy. With the political changes that came in that year, the plan of secondary instruction was entirely reorganized. By the law of Nov. 13, 1859, which gave direction to this new organization, the classical schools were divided into a lower and a higher grade. The 1 Nov., 1905, pp. 488-489.

1

school of lower grade is the ginnasio with a five years' course, and that of the higher grade the liceo with a three years' course.. By this same law of 1859, two grades of technical schools were created, the scuola tecnica and the istituto tecnico.1 The first is the more elementary, the latter offering the real scientific training. The classical schools above mentioned prepare for the university studies and the "higher callings," while the aim of the technical schools is "to discover and strengthen those properties which develop the commercial and industrial life of a nation."2

3

Of the classical schools, pupils are admitted into the ginnasio at the age of ten or eleven. During the first three years only two hours a week are devoted to mathematics, and throughout the five years of the course the work is not extensive. But in the three years of the liceo the work is much broader. It comprised in 1880 the geometry of Euclid, arithmetic, algebra, logarithms, trigonometry, and stereometry. The course in geometry in the licei in 1884 was: For the first year, the first four books of Euclid; for the second year, Books V and VI; and for the third year, solid geometry taught from a modern treatise.5

4

Up to 1904 there was one course for all students in the classical schools. By the decree of Nov. 11, 1904, the Minister of Public Instruction introduced an essential change. During the last two years of the liceo the student can now choose between two courses, which emphasize Greek and mathematics respectively.' The course in geometry, beginning with the

1 Schmid, Encyklopädie des gesammten Erziehungs, article Italien, p. 744. For a general description of these types of schools, see Hippeau, L'instruction publique en Italie. For an account of the educational development of Italy in the last century see the article on Italy in Baumeister, op. cit., 12, p. 541

2 Schmid, op. cit., p. 744

3 Degani, Some Aspects of Italian Education, pp. 26-27

5

Schmid, op. cit., p. 746

Candido, Sur la fusion de la planimétrie et de la stéréométrie dans l'enseignement de la géométrie élémentaire en Italie, Ens. Math., 1899, pp. 204215. Hereafter referred to as Candido.

Battazzi, Un essai de réforme des études moyennes classiques en Italie, Ens. Math., 1905, pp. 400-406.

7 'This elective principle has met with strong opposition from teachers of mathematics in Italy. At the meeting of the association "Mathesis" held in Milan, April 21 and 22, 1905, it was resolved that the association feels that a single program of elementary mathematics should be obligatory for all pupils and for all classes of the liceo. Battazzi, op. cit., p. 403.

last two years of the ginnasio, comprises plane geometry, including general conceptions, equality of figures, and some notions of equivalence. In the first year of the liceo, the work includes relations of positions, equality of solids, proportion and similarity of plane figures, theory and application of mensuration to plane figures, and practical rules for measuring solids and surfaces not plane. In the second and third years are taught the equivalence and similarity of solids, theory of the measure of surfaces not plane and of solids, and the application of algebra to geometry. Algebra and trigonometry are begun the first year of the liceo, after the introduction of geometry.

The geometric traditions in Italy have on the whole been Euclidean. In ancient Piedmont, where the French influence was strong, Legendre was preferred to the rigor of Euclid, and the provinces which threw off the yoke of Austria used books written with a commercial aim. These were not satisfactory, in particular to Cremona, who was then teacher in a secondary school in Lombardy. Not wishing to adopt such books, he urged the use of better ones. He was appointed in 1867 by his government "to lay out the general lines of a reform in the teaching of geometry in the classical schools." He immediately suggested a return to Euclid, pure and simple, and in this he was supported by Brioschi and Betti, who had edited an edition of the "Elements." The government acted on the recommendation of Cremona.2 The program of 18843 shows the results of this recommendation, but, judging from the character of important texts in use about that time, we are not to believe that Euclid was strictly adhered to. As for the teaching of geometry at the present time, the

4

1 Loria, op. cit., Ens. Math., 1905, pp. 11-20.

"In the preface of Sannia and D'Ovidio's geometry (1888, 7th edition) is found the statement that in 1867 the Italian government had ordered a return to Euclid. The practical tendencies in Legendre are also discouragingly mentioned.

3 See above, p. 113.

* The sequence in the geometry of Sannia and D'Ovidio is practically that of Legendre. Numerical work is found in mensuration and algebra is employed in proportion. The book of Faifofer (1887), as the preface states, is intended primarily for use in the technical and normal schools. The work is introduced from the practical standpoint and proportion is at first treated arithmetically. Loria (Ens. Math., p.12) states indirectly that this text was used in the licei.

1

`program of 1904, already referred to, shows no close adherence to Euclid. The sequence of subject-matter, in particular, shows a marked departure from the "Elements." That the actual teaching is away from Euclid is seen from a statement of Professor Loria. He says, "The last of the Italian mathematicians who have written on elementary geometry are Enriques and Amaldi, who have attached the new to the traditional Euclid, and propose in their recent book to have a text that fits the actual conditions in the schools."

3

Italy, like France, has in recent years been agitating the simultaneous teaching of plane and solid geometry. The text of De Paolis, which appeared in 1884, embodies this aim. Although the book was somewhat beyond the capacity of immature students, some young teachers, "braving critics as well as difficulties, " had the temerity to adopt it in some of the licei. A little later appeared the geometry of Professor Andriani, which also used the method of fusion. According to Candido, Andriani went too far and forced analogies between plane and solid geometry. A pupil of De Paolis, Dr. Guilio Lazzeri, professor in the Royal Academy of Leghorn, adopted the new method and influenced his colleagues to do likewise. He wrote out a course himself in 1887 and another in 1889. This was tested in teaching and resulted in the "Elementi di geometria” by Lazzeri and Bassani, which appeared in 1891. Candido says1 that, since the work was more practical and serviceable than the one by De Paolis, it received favorable criticism and was adopted in many licei. The text comprises five books. The first three are independent of number and treat the properties of position and of magnitude in the plane and in space which are derived from the fundamental notion of equality. Book IV is on the theory of equivalent magnitudes. It is also free from number. Book V treats the theory of proportional magnitudes and of measures. Number is here involved.

Since the above book first appeared, the "fusion" idea has found place in the texts of Professor Veronese (1897) and of Pro

[blocks in formation]

fessor Reggio (1898).1 Attention has also been given to this question by the Association Mathesis, which organization has for its aim the betterment of the teaching of mathematics. At its meeting in 1896 one of the first questions discussed was that of "fusion." This subject was discussed in later meetings, the idea being to give the teachers a choice of the two methods in their work. In 1898 the association voted in favor of the new movement. On the whole this movement seems to have progressed in Italy almost to the extent that it has in France. fact, judging from the number of texts in Italy embodying the idea of "fusion," in this respect the latter country has gone beyond France. In both countries, prominent teachers' associations have passed favorable votes on the question, and in France the Minister of Education has decreed in favor of its use in the lycees."

RUSSIA

In

The last thirty years of the nineteenth century saw the reorganization and extension of the Russian public school system. The secondary system for the education of women

1 Candido, p. 207.

'An organization of secondary school teachers of mathematics, existing since 1895.

3 Professor Henri de Amicis read a paper on "Opportunities in Teaching for the Fusion of Plane Geometry with Solid Geometry." p. 207.

'Candido, p. 211.

See Candido,

According to Ripert (Ens. Math., 1899, p. 62) the association gave recommendations to the Minister of Education in May, 1897.

5 In England, Germany, and Italy it is being advocated that the course in elementary mathematics be enriched by bringing in phases of practical higher mathematics. Professor Perry stands for this very thing in England (see below, pp. 126-128), Professor Loria in Italy (see Battazzi, op. cit., pp. 405-406), and Professor Klein in Germany (see Klein, Über den mathematischen Unterricht an den höhern Schulen, in Zeitschrift für mathematischen und Naturwissenschaftlichen Unterrichts, 1902, pp. 114-125). Bobynin, L'enseignement mathématique en Russie. État actuel. seignement primaire. Ens. Math., 1899, pp. 420-446.

6

En

Bobynin, L'enseignement mathématique en Russie. État actuel. Enseignement secondaire. Ens. Math., 1903, pp. 237-261.

For the more general features of education in Russia, see Hippeau, L'instruction publique en Russie; Beer und Hochegger, op. cit.; and the article on Russia in Baumeister, op. cit., I2, pp. 561-576.

« PrejšnjaNaprej »