**Jakub Jernajczyk**

*Academy of Art and Design, Wrocław, Poland*

**Thinking in images – mathematical inspirations in contemporary conceptual art**

Conceptual art, developed from the second part of the twentieth century, emphasizes the ideas which are the basis of the process of creation rather than focusing on the material results of this process. On the one hand this extreme simplification or rejection of the physical representation of the artwork is one of the main criticisms of conceptual art, but at the same time it is a catalyst for pure abstraction and theoretical growth. It is not surprising that many members of this movement, whilst searching for inspiration for their creation, glean from topics of philosophy or mathematics.

During my speech I will present a selection of artworks inspired by concepts of mathematics or philosophy of mathematics, which were created by pioneers of polish conceptualism as well as by younger artists: M. Aleksandrowicz, J. Chwałczyk, S. Dróżdż, W. Gołkowska, W. Gołuch, Ł. Huculak, J. Jernajczyk, M. Jędrzejewski, E. Smoliński. All of this creators are connected with Wroclaw artistic scene – one of the most important centres of growth of polish conceptual art.

Among these examples one can find artistic realizations in which geometrical analysis becomes a point of entry for philosophical speculation.

**Vladimir Mityushev**

*Pedagogical University of Cracow, Poland*

**Higher education in computer epoch: **

**How to teach biology, chemistry, economy, engineering, geography, informatics ... and mathematics? **

Mathematical Modeling and Computer Simulations spread through modern science and technology. However, this topic does not take a proper place in higher education, especially at the beginning level. There is a gap between the classical mathematical theory learned by students and its applications. Computer implementations are frequently reduced to orders as in army to put a computer button to get a result. The goal of this talk is an introduction into interdisciplinary approaches to outline Mathematical Modeling using simple mathematical descriptions, making it accessible for first- and second-year students. The main methods and principal schemes are selected and clearly presented as a unified short course *Introduction to Mathematical Modeling and Computer Simulations*, see the textbook www.amazon.com/Vladimir-V.-Mityushev/e/B001K8D332

**Zbigniew Semadeni **

*University of Euroregional Economy, Józefów-Warsaw, Poland*

**Rhythms, gestures, subitizing and learning to count **

According to Edyta Gruszczyk-Kolczyńska, the origins of learning to count are traced back to rhythmic structures which are formed in the brain during the prenatal period (stimulated by auditory rhythms of maternal heartbeats), then to infant’s gestures: this, this, this,… and to nursery rhythms and rhythmic counting. This is the first, crucial period; it is followed by a period of mastering counting procedures and the passage to the number concept and arithmetic operations.

Subitizing is the ability of perceiving the number of a small group of items at a glance without counting and immediately knowing how many items are seen. Numerical judgments made for 1 to 4 objects by means of a direct perceptual-apprehension mechanism are very fast, accurate and confident. This ability has a strong genetic component and is a set-before in the sense of David Tall. However, subitizing is limited to a few small numbers and does not lead to the general concept of a natural number, which is based on unlimited counting and the idea *so it goes on*. The question of whether subitizing is justly regarded as prior and inferior to ordinary counting will be discussed.

**Ingo Witzke **

*University of Siegen, Germany*

**Epistemological Beliefs about Mathematics in Education**

Based on evidence from theoretical and empirical research it is quite clear that beliefs play a decisive role in mathematical learning processes. Although it is still somewhat difficult to describe and measure direct effects, there seems no doubt that (epistemological) beliefs, belief systems – or in the German term, “Auffassungen” – of mathematics play a major role on “how one chooses to approach a problem, which techniques will be used or avoided, how long and how hard one will work on it, and so on. The belief system establishes the context within which we operate [...],” (Schoenfeld, 1985, p. 45). Looking at material used in present mathematics classrooms and empirical studies with a focus on beliefs, for example, in the domain of Calculus, we can identify interesting parallels to historical cases in the late 17th early 18th century. Especially on the level of epistemic beliefs this view back into the history of mathematics provides us with valuable insights and legitimations, as I will argue in my talk, for the present and future way of how to support mathematical learning processes in school and pre-service teachers’ education.

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