Extracurricular language activities in higher education: Perspectives of teachers and students

This Master’s thesis researches the topic “Extracurricular language activities in higher education: Perspectives of teachers and students”. In the light of several learning theories, namely, Self-Determination Theory, Social Learning Theory and Incidental Learning Theory, extracurricular participation in language related activities is studied. The main aims of the research are as follows: to study how extracurricular language activities can be organized and supported by the education institution; to investigate how such activities can promote the participants’ learning; and, to research how these activities can be developed and improved in the future. Due to the qualitative character of this research, the empirical data collected through interviews and their thematic analysis allow to study the participants’ perceptions on the above-mentioned issues. Among other results of the research, it can be noted that the organizers of extracurricular language activities and the participants of the activities may have different perspectives on the aims of the activities, as well as their advantages. Additionally, it has been found that the participants of activities would often speak on certain categories that imply the connection to some learning theories, which allows to hypothesize that some learning could be observed in those participants, following participation in extracurricular activities. This is an implication for further research in the area, which can focus on correlations between participation in extracurricular language activities and learning outcomes of the participants.

Privileged Words and Sturmian Words

This dissertation has two almost unrelated themes: privileged words and Sturmian words. Privileged words are a new class of words introduced recently. A word is privileged if it is a complete first return to a shorter privileged word, the shortest privileged words being letters and the empty word. Here we give and prove almost all results on privileged words known to date. On the other hand, the study of Sturmian words is a well-established topic in combinatorics on words. In this dissertation, we focus on questions concerning repetitions in Sturmian words, reproving old results and giving new ones, and on establishing completely new research directions. The study of privileged words presented in this dissertation aims to derive their basic properties and to answer basic questions regarding them. We explore a connection between privileged words and palindromes and seek out answers to questions on context-freeness, computability, and enumeration. It turns out that the language of privileged words is not context-free, but privileged words are recognizable by a linear-time algorithm. A lower bound on the number of binary privileged words of given length is proven. The main interest, however, lies in the privileged complexity functions of the Thue-Morse word and Sturmian words. We derive recurrences for computing the privileged complexity function of the Thue-Morse word, and we prove that Sturmian words are characterized by their privileged complexity function. As a slightly separate topic, we give an overview of a certain method of automated theorem-proving and show how it can be applied to study privileged factors of automatic words. The second part of this dissertation is devoted to Sturmian words. We extensively exploit the interpretation of Sturmian words as irrational rotation words. The essential tools are continued fractions and elementary, but powerful, results of Diophantine approximation theory. With these tools at our disposal, we reprove old results on powers occurring in Sturmian words with emphasis on the fractional index of a Sturmian word. Further, we consider abelian powers and abelian repetitions and characterize the maximum exponents of abelian powers with given period occurring in a Sturmian word in terms of the continued fraction expansion of its slope. We define the notion of abelian critical exponent for Sturmian words and explore its connection to the Lagrange spectrum of irrational numbers. The results obtained are often specialized for the Fibonacci word; for instance, we show that the minimum abelian period of a factor of the Fibonacci word is a Fibonacci number. In addition, we propose a completely new research topic: the square root map. We prove that the square root map preserves the language of any Sturmian word. Moreover, we construct a family of non-Sturmian optimal squareful words whose language the square root map also preserves.This construction yields examples of aperiodic infinite words whose square roots are periodic.