Modern trends in the teaching of mathematics *

There are no prerequisites.

The course explores contemporary approaches to teaching mathematics made possible by digital technologies. Emphasis is placed on how such technologies enable alternative teaching models, such as the flipped classroom, problem-based learning, and the use of freely available instructional materials. We discuss how mathematics instruction can, beyond transmitting core knowledge, also support broader goals such as fostering independent learning, critical thinking, and situating mathematical content in wider contexts—social, scientific, or cultural.

The second part of the course focuses on the practical use of digital technologies in teaching, including real-time knowledge checks, online classrooms, video and animation, and interactive materials. Modern developments such as artificial intelligence and participation in online learning communities are also considered. A key objective throughout is to develop the ability to critically assess the use of technology in educational settings, rather than simply applying it uncritically or for its own sake.

1. A. Engel: Exploring mathematics with your computer, Washington : The Mathematical Association of America, cop. 1993.
2. A. Orton: Learning Mathematics: Issues, theory and classroom practice, 3rd ed., London : Continuum, 2004.
3. D. L. Ronis: Problem-based learning for math & science : integrating inquiry and the internet, 2nd ed., Thousand Oaks : Corwin Press, cop. 2008.
4. M. Selinger, ed.: Teaching mathematics, London : Routledge; Milton Keynes: The Open University, 1994.

Students develop an understanding of contemporary didactic approaches to teaching mathematics and the opportunities offered by digital technologies. They become capable of thoughtfully designing instruction that encourages active student participation, independent learning, and the placement of mathematical content in a broader context. They gain the ability to critically assess teaching methods and digital tools in terms of pedagogical effectiveness, accessibility, and appropriateness. Students are equipped to use modern technologies as aids in achieving diverse educational goals and to adapt instruction responsively to students’ needs and teaching circumstances.

The student understands contemporary didactic approaches and the role of digital technology in mathematics education. They are able to design lessons with active learning, critically assess digital tools in pedagogical contexts, integrate freely available learning resources, and adapt their practice to student needs and teaching conditions.

Lectures, exercise sessions, project work, consultations

Students do their exercise assignments and a project with its presentation.
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Andrej Bauer:
• LUKŠIČ, Primož, HORVAT, Boris, BAUER, Andrej, PISANSKI, Tomaž. Practical E-Learning for the Faculty of Mathematics and Physics at the University of Ljubljana. Interdisciplinary journal of knowledge & learning objects. 2007, vol. 3, str. 73-83. [COBISS-SI-ID 14269529]
• BAUER, Andrej. Five stages of accepting constructive mathematics. Bulletin (new series) of the American Mathematical Society. 2017, vol. 54, no. 3, str. 481-498. [COBISS-SI-ID 18066265]
• MASSRI, Besher M., PITA COSTA, João, GROBELNIK, Marko, BRANK, Janez, STOPAR, Luka, BAUER, Andrej. A global COVID-19 observatory, monitoring the pandemics through text mining and visualization. Informatica : an international journal of computing and informatics. [Tiskana izd.]. Mar. 2022, vol. 46, no. 1, str. 49-55. [COBISS-SI-ID 107602179]
• HASELWARTER, Philipp Georg, BAUER, Andrej. Finitary type theories with and without contexts. Journal of automated reasoning. Dec. 2023, vol. 67, iss. 4, article no. 36, 87 str. [COBISS-SI-ID 168229379]

Matija Pretnar:
• LUKŠIČ, Žiga., PRETNAR, Matija. Local algebraic effect theories. Journal of Functional Programming, ISSN - 1469-7653, 2020, vol. 30, E13, 27 strani [COBISS-SI-ID – 53281795]
• FORSTER, Y., KAMMAR, O., LINDLEY, S., PRETNAR, M. (2019). On the expressive power of user-defined effects: Effect handlers, monadic reflection, delimited control. Journal of Functional Programming, ISSN - 1469-7653, 2019, vol. 29, E15, 43 strani [COBISS-SI-ID – 18852441]
• LOKAR, Matija, PRETNAR, Matija. A low overhead automated service for teaching programming. Koli Calling '15: Proceedings of the 15th Koli Calling Conference on Computing Education Research, 2015, 132–136 [COBISS-SI-ID – 17536089]