Zimní semestr 2018/2019


11.10. 2018

Didactic research on the conceptualization of the continuum

Viviane Durand-Guerrier (Institut Montpelliérain Alexander Grothendieck, CNRS, Univ. Montpellier, France)

The continuum is one of the most difficult mathematical concepts for undergraduate students. We hypothesize that among the difficulties they face in relation with this notion, the graphical evidence provided by the number line fosters the idea of a dichotomy between discreteness and continuity, hiding the property of density-initself, i.e. the intrinsic density with respect to order in a totally ordered set. We will first provide evidences of the weakness of fresh French university students’ knowledge about real numbers. Then, we briefly present Dedekind’s construction of real numbers, which relies on the intuitive idea of the continuous line, and its proof of completeness. Finally, we will present a didactical situation aimed at fostering the understanding of the relationships between discreteness, density-in-itself and continuity for an ordered set of numbers that raise epistemological question thta can be put in relationships with Dedekind construct.

This presentation relies on two papers: Durand-Guerrier, V. (2016) Conceptualization of the continuumn an educational challenge for undergraduate students, International Journal of Research in Undergraduate Mathematics Education, 2, 338–361 Durand-Guerrier, V. & Tanguay, D. Working on proofs as contributing to conceptualization – The case of IR completeness. In Stylianides, Andreas J., Harel, Guershon (Eds.) Advances in Mathematics Education Research on Proof and Proving, ICME-13 Monograph, Springer.

18.10. 2018

How real are „real-world problems“ in textbooks?

Andreas Ulovec (University of Vienna, Austria)

It has long since proposed that using real-world problems in teaching and learning mathematics have a positive effect on motivation and learning outcomes. Text book authors responded to that by creating a large number of word problems with a supposedly real-world context. But how realistic are those real-world contexts? This talk will present the results of an ongoing study of Austrian mathematics text books, showing that a fair number of “real-world” problems are not actually taken from the real world, either because their context is not out of the students’ real life, their data is not realistic, or the questions asked to be answered are not questions that would occur in real life. A number of examples of such tasks will be presented. The talk will conclude with a number of positive examples of word problems with reasonable data and context, developed by students, text book authors, and in the framework of several international collaboration projects.

1.11. 2018

Researching From The Inside: confessions of a life-long phenomenologist

John Mason (Open University, Great Britain)

Influenced by my working conditions and by some key experiences, I spent many years articulating a way of working (teaching, researching) which emphasises lived experience. I called it the Discipline of Noticing. Participants will beg invited to engage in some tasks which may spark direct experience of noticing and issues surrounding it, for informing both teaching and researching.

15.11. 2018

Teaching with technology: Mathematics teachers‘ classroom practices of GeoGebra use in the context of English secondary school mathematics

Gulay Bozkurt (Eskisehir Osmangazi University, Turkey)

Although the influence of new technologies on education has been increasing over recent decades, the incorporation of technology, particularly into mathematics education, has been slow. It has become apparent that teachers have a central role in the integration of technology in mathematics classrooms, which needs more attention when it comes to researching this issue. This research aimed at developing a more comprehensive understanding of technology integration in classrooms, by examining further a proposed model of key structuring features of classroom practice (Ruthven, 2009) which shape the use of technology in lessons and the kinds of professional knowledge required. Focusing on the use of GeoGebra (Dynamic Mathematics Software) in the context of English secondary school mathematics, this case study investigated the teaching practices, and craft knowledge of three teachers. The case study analysis, using data triangulation of interviews and lesson observations, illustrated ways in which teachers adapted their classroom practices and provided some indications of the growth of their craft knowledge in the course of appropriating GeoGebra. The main conclusion was that although teachers’ classroom practices with GeoGebra appeared consistent across the topics, the stage they were at in terms of learning to teach with this software indicated differences especially in regard to establishing a functioning resource system and appropriate activity formats, and to developing a script for handling those topics.

29.11. 2018

From abstract art to geometrical understanding. Visualisation, manipulation and learning

Paola Vighi (Univ. of Parma, Italy)

The seminar describes and analyses an activity realised in Kindergarten School with children 5-6 years old. The starting point is a picture of Kandinsky, titled “Soft hard”, and its reproduction made by pupils, following particular tasks assigned by the teacher. The activity involves the concept of space, the investigation of geometrical figures and their mutual positions and especially the geometrical transformations. The analysis of the results furnishes information on child’s approach to geometrical knowledge and understanding and interesting suggestions on possible improvements of didactical activity.

13.12. 2018

Matematika v žonglování / žonglování v matematice

Michal Zamboj (PedF UK)

Je možné jev jako žonglování matematicky popsat? Jak a proč to vůbec dělat? Matematický zápis žonglování popíšeme pomocí teorie celočíselných posloupností, teorie grafů či teorie copánků a ukážeme si několik grafických reprezentací. Poukážeme na odlišnosti jednotlivých zápisů vzhledem k praktickému žonglování. Naučíme se vytvářet vlastní žonglérské triky a spočítáme kolik triků je možné žonglovat a za jakých vstupních podmínek. Samozřejmostí jsou praktické ukázky.

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