Objectives and Content of the Mathematics E-learning Course Preparing Students for the School-leaving Exam in Mathematics


Information and communication technologies (ICT) can help solve the problems connected with forming mathematical competencies in students and are used in the process of teaching mathematics. The first part of the paper presents the theoretical background of the subject matter, including: the description of mathematical competencies and their identification at secondary school in Poland, Niemierko’s taxonomy, the programmed learning theory, and the structure of the system of education/learning in the e-learning environment. It expresses the preconditions, expected results, concepts, objectives, hypotheses, and research methods. The practical part describes the structure of “Mathematics with Moodle,” a system for individual learning based on the original authorial MatLearn module, and its graphic representation. A didactic tool is proposed – an e-learning course preparing students for the school-leaving exam in mathematics and improving students’ mathematical competencies. Its aim is to increase the level of competencies, especially those which have not been mastered yet. In order to construct study activities in the course, the programmed learning principles and Niemierko’s taxonomy were used.


information and communication technologies (ICT); key competencies; mathematical competencies; e-learning; Niemierko’s taxonomy; programmed learning; MatLearn module; Mathematics with Moodle

Arendt, H. (2000). Kondycja ludzka. Trans. A. Łagodzka. Warsaw: Fundacja Aletheia.

Bertrand, Y. (1998). Soudobé teorie vzdělávání. Praha: Portál.

Clark, R. C. & Mayer, R. E. (2002). E-learning and the science of instruction: Proven guidelines for consumers and designers of multimedia learning. San Francisco: Pfeiffer.

Czerepniak-Walczak, M. (2010). Badanie w działaniu. In S. Palka (Ed.), Podstawy metodologii badań w pedagogice (pp. 319–337). Gdańsk: Pedagogika GMP.

Escuder, A. & Furner, J. M. (2012). The impact of GeoGebra in math teachers’ professional develop- ment. Accessed 10 February 2017. Retrieved from http://archives.math.utk.edu/ICTCM/VOL23/S113/paper.pdf.

Friedman, T. L. (2005). The world is flat: A brief history of the twenty-first century. Stuttgart: Farrar, Straus and Giroux.

Heba, A. (2010). Information and communication technologies and e-learning in the opinion of teachers and students of secondary schools in Poland. In M. Drlík, J. Kapusta, & P. Švec (Eds.), Proceedings from DIVAI 2010 Distance Learning in Applied Informatics (pp. 209–213). Nitra: Constantine the Philosopher University in Nitra, Faculty of Natural Sciences, Department of Informatics.

Heba, A. (2014). Mathematical competence development using eLearning (Doctoral Dissertation). University of Ostrava, Ostrava.

Heba, A., Kapounová, J., & Smyrnova-Trybulska, E. (2014a). Theoretical conception and some practical results of the development of mathematical competences with use of e-learning. International Journal of Continuing Engineering Education and Lifelong Learning, 24(3/4), 252–268.

Heba, A., Kapounová, J., & Smyrnova-Trybulska, E. (2014a). System for individual learning of mathematics. In K. Kostolányová & J. Kapounová (Eds.), Proceedings from Information and Communication Technology in Education (ICTE-2014) (pp. 76–86). Rožnov pod Radhoštěm: University of Ostrava.

Heba, A., Kapounová, J., & Smyrnova-Trybulska, E. (2014a). Mathematics and eLearning or how to work with students before exam. In J. Kapounová (Ed.), Information and communication technologies in education overview in Visegrad countries (pp. 92–102). Ostrava: University of Ostrava.

Hudecová, D. (2003). Revize Bloomovy taxonomie edukačních cílů. Accessed 11 November 2011. Retrieved from http://www.msmt.cz/Files/DOC/NHRevizeBloomovytaxonomieedukace.doc.

Jang, H. (2016). Identifying 21st century STEM competencies using workplace data. Journal of Science Education and Technology, 25(2), 284–301.

Journal of Laws 2012, item 977. Rozporządzenie Ministra Edukacji Narodowej z dnia 27 sierpnia 2012 r. w sprawie podstawy programowej wychowania przedszkolnego oraz kształcenia ogólne- go w poszczególnych typach szkół. Accessed 11 November 2016. Retrieved from http://isap.sejm. gov.pl/DetailsServlet?id=WDU20120000977.

Juszczyk, S. (2001). Statystyka dla pedagogów. Toruń: Wydawnictwo Adam Marszałek.

Kapounová, J. & Pavlíček, J. (2003). Počítače ve výuce a učení. Ostrava: University of Ostrava.

Kelley, T. R. & Knowles, J. G. (2016). A conceptual framework for integrated STEM education. International Journal of STEM Education, 3(11). Accessed 8 July 2016.
Retrieved from https:// stemeducationjournal.springeropen.com/articles/10.1186/s40594-016-0046-z.

Key competences for lifelong learning. European Reference Framework. (2007). Luxembourg: Office for Official Publications of the European Communities.
Accessed 10 February 2013. Retrieved from http://www.britishcouncil.org/sites/britishcouncil.uk2/files/youth-in-ac.... pdf.

Kim, C. M., Kim, D., Yuan, J. M., Hill, R. B., Doshi, P., & Thai, C. N. (2015). Robotics to promote elementary education pre-service teachers’ STEM engagement, learning, and teaching. Compu- ters & Education, 91, 14–31.

Kirkpatrick, J. & Kirkpatrick K. W. (2009). Kirkpatrickův čtyřúrovňový model: nový pohled po 50 letech 1959-2009. Accessed 05 January 2011. Retrieved from http://www.develor.cz/develorcz_ files/Files/kirkpatrickovy4urovnenovypohledpo50%20letech2.pdf.

Larson M. (2017) Math education is STEM education! Accessed 20 July 2017. Retrieved from https:// www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Matt-... Education-Is-STEM-Education!/.

Niemierko, B. (1999). Pomiar wyników kształcenia. Warszawa: WSIP.

Piaget, J. (1977). The development of thought: Equilibrium of cognitive structures. New York: Viking Press.

Piaget, J. (1985). The equilibrium of cognitive structures. The central problem of intellectual develop- ment. Trans. T. Brown & K. J. Thampy. Chicago: University of Chicago Press.

Recommendation of the European Parliament and of the Council of 18 December 2006 on key competences for lifelong learning. (2006). Accessed 10 February 2013. Retrieved from http:// eurlex.europa.eu/LexUriServ/LexUriServ.do?uri=OJ:L:2006:394:0010:0018:en:PDF.

Schmidt, M. & Fulton, L. (2016). Transforming a traditional inquiry-based science unit into a STEM unit for elementary pre-service teachers: A view from the trenches. Journal of Science Education and Technology, 25(2), 302–315.

Skinner, B. F. (1974). About Behaviourism. London: J. Cape.

Smyrnova-Trybulska, E. (2009). On principles of the design and assessment of courses. In M. Hrubý (Ed.), Distance Learning, Simulation and Communication 2009 (pp. 159–165). Brno: University of Defence.

Smyrnova-Trybulska, E. & Stach, S. (Eds.). (2012). Wykorzystanie LCMS Moodle jako systemu wspomagania nauczania na odległość. Katowice: Wydawnictwo Uniwersytetu Śląskiego, Studio-Noa.

Smyrnova-Trybulska, E., Morze, N., Kommers, P., Zuziak, W., & Gladun, M. (2016). Educational robots in primary school teachers’ and students’ opinion about STEM education for young learners. In P. Kommers, Tomayess Issa, Theodora Issa, E. McKay, & P. Isaías (Eds.), Pro- ceedings of the International Conferences on Internet Technologies & Society 2016 (ITS 2016), Educational Technologies 2016 (ICEduTech 2016), and Sustainability, Technology and Education 2016 (STE 2016) (pp. 197–204). IADIS Press.

Uttal, D. H. & Cohen, C. A. (2012). Spatial thinking and STEM education: When, why, and how? Psychology of Learning and Motivation, 57, 147–181.

Weicker, N. (2005). Lernmodelle in der Übersicht. In Didaktik der Informatik (Lern-modelle). Accessed 8 March 2012. Retrieved from http://www.fmi.unistuttgart.de/fk/lehre/ss04/didaktik/lernmodelle.pdf.

Published : 2017-02-01

HebaA., Smyrnova-TrybulskaE., & KapounováJ. (2017). Objectives and Content of the Mathematics E-learning Course Preparing Students for the School-leaving Exam in Mathematics. International Journal of Research in E-Learning, 3(1), 109-124. Retrieved from https://journals.us.edu.pl/index.php/IJREL/article/view/8398

Agnieszka Heba 

PhD, University of Silesia in Katowice, Faculty of Ethnology and Educational Science in Cieszyn, Poland

Eugenia Smyrnova-Trybulska 
Uniwersytet Śląski  Poland

PhD, hab., associate professor, University of Silesia in Katowice, Faculty of Ethnology and Educational Science in Cieszyn, Poland

Jana Kapounová 

RNDr, PhD, professor, University of Ostrava, the Czech Republic

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

The Copyright Owners of the submitted texts grant the Reader the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution-Share-Alike (CC BY SA). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.

1. License

The University of Silesia Press provides immediate open access to journal’s content under the Creative Commons BY-SA 4.0 license (http://creativecommons.org/licenses/by-sa/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY-SA 4.0 license.

2. Author’s Warranties

The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s.

If the article contains illustrative material (drawings, photos, graphs, maps), the author declares that the said works are of his authorship, they do not infringe the rights of the third party (including personal rights, i.a. the authorization to reproduce physical likeness) and the author holds exclusive proprietary copyrights. The author publishes the above works as part of the article under the licence "Creative Commons Attribution-ShareAlike 4.0 International".

ATTENTION! When the legal situation of the illustrative material has not been determined and the necessary consent has not been granted by the proprietary copyrights holders, the submitted material will not be accepted for editorial process. At the same time the author takes full responsibility for providing false data (this also regards covering the costs incurred by the University of Silesia Press and financial claims of the third party).

3. User Rights

Under the CC BY-SA 4.0 license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor.

4. Co-Authorship

If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.

I hereby declare that in the event of withdrawal of the text from the publishing process or submitting it to another publisher without agreement from the editorial office, I agree to cover all costs incurred by the University of Silesia in connection with my application.