**Author(s):**Algirdas Ažubalis

**Journal:**Evolution of Science and Technology

ISSN 2029-2430

**Volume:**1;

**Issue:**1;

**Start page:**50;

**Date:**2011;

Original page

**Keywords:**didactics of mathematics | course book | articles

**ABSTRACT**

Mečys Mačernis (1897–1968) taught elementary mathematics and didactics at the National Pedagogical Institute of Klaipėda in 1935–1939. He studied at the universities of Berlin and Königsberg. From 1926 to 1934 he worked as the head master at Tauragė Teachers’ Semi-nary. During the period from 1935 to 1940, M. Mačernis was as a vice-director of the National Pedagogical Institute of Klaipėda where since 1937, worked in a position of director. In 1926, he published a methodical course book for the students of the Seminary on teaching arithmetic. During 1925–1928, he published 3 articles about the didactics of mathematics. While living in Klaipėda in 1940, M. Mačernis prepared and published a methodical course book on teaching arithmetic and geometry for the students of the Institute. In 1938–1939, he completed his scientific work on the pedagogy of the Middle Ages and a large three volume composition Didactics. M. Mačernis left Klaipėda and Pedagogical Institute when this western part of Lithuania was annexed by Hitler. He went to Panevėžys and later to Vilnius which helped him to come back to Lithuania. When Lithuania was occupied by the Bolsheviks, M.Mačernis was dismissed from the position of director. In 1941, he was arrested and deported to far inland Russia. After World War II, he worked as a teacher of mathematics in Karaganda region. Having returned to Lithuania after deportation, M. Mačernis worked as a teacher of mathematics at one of the schools in Plungė. Starting from 1940, M. Mačernis did not write any scientific pedagogical book.Methodical course books of teaching mathematics written by M. Mačernis presented the teachers of Lithuania the actual ideas of connections established between teaching and practice as well as between internal and inter-subjective integration that were the issues widely discussed in Western Europe of that time.Pranas Naujokaitis (1905–1976) worked at the National Pedagogical Institute of Klaipėda as a teacher of primary school and as a lecturer of the Institute. He graduated from Marijampolė Teachers’ Seminary and then worked as a teacher in primary schools of Šakiai and Šiauliai provinces. In 1933–1935, he worked as a teacher of primary school at Marijampolė Teachers’ Semi-nary. While staying in Klaipėda, P. Naujokaitis completed his studies at the Pedagogical Institute. Within the period from 1936 to 1938, he wrote 3 articles on the didactics of mathematics and compiled a 5 section book of tasks for mathematics. He also did the sixth section but the manuscript was ruined by the military people of the Red Army accommodated at the farmstead owned by P. Naujokaitis parents during the war. Due to the publication of math course books and tasks during the Soviet occupation times, they were monopolized by the Central management in education in Moscow. Starting from 1940, P. Naujokaitis did not write anything new in this area. However, after World War II, he did a lot in the field of the Lithuanian language used in didactics: he wrote some articles, prepared visual aids and together with his colleagues wrote some course books on the didactics of the Lithuanian language for students. After the war, P. Naujokaitis worked as the head master at Marijampolė Teachers’ Seminary, gave lectures in Kaunas Teachers’ Seminary and was the head master of the fourth secondary school in Kaunas. His last work place was the Department of Evening Classes of Vilnius University in Kaunas where P. Naujokatis taught the didactics of the Lithuanian language.In his Arithmetic Tasks, P. Naujokaitis realized the ideas of connections established between teaching and practice as well as internal and inter-subjective integration emphasized by M. Mačernis. Therefore, the book was compiled of the before introduced tasks, and thus was favourably accepted by society and teachers. The course book consisted of two parts that were intended for children to explore the nearest environment because those parts of the tasks were used by the youngest pupils. Parts 3 and 4 of the book were aimed at broadening the knowledge of Lithuania. They included plenty of tasks containing historical facts and dates and different data on culture and economics. Teaching material of the tasks was deliberately and carefully selected according to the topics taking into consideration students’ age, cognitive opportunities and interests. While being trained to add up and subtract within 10 digits limit, the students were solving tasks upon the following themes: ’Birds’, ’Domestic Animals’, ’At Home’ etc. While operating with bigger digits, the children could find the tasks grouped by the topics ’In the Kitchen’, ’At the Carpenter’s’, ’On the Market’, ’Goods Weighting’, ’In the Shop’ etc. The subjects of tasks were distributed considering seasons, national and religious holidays. The students were trained to calculate solving different tasks. They were also proposed to put together a certain amount of sticks in order to compose figures, things, numerals and digits shown in the course book. Further tasks were more difficult to deal with as here, the children were instructed to make more complex geometrical figures and bodies of wooden sticks, clay and paper. Parts 1 and 2 of the course book contained a number of illustrations the objective of which was to help the children to adopt various mathematical concepts and to learn mathematical rules.Parts 3 and 4 of the book were also grouped according to the topics, for instance ‘At the Post–Office’, ‘In the Town’, ‘Rivers and Lakes of Lithuania’, ‘Lithuanian Railways’ etc. Sections regarding geometry, measuring and watching were inserted in a strict sequence. The illustrations of parts 3 and 4 of the book became more abstract as they were used by elder schoolchildren i.e. contained a lot of various schemes, tables and diagrams. The texts of the appropriate tasks are more difficult with lots of data related to geography, culture and history. Part 5 of the course book is intended for elderly students. Thus, P. Naujokaitis included many tasks to be common for everyday routine: to calculate family budget and a list of expenses, to prepare an invoice, to measure the perimeter and square of the plot of land, volume of premises. This part of the course book contains more than one hundred different drawings, schemes, tables, diagrams and examples of financial documents filling in.All the parts of the course book by P. Naujokaitis are composed following the same order: an example, an illustration including a drawing, a rule and practical tasks to learn the rule concerned. An essential feature of the book is the expansion of students’ world outlook and their moral education. Finally, the course book is interesting as a document of that time. The children were measuring the distance from their homes to school, calculating the distance to a neighbouring school and were interested in products manufactured by farmers, their prices and profits earned by the farmers and traders.In the articles on the didactics of mathematics, P. Naujokaitis was focusing on searching rational ways of teaching based on visual and practical experience gained by children.Conclusions:1. Contributions made by M. Mačernis and P. Naujokaitis into the didactics of mathematics in Lithuania can be treated as considerable. The major part of works on the didactics of mathematics written by M. Mačernis and all scientific works by P. Naujokaitis were created working at the National Pedagogical Institute of Klaipėda.2. Works by M. Mačernis and P. Naujokaitis have a considerable value for the future generations. The course books on the didactics of mathematics helped the prospective teachers with focusing on establishing connections between teaching mathematics and real life and on integrating teaching mathematics into other subjects taught. The course books by P. Naujokaitis can be treated as a wonderful example of establishing connections between mathematics, other subjects, real life, national economics and culture.3. The Bolshevik occupation did not allow M. Mačernis and P. Naujokaitis to continue their work in the area of the didactics of mathematics. Article in LithuanianStraipsnyje pristatomi matematikos pagrindus ir didaktiką Respublikos pedagoginiame institute Klaipėdoje 1935–1939 m. dėstęs Mečys Mačernis ir pavyzdinės pradinės mokyklos mokytoju bei instituto lektoriumi dirbęs Pranas Naujokaitis. Dirbdamas Klaipėdoje, M. Mačernis parengė bei išleido aritmetikos ir geometrijos mokymo metodikos vadovėlį studentams. P. Naujokaitis 1936–1938 m. parašė 3 matematikos didaktikos straipsnius ir 5-ių dalių aritmetikos uždavinyną. Straipsnis lietuvių kalba