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V diplomskem delu z naslovom Razvijanje matematičnih sposobnosti v predšolskem obdobju s pomočjo tipanke so predstavljene dejavnosti z matematičnimi tipankami, ki vključujejo matematične pojme s treh matematičnih področij: geometrije, algebre in aritmetike. Za vsako matematično področje smo izdelali veččutno tipanko, s pomočjo katere smo izvedli dejavnosti v vrtcu. Pri tem nas je zanimalo, v kolikšni meri bodo otroci preko dejavnosti s tipankami pridobili nova matematična spoznanja. Dejavnosti v vrtcu smo izvedli v dveh skupinah otrok, starih od 5 do 6 let, in jih natančneje opisali v praktičnem delu, kjer smo na podlagi pridobljenega vzorca evalvirali učinkovitost tipank pri razvoju matematičnih sposobnosti pri predšolskem otroku. Predstavili smo rezultate, in sicer koliko so otroci že imeli razvite matematične sposobnosti pred aktivnostmi s tipankami in po izvedenih aktivnostih s tipankami. Rezultate smo pridobili na podlagi vnaprej pripravljenega ocenjevalnega lista ter tako ugotovili, v kolikšni meri je tipanka pri otrocih razvijala matematične sposobnosti. In the diploma work entitled Development of mathematical skills in the pre-school period with the help of the tactile book, the activities with the mathematical tactile books are presented. They include mathematical concepts from three mathematical areas: geometry, algebra and arithmetics. For each mathematical area a multi-sensory tactile book has been made, and with its help activities in the nursery were carried out. In this context we were interested in the extent to which the children through activities with the tactile books gain new mathematical insights. Activities in the nursery were carried out in two groups of children, aged from five to six, and more specifically described in the practical part, where on the basis of the obtained sample the efficiency of tactile books in the development of mathematical skills at pre-school children was evaluated. We have introduced the results of how much the children have already developed the mathematical skills before the tactile book activities and after the activities have been carried out. The results have been obtained on the basis of predefined evaluation sheet. This way we have determined the extent to which the tactile book has helped to develop the children's mathematical skills.

Učenci s primanjkljaji na področju učenja aritmetike se spoprijemajo s pomanjkljivo in ovirano avtomatizacijo matematičnih dejstev ter postopkov, ki je pogojena s težavami semantičnega spomina, proceduralnimi ovirami in vidno-prostorskimi primanjkljaji. Zadnje ima ključen vpliv na obvladovanje pisnega računanja in usvajanje pisnih algoritmov pri aritmetiki. Namen magistrskega dela je ugotoviti, kako pri učencu s primanjkljaji pri aritmetiki izboljšati uspešnost pri izvajanju računskih operacij pisnega množenja in deljenja. V magistrskem delu je predstavljen 30-urni trening, ki je bil izveden z učencem šestega razreda. Diagnostična ocena je bila pridobljena z neformalnimi razgovori z učencem, njegovimi starši, učiteljicami, izvajalko učne pomoči ter specialno in rehabilitacijsko pedagoginjo, ki je učenca obravnavala, z analizo učenčeve dokumentacije, vprašalnikom za ugotavljanje prevladujočega učnega stila učenca ter matematičnimi preizkusi in testi za oceno obvladovanja aritmetičnih znanj in spretnosti. Znotraj treninga je prikazan pomen povezovanja aritmetičnega proceduralnega, konceptualnega in deklarativnega znanja ter smiselnost poučevanja, kjer se prepletajo načela dobre poučevalne prakse in specialnopedagoški načini pomoči (poučevanje strategij reševanja nalog z odkrivanjem povezav med dejstvi in zakoni oziroma pravili, uporaba mnemotehnik, učenje kompenzacijskih strategij reševanja aritmetičnih nalog, raba ponazoril, pomoč učencu v obliki tutorstva itd.). Primerjava začetnih in končnih rezultatov testiranja kaže, da je učenec s pomočjo treninga bolje razumel in usvojil deklarativna in konceptualna aritmetična znanja, ki so pomembna za izvajanje postopka pisnega množenja, ter napredoval na področju zapomnitve in izvedbe korakov v postopku pisnega deljenja. Pridobljeni podatki bodo v pomoč učiteljem, izvajalcem učne ali dodatne strokovne pomoči ter specialnim in rehabilitacijskim pedagogom pri oblikovanju ustreznih pristopov in načinov pomoči za učence predmetne stopnje, ki nimajo usvojenih temeljnih matematičnih znanj in spretnosti. Students with the deficiencies in the field of learning arithmetic face deficient and impeded automation of mathematical facts and procedures which is conditioned by the troubles of the semantic memory, procedural impediments, and visual-spatial deficiencies. The latter has an essential influence on mastering computation in writing and assimilating written algorithms within arithmetic. The purpose of the master’s thesis is to ascertain how to improve success in performing arithmetic operations of written multiplication and division in a student with deficiencies in arithmetic. In the master’s thesis, I present 30-hour training which was performed with a student of the sixth grade. The diagnostic evaluation was acquired by means of informal discussion with the student, with his parents, teachers, the performer of the learning assistance, special rehabilitation teacher who treated the student, the analysis of the student’s record, questionnaire for ascertaining the prevailing learning style of the student, and mathematical tests and tests for the evaluation of mastering arithmetic knowledge and skills. Within the training, the significance of connecting arithmetic procedural, conceptual, and declarative knowledge, and the sanity of teaching where the principles of good teaching practice and special teaching approaches of assistance (learning strategies of solving tasks by means of discovering connections between the facts and laws or rules, the use of mnemotechniques, learning of compensation strategies of solving arithmetic tasks, the use of depictors, assistance to the student in form of tuition, etc.) intertwine. The comparison of the initial and concluding results of testing proves that, by means of training, the student better understood and assimilated declarative and conceptual arithmetic knowledge which is important for the performance of the procedure of written multiplication, and improved in the field of retention and performance of the steps in the procedure of written division. The acquired data will be helpful to teachers, performers of learning or additional professional help, and special rehabilitation teachers in the case of forming the appropriate approaches and methods of the assistance for the students of the subject level, which did not assimilate the basic mathematical knowledge and skills.

V diplomskem delu z naslovom Uporaba ploščic za vzorčke na področju aritmetike in delov celot so predstavljene nekatere aktivnosti z uporabo teh ploščic iz seta za vzorčke. Sledili smo aktivnostim, ki so navedene v članku Hungry for Early spatial and Algebraic Reasoning. Otrokom smo najprej predstavili uporabo in pomen ploščic za vzorčke. Za večjo motivacijo in čim bolj zanimivo in razumevajočo razlago za otroke smo uporabili tudi lutko gosenico Berto, ki je otroke še bolj motivirala k sodelovanju. Otroci so se skozi aktivnosti srečali s področjem aritmetike in delov celote. This diploma work, entitled "Using pattern blocks in the field of arithmetic and parts of wholes", presents some activities by using these blocks. We have followed the activities listed in the article “Hungry for Early spatial and Algebraic Reasoning”. The children were first acquainted with how to use the pattern blocks and with their importance. To increase children’s motivation and to ensure the most interesting and sympathetic explanation for the kids, we used a doll-caterpillar named "Berta", which motivated children to participate even more. Through their activities children met with the scope of arithmetic and parts of wholes.

V diplomskem delu so prikazani in dokazani osnovni kriteriji deljivosti. V tretjem poglavju je prikazano, kako je tema deljivosti predstavljena v slovenskih osnovnošolskih učbenikih. V zadnjem poglavju pa so predstavljeni primeri nalog iz osnovnošolskih tekmovanj, ki se rešujejo s pomočjo obravnavanih kriterijev. In this graduation thesis, basic divisibility criteria are shown and proven. The third chapter shows how the topic of divisibility is presented in Slovenian primary mathematics textbooks. The final chapter presents examples of exercises from primary school mathematics competitions, which are solved with the use of divisibility criteria.

My dissertation is mainly focused on work sheets created in Smart notebook 10 which are intended for the third-grade pupils of primary school. At the beginning I am dealing with the didactic part of chosen curriculum in material which was made by me. Futhermore I am comparing available mathematic schoolbooks which are intended for the third grade. The main part contains methodical manual for users of the working sheets which were created in Smart Notebook 10. It is mainly focused on the operation, the usage and the right method of working out the particular tasks. In conclusion of my dissertation I am summarizing my conclusions of hours and I am evaluating my experience gained from teaching at the primary school during which I used the chosen working sheets.

My thesis is focused mainly on my own electronic work sheets for children with limited hand mobility - the second class of elementary school. The introduction deals with methodology of chosen topics which I have used in my work sheets. I compare teaching methods which I have used with alternative ones. The main part of my thesis aims at SMART Board 10 software for interactive whiteboard which I have used for creating my work sheets, secondly on its use, thirdly on its tools from the tool kit and at last but not at least on description of my work sheets. I also describe the teaching of a physically disabled girl with limited hand mobility that I have taught. The conclusion consists of summarizing my experience with teaching based on my work sheets and assessing my teaching lessons.

Straipsnio nagrinėjami P. Vileišio vadovėlio „Keturi svarbiausiejie veikalai aritmetikos“ (1886) vartojami aritmetikos terminai, jų kilmė, darybos būdai ir priemonės bei sinoniminė raiška. Svarbu tai, kad vadovėlyje autorius pateikia kai kurių matematikos terminų apibrėžtis. Tyrimui surinkta apie 150 terminų. Būdingas vadovėlio terminų bruožas – lietuviškumas. Vienažodžiai lietuviškos kilmės terminai, kurie eina sudėtinių terminų pagrindu, sudaro net 75,8 proc. visų rastų terminų. Dauguma šių terminų aritmetikoje nebevartojami, pvz.: iszteisinimas, padaugintinis, vaisius. Nelietuviškos kilmės terminai sudaro 21 proc., hibridiniai terminai – 3,2 proc. Vienažodžių terminų, kuriais eina pirminiai žodžiai, vadovėlyje rasta tik 2 (4,1 proc. ): labas, spugas. Didžiąją dalį antrinių žodžių sudaro dariniai (priesagų, galūnių vediniai ir vienas dūrinys) – net 95,9 proc. visų vienažodžių terminų. Vyrauja priesagų vediniai, iš kurių gausiausią grupę sudaro priesagos -imas (-ymas) vediniai, kiek mažiau priesagų vedinių sudaro terminai, padaryti su kitomis priesagomis: -urnas, -ybė, -uotis, -tis, -tojas, -alas, -ana, -ėjas, -yklė, -lė, -line, -tinis. Galūnių vediniai sudaryti su galūnėmis -is (-ys), -ė, -(i)us. Vadovėlyje vartojami sudėtiniai terminai sudaro 57,8 proc. visų rastų terminų. Tai dvižodžiai ir trižodžiai terminai, kuriuos galima išskirti į derinamojo ir nederinamojo pažyminio junginius. Didžioji dalis nagrinėjamų terminų fiksuojami akademiniame Lietuvių kalbos žodyne, bet yra terminų ar jų reikšmių, nepatekusių į tą žodyną, pvz.: stalveikslis, padaugintinis, labas. The paper examines arithmetic terms used in P. Vileišis’ textbook “Keturi svarbiausiejie veikalai aritmetikos” [The Four Most Important Arithmetic Treatises] (1886), their origin, ways and means of word-formation as well as synonymic expression. The important fact is that the author gives the definitions of some mathematical terms in the textbook. About 150 terms were collected for the research. The Lithuanian aspect is a typical feature of terms from the textbook. One-word terms of Lithuanian origin, which form the basis for composite terms, constitute as much as 75.8% of all found terms. The majority of these terms are no longer used in arithmetic, e.g. iszteisinimas, padaugintinis, vaisius. Non-Lithuanian terms constitute 21%, hybrid terms – 3.2%. Only two one-word terms (4.1%) which are primary words, i.e. labas and spugas, were found in the textbook. The majority of secondary words are formations (suffixal or ending derivatives and one compound) – as much as 95.9% of all one-word terms. Suffixal derivatives prevail; the most numerous group of them are derivatives with the suffix -imas (-ymas), whereas other suffixes are used less often: -urnas, -ybė, -uotis, -tis, -tojas, -alas, -ana, -ėjas, -yklė, -lė, -line, -tinis. Ending derivatives have the endings -is (-ys), -ė, -(i)us. Composite terms used in the textbook constitute 57.8% of all found terms. These are two-word and three-word terms that may be classified as combinations of an agreeing modifier and combinations of a non-agreeing modifier. The majority of analysed terms are recorded in the Academic Dictionary of Lithuanian; however, there are terms or their meanings that are not included in the dictionary, e.g. stalveikslis, padaugintinis, labas.

U radu se analiziraju malobrojne računice na hrvatskom jeziku koje su nastale u dopreporodnom razdoblju. Prikazuje se utjecaj prosvjetiteljskog duha koji se u 18. stoljeću širio austrijskim zemljama, te se pored ostalog odrazio i na nastanak prvih računica na hrvatskom jeziku. Rad daje cjeloviti kronološki pregled i komparaciju svih hrvatskih računica nastalih u dopreporodnom razdoblju, od pojave Šilobodove Arithmetike horvatszke (1758., Zagreb) i Zoričićeve Aritmetika u slavni jezik ilirički sastavljena (1766., Ankona), zatim prvih službenih školskih udžbenika na hrvatskom jeziku Napućenje vu brojoznanje (1780., Budim) i Upućenje u brojo-znanje (1780., Budim), do aritmetičkih udžbenika Racsun za pervu i drugu godinu skulsku Ambroza Matića (1827., Osijek) za gramatičke škole u Bosni i udžbenika Racsun iz glave za ucsitelje i ucsenike narodnih shola u Slavoniji Nikole Hadžića (1834., Osijek). Analiziran je i međusobno kompariran njihov sadržaj, korištena metodologija, doseg i stavovi zastupani u navedenim djelima. Interpretira se i uspoređuje hrvatsko matematičko nazivlje u navedenim računicama. Izvorno je dano tumačenje jasnih razlika između prvih hrvatskih računica i prvih školskih udžbenika na hrvatskom jeziku s kojima je obilježen početak sustavnog, organiziranog školskog sustava na hrvatskim područjima. Analizirani su točno određeni stručni, metodološki i didaktički principima prema kojima su udžbenici bili načinjeni u skladu s propisanim nastavnim planom i programom.

Straipsnyje, remiantis nepriklausomos Lietuvos mokyklų programomis, švietimo periodika, nagrinėjama matematikos mokymo Lietuvoje 1918-1940 m. reikšmė, turinys ir organizavimas. Si problema ypač aktuali Pirmosios Lietuvos Respublikos gyvavimo laikotarpiu, nes atkūrus nepriklausomybę jaunoje šalyje reikėjo diegti jau paplitusį Vakarų Europoje matematikos mokymo modelį, paremtą 1905 m. Meranės programa. With Lithuania's independence declaration in 1918 national education development was to be given a proper attention. According to the law of high education passed in 1919 educational system consisting of three types of schools - primary school, pro-gymnasium and gymnasium - was built. It the beginning Lithuania adopted experience of Russian schools concerning studies of different subjects. At that time mathematics syllabus consisted of arithmetic (forms 1-2), arithmetic and algebra (forms 3-4), introductory course of geometry (form 4). Besides algebra from form 5 children were taught planimetry, from form 6 - stereometry, and from form 7 - trigonometry. Moreover, pupils were suggested to broaden algebra studies with basics of equation and combination theories. When in 1924 secondary education was extended till form 12, syllabus of some teaching subjects including mathematics was begun to develop. One of the main supporters of changes in mathematics syllabus was professor Zigmas Žemaitis (University of Lithuania), who maintained the Merane conference ideas, which spread in Western Europe at that time. He suggested changing mathematics syllabus fundamentally, presenting the notion of the mathematical function already in junior forms. In 1928 the latter ideas were approved at the 1st Lithuanian Mathematics, Physics and Cosmography Teachers' Conference. These ideas had already found their reflection in the curriculum approved in 1929-1930 academic years. Since that time mathematics studies in secondary schools started with systematic arithmetic and algebra courses and introduction into systematic course of planimetry. In senior forms (forms 5-8) during mathematics classes systematic course of algebra had to be finished, the whole course of geometry was taught and some knowledge of "infinite smalls" was given. In the course of education modernization in 1936 under the reform of school education it was decided that at a gymnasium children would study 7 years, and at primary school - 6 years. So, at primary school mathematics subject was already called as calculation and during this subject lessons pupils were introduced with a wide course of arithmetic and introductory geometry (planimetry and stereometry). Later, at secondary schools (pro-gymnasium, gymnasium) mathematics included arithmetic and algebra (forms 1-2), algebra (forms 2-4) and geometry (forms 1-7) courses. In the final form mathematics syllabus was widened with credibility theory and project geometry elements were included. So, mathematics teaching in secondary school consisted of 3 weekly lessons, and in final forms (pro-gymnasium form 3 and gymnasium form 7) 4 lessons. Thus, it is evident, that mathematics teaching in Lithuania in 1918-1940 was not only organised, but directed towards modernization, following Western Europe tradition. It is also proved by two facts: mathematics syllabus was accomplished in the light of education reforms (1924, 1936) and new mathematics textbooks were published.

Diplomsko delo z naslovom Cuisenairove paličice v vrtcu je namenjeno vsem tistim, ki imajo pri vsakodnevnem delu stik z otrokom v predšolskem obdobju in jih zanima razvoj matematičnih sposobnosti predšolskega otroka. Z uporabo didaktičnih pripomočkov in igrač pri predšolskem otroku razvijamo matematično znanje, ki temelji na razumevanju. Cuisenairove paličice so didaktični pripomoček, ki omogočajo otroku samostojno raziskovanje in ga prepričajo, da matematika v vsakdanjem življenju res deluje. V svetu se že več desetletij uporabljajo za poučevanje na področju matematike, pa tudi na drugih področjih. Pri nas se uporabljajo zelo redko, vendar ne za namene poučevanja, ampak zgolj kot konstrukcijski material pri prosti igri otrok. Namen diplomske naloge je prikazati poznavanje in uporabo Cuisenairovih paličic kot didaktičnega pripomočka za področje matematike v vrtcu. Kot je bilo pričakovano vzgojiteljice Cuisenairovih paličic niso poznale po imenu, nekatere pa so jih le vizualno prepoznale. Ker ni gradiv za njihovo uporabo, so v praktičnem delu podane aktivnosti za uporabo Cuisenairovih paličic s ciljem, da bi jih vzgojiteljice uporabile in preizkusile pri usmerjenih aktivnostih iz področja matematike v vrtcu. Aktivnosti omogočajo, da otroka vpeljemo v svet matematike na način, ki bo prilagojen njegovim kognitivnim zmožnostim. Bachelor thesis, entitled “Cuisenaire rods in pre - school education”, is intended for everyone who has daily contact with preschool children and is interested in the development of their mathematical competences. Mathematical knowledge of a preschool child, which is based on understanding, is developed with the use of teaching aids. Cuisenaire rods are a manipulatives which allows children to independently explore, convincing them that mathematics is actually useful in everyday situations. The rods have been used worldwide for decades for teaching in the area of mathematics as well as other areas. The rods are rarely used in Slovenia, and even when they are, they are not used for the purposes of teaching, but merely as a construction material in free children’s play. The purpose of my bachelor thesis was to display the understanding of Cuisenaire rods and their use as a teaching aid in the area of mathematics in kindergarten. As had been expected, childcare workers did not recognize the Cuisenaire rods by their name. Some did, however, recognize them visually. Since there are no materials available for their use, the practical part of the thesis provides activities for the use of Cuisenaire rods by childcare workers with the aim of being used and tested with goal-directed activities in the area of mathematics in kindergarten. These activities allow us to introduce children to the world of mathematics with methods adapted to their cognitive abilities.

Mijo Šilobod Bolšić (1724-1787) značajni je hrvatski književnik, učitelj, glazbeni teoretičar i matematičar, te autor prve hrvatske računice "Arithmetike Horvatszke" iz 1758. godine. Značaj ove knjige leži u činjenici da je to prvo djelo matematičkog sadržaja napisano i tiskano na hrvatskom jeziku, te su se njime desetljećima služile široke narodne mase. U ovom radu istražili su se metodički elementi uočeni u knjizi, a koji su dali doprinos kasnijem razvoju matematičkog obrazovanja. Posebno su proučeni odabir, opseg i redoslijed matematičkih sadržaja, njihovo metodičko oblikovanje, teleološko određivanje matematičkog obrazovanja, primjenjivana metodička načela, te odabir i postupci rješavanja primjera. Analizom sadržaja proučena su sva 194 matematička primjera u knjizi i to kroz odabranih 11 kategorija dobivenih preliminarnom analizom. Na osnovu provedenog istraživanja, došlo se do zaključka da je Bolšić u knjizi "Arithmetika Horvatszka" pokazao izuzetnu pedagoško metodičku zrelost, te da je postavio mnoge standarde za razvijanje metodike nastave matematike i za širenje matematičkog obrazovanja.

The main content of the thesis is the analysis of elective mathematics lessons including examples of the tasks. This work could be useful mainly to teachers of primary elective mathematics. It is divided into two parts. The first one deals with the main theory. The second part is based on the analysis of particular lessons and tasks. The work also contains a set of tasks suitable for primary pupils.