**Franc Mocnik**'s parents were Andrej Mocnik, a farmer and innkeeper, and Marjana Sedej. Franc was the second of his parents' three sons. The eldest was Jakob and the youngest was Anton. Andrej and Marjana Mocnik also had three daughters but the oldest of all the children, Mica, died at the age of three while the two other daughters, Ana and Katarina, died before reaching the age of two months. In 1821, at the age of six, Franc began his schooling in the elementary school at Idrija, a town 14 km south of Cerkno. He spent three years at this school before his parents decided that he showed such promise that he should study at a "Latin school". Therefore, in 1824, he entered the Gymnasium in Ljubljana. Ljubljana, now the capital of Slovenia, is about 38 km east of Idrija.

Mocnik spent eight years at schools in Ljubljana, first attending the Gymnasium there before moving to the Lyceum where he was prepared for entry to university. At the Lyceum Mocnik had good teachers; there was the linguist and literary historian Matija Cop (1797-1835) (he drowned while swimming in Sava river) and Franc Serafin Metelko (1789-1860), the physicist Janez Krstnik Kersnik (1783-1850), the botanist Franc Hladnik (1773-1844), and the excellent mathematics professor Leopold Karol Schulz von Strassnitzki (1803-1852) from Kraków. Mocnik was fortunate that Schulz von Strassnitzki taught in Ljubljana precisely in the years when he was studying there. The influence Schulz-Strassnitzki had on Mocnik was evident for throughout his teaching career he always followed the same pedagogical principles that guided his teacher.

When he graduated from the Lyceum it appeared that Mocnik was setting himself up to study mathematics at university. However, he did not follow that route but instead entered the Roman Catholic seminary of Gorizia, a town which today is more commonly known as Gorica and is situated on the Italian-Slovenian border. Since Mocnik's younger brother Anton became a priest, one might conjecture that Mocnik's parents may have wished their sons to become priests. However, even if this were the case, it would have been a more obvious choice to continue to study theology in Ljubljana. Whatever his reasons, Mocnik spent four years from 1832 to 1836 studying theology at Gorizia. He did not seek ordination when he completed the course at Gorizia but now took on two parallel careers. One of these was as a teacher at the Normal School in Gorizia while the other was to study mathematics at university level. However, before continuing to describe Mocnik's career, we must look at someone else who lived in Gorizia at this time.

In July 1830 there had been a revolution in Paris and the French royal family, who were members of the Bourbon dynasty, had fled from Paris and, after living first in Edinburgh, then in Prague, had moved to Gorizia in 1835. Augustin-Louis Cauchy, who was an enthusiastic royalist, had left Paris in September 1830 for a self-imposed exile. Cauchy followed Charles X to Prague and was employed as a science tutor for his grandson, the Duke of Bordeaux (1820-1883). When the family moved to Gorizia, Cauchy came with them. The Duke of Bordeaux, aged fifteen at this time, was an exceptionally difficult pupil who had no desire to learn anything. Cauchy had little experience with trying to teach such pupils and became very frustrated. It was natural, therefore, that he should seek help from Mocnik, the local mathematics teacher, who was giving a great deal of thought to ways of teaching children mathematics. It is doubtful that advice from Mocnik, or anyone for that matter, would have made Cauchy's task easier, but the friendship was a very positive one for Mocnik. Cauchy encouraged him to study more mathematics and he also encouraged him to publish his ideas about teaching mathematics to school children. One very concrete outcome of this friendship was Mocnik's work *Theorie der numerischen Gleichungen mit einer Unbekannten. Mit besonderer Rücksicht auf die neueste von Cauchy erfundene Auflösungsmethode* Ⓣ which was published in 1839. Cauchy left Gorizia and returned to Paris in 1838.

Before meeting Cauchy, in addition to working as a mathematics teacher at Gorizia, Mocnik had studied at the College in Graz. There he studied elementary mathematics, physics, applied mathematics, theoretical and practical philosophy and history. His meeting with Cauchy encouraged him to undertake research at the University of Graz for his Ph.D. which was awarded on 14 April 1840. Mocnik continued to work as a teacher at Gorizia until 1846.

In the year 1846 he moved to Lviv, then in eastern Galicia but now in Ukraine, where he was appointed professor of elementary mathematics at the Technical Academy. This Academy, now the Lviv Polytechnic National University, had been founded in 1844 with Florian Schindler as its first director. At the time that Mocnik was appointed, the Academy was building up its staff, appointing professors of mathematics, physics, mechanics, chemistry, construction and geodesy. However, the revolution of 1848 saw Lviv shelled by Austrian artillery and the school building was destroyed by fire. Teaching continued, however, with classes being held on the third floor in the Town Hall.

In 1849 Mocnik was appointed as professor of mathematics at the University in Olomouc in Moravia. This was an ancient institution originally founded in 1573 but it too was greatly affected by the revolution of 1848. Following the revolution the university taught both in Czech and in German. The university, both staff and students, had mostly supported the revolution and in 1851 the government in Vienna closed the Faculty of Philosophy of the University of Olomouc as a punishment for their failing to support the government. The Minister of Education in the government was Count Leopold von Thun (1811-1888) and he requested that Mocnik should leave Olomouc and move to Ljubljana and take up the position of inspector of primary schools. Von Thun was looking for a suitably qualified and reliable person, who was not too Slavic oriented, to help build the school system. He was keen on adopting new textbooks and new methods of instruction. Mocnik did not belong to a Slavic Society so was considered by the von Thun to be acceptable politically in addition to being well qualified as an experienced teacher developing practical new teaching methods and the author of new textbooks. Von Thun insisted that the German language be used in all schools of higher education and Mocnik's books, although translated into many languages were all originally written in German. A decree was issued on 13 December 1850 making the appointment and Mocnik was sworn into the post on 21 January of the following year.

Mocnik took up this role with enthusiasm, using his ideas to improve teaching methods. His main aim in this role was to improve the general level of education for Slovenian people. Realising that there was a lack of school buildings, he tried to get the resources to build new schools. His main achievement, however, was his efforts to improve the quality of teaching, largely based on the ideas which he himself had developed. Of course, it is almost impossible to have good quality teaching if one does not have good teachers so Mocnik tried to set up better training for teachers and also to make the teaching profession more attractive to good people by improving the opportunities for professional advancement. Von Thun had insisted that secondary school education was conducted in German, but Mocnik was able to persuade him to allow teaching in primary schools to be both in Slovenian and in German.

One of the difficulties that Mocnik faced was an opposition from the Church who saw his reforms taking responsibility for education away from the Church and steering it towards a secular set up. Mocnik, himself a Roman Catholic and a man of strong Christian principles, was in no way opposed to the Church and he was able to convince the Church that he was seeking to improve the standard of education while in no way having an agenda against the Church. His work meant that he made many school visits to inspect the quality of the education they were providing. Often on these visits he would himself teach some mathematics classes to illustrate to the teachers in the school the methods he was trying to encourage. He would report on the individual schools and indicate which of the teachers were, in his opinion, doing a good job and which were not. As one might expect, many teachers opposed Mocnik's reforms, particularly when these required the teachers to work harder. For example the teachers in the Normal School in Ljubljana refused to implement the reformed curriculum which Mocnik drew up in 1851. His response was firm; any teacher refusing to implement the reformed curriculum would be instantly dismissed. With this, the teacher's opposition ended. We see from this example the powers that had been given to Mocnik.

After carrying out this work for nine years, in 1860 Mocnik moved to Graz where again he was an inspector of primary schools but now also responsible for supervising secondary schools in Styria and Carinthia. Because of a Schools Act introduced in 1869 his role changed and he became a provincial school inspector for Styria. He only carried out this role for two years before retiring in 1871 at the age of 57. He claimed his retirement was for health reasons but, although there may be some truth in this, it would appear that at least in part he retired because he was unhappy with the direction that education was taking, moving to a more liberal approach and away from the traditional values that were so important to Mocnik.

After he retired, Mocnik continued to live in Graz at his home at 5 Kroisbachgasse. He could live comfortably on his pension and was able to completely dedicate his years in retirement to writing new books, correcting earlier ones and adapting his textbooks to the new curriculum. There was nothing more important to him than his mathematical textbooks and he continued to work on them right up to the time of his death.

As a mathematician, Mocnik is best known as the author of a remarkable number of mathematics textbooks. His first book was *Lehre von den vier Rechnungsarten, Begriffe und deren aus dem Wesen unseres Zahlensystems entwickelt* Ⓣ published in 1840. It has brief explanations but is illustrated with plentiful examples and tasks for pupils to perform. He published books designed for schools on a full range of mathematical topics, the more advanced texts building on earlier more elementary books with the first part of the text recapping the material from the previous books. His books *Lehrbuch der Arithmetik* Ⓣ; *Lehrbuch der algebra* Ⓣ; and *Lehrbuch der Geometrie* Ⓣ were all published in 1850. The textbook of arithmetic and algebra for upper classes of secondary schools which he published in 1874 is quite advanced covering topics such as divergence, convergence, binomial series and interpolation. A geometry text, intended for the upper classes in secondary schools, explains in the introduction that there are several different approaches to geometry and he suggests that one should not follow only one of these but use different approaches where appropriate. He says that the:-

His books are not all texts for pupils for he also wrote books for teachers explaining his ideas on teaching mathematics. In [3] there is an overview of his many books giving an idea of their number:-... heuristic-genetic method leads the pupil by the shortest route in a successful search and thus leads to independent discovery of scientific truth. It is a method that makes a subject attractive and come alive because it constantly intensifies vigilance ... . Since each approach has its own advantages and because the pupil will find it more stimulating if multiple paths lead to the true eternal laws of geometry, I think it is appropriate, in this textbook, not to use a uniform method but rather if, in relation to a specific subject, now the first and now the second method is used.

Mocnik received several honours for his contributions to education. For example, he was awarded the Order of Franz Joseph in 1862 and on his retirement in 1871 was awarded the Order of the Iron Crown and became a Knight.Mocnik's mathematical textbooks are very numerous. According to Branko Sustar(see[9]), his last bibliography was compiled by Jose Povsic. Mocnik's textbooks were originally published in German(148textbooks in980editions)and they were translated to14other languages:39Slovenian textbooks(174editions),29Croatian textbooks(132editions),32Serbian textbooks(77editions),4textbooks for Bosnia and Herzegovina(36editions),9Albanian textbooks(13editions),9Bulgarian textbooks(23editions),39Czech textbooks(109editions),46Italian textbooks(130editions),38Hungarian textbooks(185editions),4Greek textbooks(4editions),39Polish textbooks(86editions),20Romanian(36editions),5Slovak(5editions)and40Ukrainian textbooks(74editions).

**Article by:** *J J O'Connor* and *E F Robertson*