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The present qualitative research is focused on bilingual mathematics education. The research presents findings of a case study of one bilingual Slovak and English mathematics 40-minute lesson within an after school elective bilingual mathematics course running weekly since October, 2015. The lesson took place in March, 2016, and was attended by nine learners aged 12-13, eight boys and one girl. The learners are cases of successive school additive bilingual education. The elective course as a whole is a case of immerse bilingual educational programme. In terms of sociolinguistic settings, the course lessons are cases of bilingual education with external second language. The researcher designed and realized the course lessons in terms of CLIL approach, i.e. Content and Language Integrated Learning. The main aim of the case study was to examine if bilingual mathematics instruction does or does not prevent learners from solving math word problems. Secondly, the analysis of transcription of the lesson audio-record served for identification of intercultural features which might hinder the learning process. The analysis of the transcribed audio-record indicates that the bilingual context did not prevent students from solving math word problems, although each of the students worked at their individual rate. On the other hand, some students were confused by the comma as a thousands-separator in multi-digit numbers, and this actually hindered their learning and problem solving process. This fact has been identified as an intercultural difference which had to be explicitly explained to the students. In order to lessen the possible negative influences of bilingual context on mathematics education, teachers need to predict students’ responses to various intercultural differences which students are unfamiliar with. Key words: bilingual mathematics education, CLIL, thousands-separator, land area, per cents.

In calculus lectures and seminars students frequently call for demonstrations of usefulness of a new term or proposition. Tasks about tangent or instantaneous velocity are quite legendary, showing the need for derivatives. Similarly, pictures of inscribed or circumscribed rectangles, leading to the definition of Riemann definite integral, are quite popular. In the submitted contribution we aim to demonstrate the usefulness of infinite functional series (power, Taylor), which come in useful for common calculations in physics, and also for formulation of new discoveries and theories in physics.

In general, abstraction and correct understanding of fundamental concepts play an important role in teaching practice. A good teacher not only has to know the proper meaning of concepts, but also be able to use them correctly and recognize situations in which it is sensible to use particular terms. Pupils acquire notions of terms in their early childhood and then in primary educational level, therefore primary teachers’ correct understanding of the concepts is essential. During their university studies some teacher trainees find out that they have incorrect or insufficient notion of geometric terms. This can be remedied in several ways. Useful remedy methods can be discussions, Socratic dialogue or use of various material teaching aids. We managed to interlink these three methods in a 90-minute lesson of an optional course covered in study plan of the Teacher Training Master Programme for Primary Education at Constantine the Philosopher University in Nitra, Slovakia. The students who participated in the lesson were in their first or second year of the master degree study. The submitted contribution comprises a brief description of the lesson and a summary of findings we obtained by means of worksheets filled in by the teacher trainees.