Student Perceptions of the Use of Writing in a Differential Equations Course

The use of writing to learn mathematics at the university-level is a pedagogical tool that has been gaining momentum. The setting of this study is a second-year differential equations class where written assignments have been incorporated into the course. By analyzing survey results and students' written work, we examine the extent to which students view writing as an effective learning strategy, as well as their beliefs about the relationship between mathematical writing and communication. We also discuss what students' narratives reveal about their past mathematical experiences.     

Programming and Mathematics in an Upper-Level University Problem-Solving Course

We discuss teaching and learning situations that surfaced when computer programming and mathematics were brought together in a course where students write computer code to explore mathematics problems. Combining programming and mathematics creates a rich ecosystem which, on top of traditional mathematics activities (writing solutions, proofs, etc.), offers simulation and experimentation, invites discussions about structure, requires logic and testing strategies, and handles mathematics objects with an added feeling of reality. Focusing on novice and inexperienced programmers, we look for answers to the practice-oriented question, “How do students reason through their difficulties when using programming to explore a mathematics problem?” Following literature review and methodology, we build the programming model, which we use to study students' experiences as they approach a mathematical problem by writing computer code. Our research is based on analyzing students' in-class work and class notes, author's observations of students working on their computers, and his interactions with students in class and elsewhere. In the four case studies that we present we touch upon students' difficulties in working with complex conditional statements and recurrence relations. As well, we discuss cases where resolving a programming issue demands posing and answering mathematical questions.     

Development of students’ conceptual thinking by means of video analysis and interactive simulations at technical universities

Video analysis, using the program Tracker (Open Source Physics), in the educational process introduces a new creative method of teaching physics and makes natural sciences more interesting for students. This way of exploring the laws of nature can amaze students because this illustrative and interactive educational software inspires them to think creatively, improves their performance and helps them in studying physics. This paper deals with increasing the key competencies in engineering by analysing real-life situation videos – physical problems – by means of video analysis and the modelling tools using the program Tracker and simulations of physical phenomena from The Physics Education Technology (PhET?) Project (VAS method of problem tasks). The statistical testing using the t-test confirmed the significance of the differences in the knowledge of the experimental and control groups, which were the result of interactive method application.     

Control of PDE-ODE cascades with Neumann interconnections

We extend several recent results on full-state feedback stabilization and state estimation of PDE-ODE cascades, where the PDEs are either of heat type or of wave type, from the previously considered cases where the interconnections are of Dirichlet type, to interconnections of Neumann type. The Neumann type interconnections constrain the PDE state to be subject to a Dirichlet boundary condition at the PDE-ODE interface, and employ the boundary value of the first spatial derivative of the PDE state to be the input to the ODE. In addition to considering heat-ODE and wave-ODE cascades, we also consider a cascade of a diffusion-convection PDE with an ODE, where the convection direction is “away” from the ODE. We refer to this case as a PDE-ODE cascade with “counter-convection.” This case is not only interesting because the PDE subsystem is unstable, but because the control signal is subject to competing effects of diffusion, which is in both directions in the one-dimensional domain, and counter-convection, which is in the direction that is opposite from the propagation direction of the standard delay (transport PDE) process. We rely on the diffusion process to propagate the control signal through the PDE towards the ODE, to stabilize the ODE.     

European cultural statistics in a comparative perspective: index of economic and social condition of culture for the EU countries

In the article, we present the construction of an index of economic and social condition of culture using datasets of Eurostat’s Cultural Statistics Pocketbooks from 2007 and 2011 and Eurostat’s COFOG data. The datasets allow us a broad perspective over a set of more than 200 variables in 12 domains for the EU-27 member states. Using high-dimensionally adjusted factor analysis (Metropolis–Hastings Robbins–Monro algorithm), we construct an index and determine a set of its several dimensions (as seen from the cultural statistics viewpoint). Using cluster analysis, we determine the general similarities and differences among the analysed countries and show several broadly different groupings that roughly, but not exclusively follow the divide speculated in some previous studies. The analysis therefore brings a novel and statistically developed tool to empirically follow the changes in the economic and social condition of culture from the viewpoint of cultural statistics, while the clustering of models has important consequences for empirical cultural policy and has to be verified in future studies.     

Novice teachers in the Czech Republic and their drop-out intentions

The current paper presents the results of the first research study of drop-out intentions of novice teachers in the Czech Republic. The study focuses on the reported satisfaction of novice teachers in primary and lower secondary schools with external factors that influence their socialisation and that can be seen as predictors of novice teachers' decision to stay in their current school. In the paper we present the results of quantitative research conducted in 2015–2017. Our main findings include the key significance of factors at the school level, especially the influence of school culture and climate, cooperation with colleagues and leadership. We conclude that in the Czech context teachers tend to stay in schools provided that they work in a well-functioning school, with cooperative colleagues and good head teachers.     

ASSISTING QUALITY ASSESSMENT AND IMPROVEMENT IN THE HIGHER EDUCATION INSTITUTIONS OF SLOVENIA

There are two universities in Slovenia which undertake research and teaching and offer professional services. The quality of the research performed by faculty members is assured by strict quantitative bibliographical criteria employed in the faculty rank award procedure. The criteria for teaching quality are less well defined. The new Higher Education Act of 1993, organized university staff development, the appearance of an integrated information system, and student evaluation of faculty teaching performance with the aid of student questionnaires can all be regarded as extrinsic assistance to intrinsic efforts on the part of faculty, students, and their organizations. Slovenia will endeavour to broaden and deepen its co‐operation with international organizations and foundations in the field of quality assessment and improvement of higher education institutions, particularly the quality of the teaching they offer.