Moore, J.: Oxford Academic Vocabulary Practice. OUP, 2017.
Kolaříková, Z., Petruňová, H., Timková, R.: Angličtina v akademickom prostredí – cvičebnica. Košice, Vydavateľstvo ŠafárikPress, 2021.
Tomaščíková, S., Rozenfeld, J. Developing Academic English in Speaking and Writing. Vydavateľstvo ŠafárikPress, 2021.
McCarthy, M., O´Dell, F.: Academic Vocabulary in Use. CUP, 2008.
Štepánek, L., J. De Haff a kol.: Academic English-Akademická angličtina. Grada Publishing, a.s., 2011.
Armer, T.: Cambridge English for Scientists. CUP, 2011.
lms.upjs.sk
Completion of e-course English for PhD Students (lms.upjs.sk), consultations (1-3).
Written assignments - Professional/Academic CV, Short Academic Biography.
English, level B2 according to CEFR
Specific aspects of academic and professional English with focus on correct pronunciation, vocabulary development (noun and verb collocations, phrasal verbs, prepositional phrases, word-formation, formal/informal language, etc.), selected aspects of English grammar (prepositions, grammar tenses, passive voice, etc.), academic writing (professional/academic CV, Short Academic Biography).
The development of students´ language skills - reading, writing, listening, speaking; improvement of their linguistic competence - students acquire knowledge of selected phonological, lexical and syntactic aspects; development of pragmatic competence - students acquire skills for effective and purposeful communication, with focus on Academic English and English for specific/professional purposes, level B2.
Moore, J.: Oxford Academic Vocabulary Practice. OUP, 2017.
Kolaříková, Z., Petruňová, H., Timková, R.: Angličtina v akademickom prostredí (cvičebnica). UPJŠ Košice, 2021.
Tomaščíková, S., Rozenfeld, J. Developing Academic English in Speaking and Writing. Vydavateľstvo ŠafárikPress, 2021.
McCarthy, M., O´Dell, F.: Academic Vocabulary in Use. CUP, 2008.
Štepánek, L., J. De Haff a kol.: Academic English-Akademická angličtina. Grada Publishing, a.s., 2011.
Armer, T.: Cambridge English for Scientists. CUP, 2011.
Test, oral exam in accordance with the exam requirements (available at the web-site of the LTC and in MS TEAMS)
B2 level according to CEFR
Academic communication (self-presentation, presenting at scientific meetings and conferences). Specific aspects of academic and professional English with focus on vocabulary development (formality, academic word-list), English grammar (passive voice, nominalisatio), language functions (expressing opinion, cause/effect, presenting arguments, giving examples, describing graphs/charts/schemes, etc.). Cross-language interference.
The development of students´ language skills - reading, writing, listening, speaking, improvement of their linguistic competence - students acquire knowledge of selected phonological, lexical and syntactic aspects, development of pragmatic competence - students can efectively use the language for a given purpose, with focus on Academic English and English for specific/professional purposes, level B2.
1. G. Birkhoff, S. MacLane : Prehľad modernej algebry, Alfa, Bratislava 1979.
2. J. J. Rotman: Advanced Modern Algebra, Amer. Math. Soc., 2010.
3. S. Roman: Lattices and Ordered Sets, Springer 2008.
passing the exam
Slovak or English
Groups, rings, fields of algebraic numbers, Galois groups, Boolean algebras and lattices.
The students will gain a deeper knowledge about the most important algebraic stuctures (group,ring, field, Boolean algebra) and their applications in various disciplines of mathematics as well as outside mathematics.
Citation in a national scientific journal
Obtaining a citation demonstrates broad and very well-founded scientific knowledge in the researched field, based on the ability to formulate research questions, to reflect on a scientific problem in such a way that generates new knowledge. At the same time, a citation in an indexed source demonstrates the competence to communicate new knowledge, which is a significant contribution to scientific knowledge, at the highest expert level.
Obtained citation registered in SCI or Scopus.
Obtaining a citation demonstrates broad and very well-founded scientific knowledge in the researched field, based on the ability to formulate research questions, to reflect on a scientific problem in such a way that generates new knowledge. At the same time, a citation in an indexed source demonstrates the competence to communicate new knowledge, which is a significant contribution to scientific knowledge, at the highest expert level.
Completion of a certified professional/training course.
The PhD student acquires up-to-date scientific knowledge, develops the capabilities of scientific work and familiarizes himself with the methodologies of making scientific knowledge available. He confronts his own knowledge and skills with other course participants, develops the abilities of peer discussion in the given scientific field.
Obtained citation registered in SCI or Scopus.
Obtaining a citation demonstrates broad and very well-founded scientific knowledge in the researched field, based on the ability to formulate research questions, to reflect on a scientific problem in such a way that generates new knowledge. At the same time, a citation in an indexed source demonstrates the competence to communicate new knowledge, which is a significant contribution to scientific knowledge, at the highest expert level.
Obtained citation in a foreign scientific journal.
Obtaining a citation demonstrates broad and very well-founded scientific knowledge in the researched field, based on the ability to formulate research questions, to reflect on a scientific problem in such a way that generates new knowledge. At the same time, a citation in an indexed source demonstrates the competence to communicate new knowledge, which is a significant contribution to scientific knowledge, at the highest expert level
1. J. Matoušek, J. Nešetřil: Invitation to Discrete Mathematics, Univerzita Karlova - Nakladatelství Karolinum, Praha 2000.
2. E. Scheinerman: Mathematics - a Discrete Introduction. Brooks/Cale, Pacific Grove, USA, 2002.
In the covered areas of discrete mathematics the ability to formulate definitions and statements, to present proofs of statements, to explain individual steps in proofs, to find alternative proofs of statements using the means and approaches of school mathematics, to know the relationships between the individual results and to solve selected problems related to given topics is required.
The evaluation is based on the results of the oral exam.
Slovak or English
Combinatorial counting. Basic combinatorial principles and methods. Proofs in discrete mathematics. Discrete probability. An introduction to the theory of graphs. Basic cryptography
Mastered basic methods and principles of discrete mathematics.
Antoch, J., Čihák, M., Prachař, J.: Použití programu MUPAD ve středoškolské výuce, Pravděpodobnost a statistika na střední škole, Univerzita Karlova v Praze, Matfyzpress, 2005.
Balacheff, N., Kaput, J., J.: Computer-based learning environments in Mathematics. In: International Handbook of Mathematics Education (editor: Bishop, A., J. et al.), Kluwer Academic Publishers, London, 1996, s. 469-501.
Dubinsky, E., Tall, D.: Advanced mathematical thinking and the computer. In: Advanced mathematical thinking (editor Tall, D.), Kluwer Academic Publishers, 2002, s. 231-243.
Fulier, J., Ďuriš, V., Frantová, P.: CAS (systémy počítačovej algebry) vo vyučovaní matematiky, Univerzita Konštantína Filozofa v Nitre, 2007.
Oldknow, A., Taylor, R., Tetlow, L.: Teaching Mathematics Using ICT, Bloomsbury Publishing, 2010.
Vaníček, J.: Počítačové kognitivní technologie ve výuce geometrie, Univerzita Karlova v Praze, 2009.
Orientation in basic concepts related to computer-assisted education. Demonstrating an overview of the possibilities of using different types of modern digital technologies to support active learning of mathematics. Ability to effectively use different types of digital technologies depending on the types of solved mathematical problems. Ability to assess the resources for mathematics education available on the Internet in terms of the extent and way of their use in teaching mathematics.
Evaluation:
Elaboration of a seminar work on a topic agreed with the teacher. Final exam.
Slovak or English
Characteristics of possibilities of use, benefits and negative aspects of digital technologies in mathematics education.
Support of digital technologies in the application of innovative approaches to the teaching mathematics: constructivist approaches to learning, guided research, research approaches to teaching, peer instruction method, project method.
Development of selected digital competencies in the teaching of mathematics.
Data representation and mathematical modeling in a digital environment. Modeling activities in teaching mathematics.
Investigation of properties of shapes, geometric relations and functional dependencies using dynamic geometric systems.
Didactic aspects of e-learning. Strategies to support active learning in e-learning. Implementing feedback and providing contingent tutoring in digital learning materials.
Interactive mathematical documents created using CAS.
The student is able to characterize the basic possibilities and procedures of work in various types of modern digital technologies usable to support mathematical education. The student is able to give suitable examples from school mathematics, in solving which it is possible to effectively use specific digital technologies. The student is able to design a procedure for the use of digital technologies to support the various stages of the learning process and the application of inquiry approaches in the teaching of specific mathematical topics. The student is able to use critical thinking in planning the teaching of mathematics and creating a stimulating learning environment with a high degree of dynamism and interactivity, and in assessing the possibility of using educational resources available on the Internet.
Obtaining the required number of credits in the prescribed composition according to the UPJŠ study regulations, preparation and defense of the thesis, successfully completed dissertation examination.
The PhD student demonstrated the prerequisites for successful continuation of the study by fulfilling the conditions prescribed by the study regulations for the study and scientific part of the doctoral study related to the topic of the dissertation.
Slovak and English
Slovak and English
B. Barton: The Language of Mathematics. Telling Mathematical Tales, Springer, 2008.
J. Barwise, J. Etchemendy: Language, Proof and Logic, Seven Bridges Press, 1999.
W. W. Esty: The Language of Mathematics, Montana State University, USA, 2008.
C. Lee: Language for Learning Mathematics. Assessment for Learnig in Practice, Open University Press, 2006.
T. Sundstrom: Mathematical Reasoning, Pearson Education, 2007.
exam
The role and use of variables in the structure of mathematical expressions. Order of operations. Reading of mathematical text. Reading and writing arithmetic procedures in algebraic expressions. The key concept of set and its substance. The concept of functional dependency. The theory of solving equations and inequalities. Language of mathematical logic. Generalisation in mathematics.
The goal of the Language of Mathematics is for students to assimilate the basic concepts, reasoning patterns, and language skills that are fundamental to Mathematics.
Final thesis consultant.
By consulting the final thesis, the PhD student demonstrates broad and scientifically based knowledge in the field of study, as well as knowledge of a wide range of methods and approaches. Demonstrates the ability to critically assess a professional problem and its proposed solution, as well as to evaluate it and possibly propose another solution. He applies knowledge and skills from the field of pedagogical sciences to his own field.
A. M. Bruckner, J. B. Bruckner, B. S. Thomson: Real Analysis, Prentice Hall, 1997.
T. Neubrunn, B. Riečan: Miera a integrál, Veda, Bratislava, 1981.
B. Riečan, T. Neubrunn: Teória miery, Veda, Bratislava, 1992.
Т. А. Леонтьева, В. С. Панферов, В. С. Серов: Задачи по теории функций действительного переменного, Издательство Московского университета, Москва, 1997.
exam
Slovak or English
Rings sigma-rings. Measure. Outer measure. Lebesgue measure. Measurable sets. Measurable
functions. Legesgue integral. Lebesgue integral versus Riemann integral. Calculations of Lebesgue
integrals. Applications.
Understanding of the basic rigorous ideas of Mathematical Analysis.
A. H. Schoenfeld: Cognitive science and mathematics education, Routledge, 1987
Thomas P. Carpenter, John A. Dossey, Julie L. Koehler: Classics in mathematics education research, NCTM, 2004
W.W. Esty: The Language of Mathematics, 2008
F. Klein: Elementary Mathematics from an Advanced Standpoint, 1945
It is based on the results of written and oral exam.
Slovak
Language of Mathematics; syntax and semantics; sets, relations, rational and irrational numbers, equations and inequations in reals; elementary functions
Obtain knowledge about the structure of elementary mathematics with respect to advanced mathematics; the development of mathematical skills of prospective teachers.
Publication accepted in a national journal as author/co-author.
By publishing in a national journal as an author/co-author, the PhD student demonstrates a high level of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
Active participation in the home conference.
By actively participating in the national scientific conference, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology in his scientific field. He demonstrates the ability to reflect on a specific scientific problem by using the latest approaches and applying them critically. Demonstrates competence in using existing theories and concepts in an innovative way, as well as generating new original scientific knowledge and communicating research results to a wider audience using adequate means and through the Slovak language.
Active participation in a national conference with foreign participation.
By actively participating in a scientific conference, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology in his scientific field. He demonstrates the ability to reflect on a specific scientific problem by using the latest approaches and applying them critically. Demonstrates competence to use existing theories and concepts in an innovative way, as well as generate new original scientific knowledge and communicate research results to a wider audience by adequate means and through Slovak or a foreign language.
A publication published in a non-reviewed foreign or national journal as an author/co-author.
By publishing in a non-reviewed foreign or national journal as an author/co-author, the PhD student demonstrates the ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The phD student demonstrates the ability to finalize his own thoughts in a written speech.
Work in the organizing committee of the conference
By working in the organizing committee of the conference, the PhD student demonstrates the abilities and competences to organize a scientific or professional event independently or in a team, to manage the implementation in terms of time and content, to communicate effectively verbally and in writing using various technical means as needed, including in a foreign language at a professional level with various types of people, if necessary, correctly recommend solutions or make independent decisions.
Direct teaching activity 1 semester hour
Through pedagogical activity, the PhD student demonstrates the ability to transfer and integrate knowledge from his own field of study into education. He is able to select and apply the right techniques and strategies of study group management, higher education and evaluation of learning outcomes. He is capable of designing and implementing part of the educational process in accordance with current trends in higher education and the requirements placed on the level of communication and digital competencies.
Direct teaching activity 2 semester hours
Through pedagogical activity, the PhD student demonstrates the ability to transfer and integrate knowledge from his own field of study into education. He is able to select and apply the right techniques and strategies of study group management, higher education and evaluation of learning outcomes. He is capable of designing and implementing part of the educational process in accordance with current trends in higher education and the requirements placed on the level of communication and digital competencies.
Direct teaching activity 3 semester hours
Through pedagogical activity, the PhD student demonstrates the ability to transfer and integrate knowledge from his own field of study into education. He is able to select and apply the right techniques and strategies of study group management, higher education and evaluation of learning outcomes. He is capable of designing and implementing part of the educational process in accordance with current trends in higher education and the requirements placed on the level of communication and digital competencies.
Direct teaching activity 4 semester hours
Through pedagogical activity, the PhD student demonstrates the ability to transfer and integrate knowledge from his own field of study into education. He is able to select and apply the right techniques and strategies of study group management, higher education and evaluation of learning outcomes. He is capable of designing and implementing part of the educational process in accordance with current trends in higher education and the requirements placed on the level of communication and digital competencies.
Active involvement in the popularization of science.
Demonstrated ability to present science to the lay public, use interactive methods of scientific communication, identify the target group and adapt the communication language to the level of professional knowledge. A PhD student is able to arouse interest and motivate specific target groups in the field of his scientific work, but also in the wider context of science.
A publication published in a peer-reviewed foreign or national proceedings as an author/co-author.
By publishing in a peer-reviewed foreign or national journal as an author/co-author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
Presentation at the seminar
By actively participating in the seminar, the PhD student demonstrates the ability to identify, evaluate, and apply correct scientific methods or research methodology in his field of study. He demonstrates the ability to reflect on a specific scientific problem by using the latest approaches and applying them critically. Demonstrates competence in using existing theories and concepts in an innovative way, as well as generating new original scientific knowledge and communicating research results by adequate means and through Slovak or a foreign language.
Publication accepted in a foreign journal as an author/co-author.
By publishing in a foreign journal as an author/co-author, the PhD student demonstrates a high level of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
Active participation in an international conference abroad.
By actively participating in an international scientific conference abroad, the phD student demonstrates a high level of ability to identify, evaluate, and apply correct scientific methods or research methodology in his scientific field. He demonstrates the ability to reflect on a specific scientific problem by using the latest approaches and applying them critically. Demonstrates competence to use existing theories and concepts in an innovative way, as well as generate new original scientific knowledge and communicate research results to a wider audience by adequate means and through a foreign language.
Scientific work after being sent to the editorial office as an author/co-author.
By sending a manuscript to the editors of a scientific journal as an author/co-author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to formulate his own ideas in a structured form.
Active participation in an international conference abroad.
By actively participating in an international scientific conference abroad, the phD student demonstrates a high level of ability to identify, evaluate, and apply correct scientific methods or research methodology in his scientific field. He demonstrates the ability to reflect on a specific scientific problem by using the latest approaches and applying them critically. Demonstrates competence to use existing theories and concepts in an innovative way, as well as generate new original scientific knowledge and communicate research results to a wider audience by adequate means and through a foreign language.
Publication accepted in a journal of category Q1 as co-author.
By publishing in a journal of category Q1 as a co-author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
Publication accepted in a journal of category Q1 with author's share at least 25%.
By publishing in a journal of category Q1 as the first or corresponding author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas. A significant author's share will have a substantial impact on the number and quality of the publication results, on the implementation of software support for research, and on the formal processing of the publication itself in terms of content and graphics.
Publication accepted in a journal of category Q2 as co-author.
By publishing in a journal of category Q2 as a co-author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
Publication accepted in a journal of category Q2 with author's share at least 25%.
By publishing in a journal of category Q2 as the first or corresponding author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas. A significant author's share will have a substantial impact on the number and quality of the publication results, on the implementation of software support for research, and on the formal processing of the publication itself in terms of content and graphics.
Publication accepted in a journal of category Q3 as co-author.
By publishing in a journal of category Q3 as a co-author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
Publication accepted in a journal of category Q3 with author's share at least 25%.
By publishing in a journal of category Q3 as the first or corresponding author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas. A significant author's share will have a substantial impact on the number and quality of the publication results, on the implementation of software support for research, and on the formal processing of the publication itself in terms of content and graphics.
Publication accepted in a journal of category Q4 as co-author.
identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas.
Publication accepted in a journal of category Q4 with author's share at least 25%.
By publishing in a journal of category Q4 as the first or corresponding author, the PhD student demonstrates a high degree of ability to identify, evaluate, and apply correct scientific methods or research methodology. He demonstrates the ability to reflect on a scientific problem by using the latest approaches and applying them critically. He demonstrates the competence to use existing theories and concepts in an innovative way, as well as to generate new original scientific knowledge, which he can publish according to the highest qualitative and ethical standards of the field. The PhD student demonstrates the ability to critically evaluate and respond to reviewers' suggestions, to finalize his own ideas. A significant author's share will have a substantial impact on the number and quality of the publication results, on the implementation of software support for research, and on the formal processing of the publication itself in terms of content and graphics.
Co-investigator of the domestic project
The PhD student demonstrates the ability to participate in teamwork, to bring his own contribution to the solution of the project objective and to take responsibility for the assigned tasks. By solving the domestic project, he acquires the ability to implement the project intention according to the established procedure, to follow the project schedule, to coordinate his own activities with colleagues, to participate in the creation of outputs. The PhD student gains valuable experience from the practical course of the grant project.
1. Utts, J.M., Heckard, R.F. (2021), Mind od Statistics, 6th ed., Thomson Brooks/Cole
2. Peck, R., Short, T. (2019), Statistics: Learning from Data, 2nd ed., Cengage Learning
3. Box, G.E.P., Hunter J.S., Hunter W.G. (2005), Statistics for Experimenters: Design, Innovation, and Discovery, 2nd ed., Wiley-Interscience
4. Fox, J., (2017), Using the R Commander, Taylor&Francis
5. Gavora, P. (2001) Úvod do pedagogického výskumu, UK Bratislava (in Slovak)
6. Burke Johnson, R., Christensen, L.B. (2019), Educational Research: Quantitative, Qualitative, and Mixed Approaches, 7th ed., Sage Publications, Inc
Individual project work. Exam.
Slovak
1. Basic concepts and principles of statistical methods for didactical experiment design and data collection.
2. Data visualization, data reduction in an MS Excel spreadsheet and statistical software R.
3. Basic principles of statistical inference. Estimation Theory. (2 weeks)
4. Regression and correlation analysis. Relationships between quantitative variables.
5. Goodness-of-Fit tests and contingency tables. Relationships between qualitative variables.
6. Testing hypotheses. Parametric testing methods. (2 weeks)
7. Analysis of variance.
8. Nonparametric methods of testing.
9. Quantitative oriented research, research methods - observation, scaling, questionnaire, interview.
10. Validity and reliability of research instruments.
The student should know and be able to apply basic concepts and principles of statistical methods using a PC and software R in the design of didactical experiment, in obtaining and processing the results with the subsequent statistical interpretation.
Membership in the research team of an international project.
Active involvement by solving a specific task within a team of international project solvers. The PhD student demonstrates the ability to work in a team, take responsibility for the assigned task, adhere to the time schedule and fulfill the project outputs. The PhD student gains personal experience from the implementation of an international project, participation in its key stages, creation of measurable outputs, grant funding of science.
Co-investigator of the applied research project
The PhD student demonstrates the ability to participate in teamwork, to bring his own contribution to the solution of the project objective of applied research and to take responsibility for assigned tasks. By solving an applied research project, he acquires the ability to implement the project objective according to the established procedure, to follow the project schedule, to coordinate his own activities with colleagues, to participate in the creation of applied research outputs. The PhD student gains valuable experience from the practical course of a grant project with a focus on applied research
Co-worker of project supported by internal grant schemes (VVGS)
The PhD student demonstrates the ability to participate in teamwork, to bring his own contribution to the solution of the project objective within the internal grant system at UPJŠ. By solving the internal VVGS grant, he acquires the ability to implement the project plan according to the established procedure, adhere to the project schedule, coordinate his own activities with colleagues, and participate in the creation of outputs. The PhD student gains valuable experience from the practical course of the grant project.
A created software product stored in a public repository.
The PhD student demonstrates the ability to create a stand-alone or supporting software product in a form that can be used by other researchers.
M.Hejný a kol.: Teória vyučovania matematiky (Teaching mathematics theory), SPN Blava 1989,
J.Kopka: Hrozny problému ve školské matematice (Clusters of problems in school mathematics. Ústí nad Labem,1999
R.Fischer,G.Malle: Človek a matematika (Human and mathematics), SPN Bratislava 1992
A. Plocki: Pravdepodobnosť okolo nás (Probability about us), KU Ružomberok, 2004
A. H. Schoenfeld: Cognitive science and mathematics education, Routledge, 1987
R. Švařiček, K. Šeďová: Kvalitatívni výzkum v Pedagogických vědách (Quantitative research in pedagogical sciences), Portál Praha, 2007
Thomas P. Carpenter, John A. Dossey, Julie L. Koehler: Classics in mathematics education research, NCTM, 2004
Examination
Slovak
Creating definitions in mathematics and teaching mathematics - 2 w. Structure, diagnostics and development of key mathematical competences -2. Phylogeny and ontogeny of teaching topics according to the State Education Programme - equations and inequalities, infinitesimal calculus, combinatorics, probability and statistics - 2. Planimetry, stereometry, analytical geometry. Assessment in mathematics, standards development and didactic tests - 2. Educational Research in Mathematics Education, comparison of quantitative and qualitative research - 3.
Obtain knowledge about the structure of the process of knowledge in mathematics, the development of mathematical skills, acquire the methodology of quantitative and qualitative research in Mathematics Education.
Ball, D. L., Thames, M. H., & Phelps, G. Content knowledge for teaching: what makes it special? Journal of Teacher Education, 59, 389-407, 2008
Bishop, A.J. et al. (eds.), International Handbook of Mathematics Education 1/2, Kluwer Academic Publishers,1996
Bishop, A.J. (ed.). Second International Handbook of Mathematics Education 1/2, Kluwer Academic Publishers, 2003
Brousseau, Guy, Novotná, Jarmila a Sarrazy, Bernard. Didactic contract. In: Lerman, Stephen (ed.), Encyclopedia of Mathematics Education, 153-159, Springer, 2014.
Carrillo, J., Climent, N., Montes, M., Contreras, L., Flores-Medrano, E., Escudero-Ávila, D. . . . Muñoz-Catalán, M. C. et al. The mathematics teacher’s specialised knowledge (MTSK) model. Research in Mathematics Education, 20, 236–253, 2018
Hejný, M. a kol. Teórie vyučovania matematiky 2. Bratislava: SPN, 1991
Hejný, M. a Kuřina, F. Dítě škola matematika. Praha: Portál, 2009
Hejný, M.; Novotná, J.; Stehlíková, N. Dvacet pět kapitol z didaktiky matematiky. Praha: PedF UK, 2004
Kaiser, G., Presmeg, N.: Compendium for Early Career Researchers in Mathematics Education, Springer, 2019
Miles, M. B., Huberman, A. M., Saldana, J.: Qualitative Data Analysis. SAGE Publications, Inc., 2014
Polya, G. How to solve it. Princeton University Press, 1945
Sriraman, B. English, L.: Theories of Mathematics Education, Springer, 2010
Strauss, A., Corbinová, J. Základy kvalitativního výzkumu. Postupy a techniky zakotvené teorie, Brno: 1999
Vondrová N., Rendl, M. a kol. Kritická místa matematiky základní školy v řešení žáků. Praha: Karolinum, 2016
Seminar work and its presentation at the seminar – development of a proposal for the methodology of self research and literature review with the aim to place the research in the national and global context.
Slovak
The course deals with various research methods used in didactic of mathematics, important topics in mathematics teacher education, as teaching and learning big ideas in mathematics, models of mathematics teacher knowledge (MKT – Mathematics Teacher Knowledge, MTSK – Mathematics Teacher Specialized Knowledge) and recognized theories of mathematics teaching and learning such as Realistic mathematics education, Theory of didactical situations in mathematics, Van Hiele's theory of geometric thinking, etc. The aim of the course is to deepen knowledge and acquire research skills in the didactics of mathematics.
The graduate of the course will compile literature review, which is related to the topic of the dissertation. This research will help him/her to orient himself/herself
- in the current research in didactics of mathematics on national and international level in order to be able to include self research to these contexts.
- in the different research methods used in the didactics of mathematics, so that he/she will be able to choose methods for his/her own research appropriately.
Elaboration of reviewer report
The PhD student demonstrates broad and scientifically based knowledge in the field of study, as well as knowledge of a wide range of methods and approaches. Demonstrates the ability to critically assess a professional problem and its proposed solution, as well as to evaluate it and possibly recommend another solution. He applies knowledge and skills from the field of pedagogical sciences to his own field.
Kopka. J.: Zkoumání ve školské matematice, Ružomberok, 2006.
Hejný, M., Novotná, J., Stehlíková, N.: Dvacet pět kapitol z didaktiky matematiky, Univerzita Karlova v Praze, 2004.
De Villiers, M., D.: Rethinking proof with The Geometer's Sketchpad. Key Curriculum
Press, 2003.
Held, Ľ. a kol.: Výskumne ladená koncepcia prírodovedného vzdelávania. Pedagogická fakulta Trnavskej univerzity v Trnave, 2011.
Characterization of research approach to mathematics teaching. Gain an overview of ways to implement a research approach to the teaching of mathematics and methods of developing students' skills for scientific work. Ability to plan the application of a research approach to the teaching of specific mathematical topics and to describe the preparation of appropriate teaching aids for teaching.
Assessment method: exam.
Slovak or English
The concept of the IBSE method and the possibilities of its implementation in mathematics education.
Case studies of the use of research methods in teaching specific mathematical topics.
Structure of competencies for scientific work from the perspective of the student / pupil.
Possibilities of using digital technologies in the application of research approaches to the teaching of mathematics.
Acquisition of basic principles and procedures in applying the research approach to mathematics education. Gain practical experience with the creation of methodological and teaching materials for teaching mathematics at primary and secondary schools.
Supervision of Student's Scientific Activity
By guiding a student within the SOČ or ŠVOČ, the PhD student demonstrates broad and scientifically based knowledge in the field of study, as well as knowledge of a wide range of methods and approaches. Demonstrates the ability to critically assess a professional problem and its proposed solution, as well as to evaluate it and possibly propose another solution. He applies knowledge and skills from the field of pedagogical sciences to his own field.
Supervisor of the final thesis.
By supervising the final thesis, the PhD student demonstrates broad and scientifically based knowledge in the field of study, as well as knowledge of a wide range of methods and approaches. Demonstrates the ability to critically assess a professional problem and its proposed solution, as well as to evaluate it and possibly propose another solution. He applies knowledge and skills from the field of pedagogical sciences to his own field.
Completion of a foreign study stay lasting at most 30 days.
By completing a shorter study stay, the PhD student demonstrates the ability to reflect on research problems and work critically with sources at an expert level and in an interdisciplinary context, while being able to generate new knowledge. He is able to actively communicate at an expert level in more than one language. He acts as a responsible independent scientist, works independently and in a group with the aim of pushing the boundaries of knowledge and transferring them to other areas of research, to practice and to the wider public. He can competently argue and explain his ideas.
Completion of a foreign study stay lasting more than 30 days.
By completing the study stay, the PhD student demonstrates the ability to reflect on research problems and work critically with sources at an expert level and in an interdisciplinary context, while being able to generate new knowledge. He is able to actively communicate at an expert level in more than one language. He acts as a responsible independent scientist, works independently and in a group with the aim of pushing the boundaries of knowledge and transferring them to other areas of research, to practice and to the wider public. He can competently argue and explain his ideas
Principal investigator of an internal grant (VVGS)
The PhD student demonstrates the ability to process a successful application for his own research problem within the internal grant system at UPJŠ. Acquires skills with the design of research stages, their time schedule, measurable outputs and adequate distribution of funds. The very solution of the internal VVGS grant acquires the ability to implement the project intention according to the established procedure, to be responsible for achieving the set outputs. As a responsible researcher, the PhD student acquires competencies in project management, its administration, and presentation of results.
Proceedings of the Spring School of Doctoral Students.
Active participation in the Spring School of PhD students of UPJŠ.
1. Interdisciplinary lectures from the fields of medicine, natural sciences, law, public affairs, humanities. Lecturers - top foreign or national experts from the mentioned fields.
2. Scientific lectures in sections created within related disciplines. Lecturers - top experts from UPJŠ from the mentioned fields.
3. Scientific contributions of PhD students in sections of related fields.
4. Panel discussions on the issue of PhD studies and current trends in the development of scientific disciplines at UPJŠ.
By actively participating in the Spring School of PhD Students of UPJŠ, the PhD student demonstrates a high level of ability to process the issues of his dissertation for a multidisciplinary audience with an emphasis on clarifying the motivation, scientific problem, processing methodology and own contribution to the solution of the selected topic. The PhD student demonstrates the ability to professionally discuss various research topics, present his own positions and accept a plurality of opinions. Demonstrates the ability to communicate research results to a wider professional audience with adequate means and through the Slovak language.
Beránek, J. (2023). Moderní pedagogické metody a přístupy. Praha: Portál.
Fiala, M. (2023). Didaktika a metodika v současné škole. Praha: Grada Publishing.
Kováč, M. (2023). Vzdelávanie v 21. storočí: Inovatívne prístupy a metódy. Nitra: Vydavateľstvo UKF v Nitre.
Koudelka, J. (2023). Moderní didaktika a její aplikace. Praha: Karolinum.
Křížová, M., & Šebová, P. (2023). Vzdělávání učitelů: Teoretické a praktické přístupy. Praha: Triton.
Kučerová, M. (2023). Vzdělávání učitelů a profesionální rozvoj. Praha: Triton.
Mocová, M., & Lázňovská, M. (2023). Pedagogika a jej aplikácie v praxi. Bratislava: Vydavateľstvo Spolku slovenských pedagogických pracovníkov.
Novák, J., & Pol, M. (2024). Pedagogické výzkumy a inovace ve vzdělávání. Praha: Portál.
Sikora, J. (2022). Didaktika a metodika vzdelávania: Nové výzvy a trendy. Bratislava: Vydavateľstvo Univerzity Komenského v Bratislave.
Škoda, J. (2022). Efektivní výuka: Praktické strategie a metody. Praha: Grada Publishing.
Švec, J. (2023). Didaktika a školní politika: Teorie a praxe. Praha: Grada Publishing.
Vojtová, K. (2024). Diferenciace a inkluze ve vzdělávání. Praha: Wolters Kluwer.
1. Development of a teaching diary—100%
2. Compulsory active participation and attendance in accordance with the Study Regulations.
slovak
The personality of a university teacher. Teaching styles. Student in university education. Student learning styles. Possibilities of adapting teaching styles and student learning styles. University teacher–student interaction and communication in the teaching process. Pedagogical competencies of a university teacher. Didactic analysis of the curriculum; teaching materials and textbooks. Forms of university teaching. Methods of university teaching. Verification methods and student assessment. Creation of a didactic test. Designing university teaching process. University teacher self-reflection.
After completing the course, the student will acquire knowledge, skills, and competencies, i.e., will be able to:
Knowledge
Define and apply basic didactic principles, methods, forms, and tools in the teaching process of university-level professional subjects. Identify and specify educational procedures of a university teacher aimed at effective teaching management, pedagogical diagnostics, and assessment of learning outcomes. Recognize different approaches to pedagogical evaluation and their impact on improving the quality of the educational process at the university level.
Skills
Implement effective educational methods and techniques into the teaching of professional subjects, tailored to the needs of university students. Conduct pedagogical diagnostics, assess students' progress, and apply appropriate evaluation methods to improve learning outcomes. Analyze and reflect on one's own teaching process, identify areas for improvement, and enhance the teaching of professional subjects, including the rationalization of the time and content structure of teaching. Present specific proposals for improving the teaching process, including the use of new technologies and innovative pedagogical approaches.
Competencies
Confidently and effectively manage the teaching of university subjects, applying educational competencies that consider the specifics of higher education. Critically reflect on one's own pedagogical practice and the learning outcomes of students to improve teaching methods and achieve a higher quality of the educational process. Apply innovative solutions to streamline and optimize the teaching process, aiming to increase the engagement and success of university students.
Alexitch, L. R. (2005). Applying social psychology to education. Social Psychology.–Еd.: Schneider F., Gruman J., Coutts L.–Sage Publications, Inc, 205-228.
Fry, H., Ketteridge, S., & Marshall, S. (2008). A handbook for teaching and learning in higher education: Enhancing academic practice. Routledge.
Mareš, J.: Pedagogická psychologie. Portál, 2013.
Kniha psychologie. Universum, 2014
Čáp, J., Mareš, J.: Psychologie pro učitele. Praha: Portál 2007.
Vágnerová, M.: Školní poradenská psychológie pro pedagogy. Praha: Karolínum 2005.
Cuevas, J. A., Childers, G., & Dawson, B. L. (2023). A rationale for promoting cognitive science in teacher education: Deconstructing prevailing learning myths and advancing research-based practices. Trends in neuroscience and education, 100209.
Case study, micro-output, its analysis
Current modifications of the course are listed in the electronic bulletin board of the course.
slovak
The content of the course is based on selected psychological knowledge of cognitive psychology, psychology of emotions and motivation, personality psychology, developmental, social, educational psychology and health psychology. Teaching is realized by a combination of lectures with interactive, experiential methods, discussion, open communication with mutual respect, support of independence, activity and motivation of students. Syllabus: University teacher and his work in the teaching process with a focus on: teachers in relation to themselves (cognitive, personal, social and competencies in the use of methods), in relation to students and as part of the teacher-student relationship on the basis of selected areas of cognitive psychology, psychology of emotions and motivation, developmental psychology, social psychology, educational psychology and health psychology with application to the university environment
After completing the course, students will gain knowledge that allows them to understand, summarize and explain selected psychological knowledge from cognitive psychology, emotion and motivation psychology, personality psychology, developmental, social, educational psychology and health psychology. They will acquire skills to apply the above psychological knowledge necessary for the professional, competent performance of university teaching practice of doctoral students
to create and implement the teaching of a professional topic with applied psychological knowledge
and develop the competences to create and implement teaching of a professional topic with the application of psychological knowledge, as well as to evaluate their performance and the performance of their classmates in the form of constructive feedback.