313.902 (16W) Didaktische Aspekte der Wahrscheinlichkeitsrechnung

Wintersemester 2016/17

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Erster Termin der LV
07.10.2016 14:00 - 17:30 , V.1.04
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Überblick

Lehrende/r
LV-Titel englisch
Didactic aspects of probability
LV-Art
Vorlesung-Übung (prüfungsimmanente LV )
Semesterstunde/n
2.0
ECTS-Anrechungspunkte
2.0
Anmeldungen
6 (25 max.)
Organisationseinheit
Unterrichtssprache
Englisch
LV-Beginn
01.10.2016

LV-Beschreibung

Intendierte Lernergebnisse

This course of lectures will be given in an interactive format whereby students are also expected to take some initiative themselves and engage in the ideas discussed. The didactics of probability is a relatively new discipline, about 40 years old, within the context of didactics, which has a longer tradition, especially in Europe. There are a number of key references, but the intention is that students should refer to specific ideas and chapters rather than read complete books. The lectures will cover a range of topics an inter-related way, since connections are a key component of any didactics. Context is also important but can vary both within and between countries, in the way that mathematics is actually taught. Personal reflection is also important to help students develop understanding of didactics; this means thinking about how a pupil develops his or her own understanding of key ideas through the school process. The key themes which will be developed are listed below. When talking about children in school, the word ‘pupil’ rather than ‘student’ will be used. Also reference will be made to a teacher in the school situation, and lecturer or professor in the university situation; a student training to be a teacher may be called a trainee teacher.

Lehrmethodik

Pre-requisites

It is expected that students are familiar with the basic ideas of probability up to Bayes theorem and also have an awareness of links between probability and statistics in terms of distributions. However, from a technical point of view, a detailed knowledge of probability distributions is not required. No prior knowledge of psychology or didactics will be required.

Course Dates

Since this course is being given by a guest professor, the lectures will be presented within a more intensive schedule over several weeks. These sessions are planned for Fridays starting on 7/10/16 and continuing on 21/10/16, finishing with an examination on 9/12/16. There will also be work/readings set and assessed during the course at agreed times.

Inhalt/e

Course outline: 313.902 Autumn 2016

  • The history of probability has been complicated and the basic ideas, which are quite simple emerged rather late historically, compared to geometry and number. An axiomatic approach had to await the 20th century. Some lectures will explore the reasons for the late emergence of probability with the famous correspondence between Fermat and Pascal in the 17th century.
  • The underlying philosophical positions for probability have been contentious ever since Laplace and others recognised the fundamental deficiencies in the principle of equal likelihood, which remains the initial approach in the school curriculum. These ideas will be explored over several lectures.
  • Probability, like other areas of mathematics has generated its own share of paradoxes and fallacies. Some will be presented at the beginning of the course for students to consider. Others will be integrated into the course as it develops.
  • Amongst the ideas studied will be the normal axioms (basic notions) of probability, the simple laws and the ideas underlying the axiomatic approach of Kolmogorov, as the formal answer to Hilbert’s call at the beginning of the century.
  • Didactics draws on a number of other disciplines from the social sciences, most notably from psychology. The standard first text is by Piaget and Inhelder and another one is by Fischbein.
  • The content of the probability curriculum in school will be discussed, mainly for secondary (grades 6-12) stages. The key ideas which are usually taught will be outlined. The main ideas and theorems which are included in the school curriculum will be highlighted. Students will be asked to reflect on how this compares to their own experience.
  • The methods of teaching probability will be explored. Often ideas in mathematics are presented in a relatively formal way. Teachers explain ideas and then give exercises and examples for pupils to practise. There are a number of other approaches as described below. Students will be expected to reflect on these and the extent to which they have experienced them, as well as on their effectiveness.
  • In teaching methods there is a place for discussion of ideas to further pupils’ understanding, especially in probability.
  • There is a place in teaching methods for practical work and simulations: the relevance of these approaches in probability will be analysed.
  • Investigational work is seen as another teaching approach which needs to be considered in the didactics of probability.
  • Another way of understanding probability is by modelling situations. Modelling as an approach will be described, analysed and evaluated.
  • The role of computers in didactics has increased exponentially in the last few decades and the didactics of probability has also been affected.
  • The course covers a wide range of stimulating and interesting ideas. The expectation is for active participation of students who attend. Indeed there may be times when a pair or small group of students may be asked to give a short presentation themselves.
  • A number of readings will be suggested during the course. It is intended that all students will be undertake study of some readings, whilst wider texts will be available for those interested in studying some ideas in more depth.

Initial Assignment (not assessed)

Do task 1 if your birthday is January to June; do task 2 if your birthday is July to December. Discuss with others in the group who have done the same task and be prepared to present your ideas to the rest of the group. .

Literatur

Barnett, V. (1973). Comparative statistical inference. New York: Wiley.

Bloom, B (1956). Taxonomy of educational objectives. Mckay (Longman).

Cockcroft, W. (1982). Mathematics counts. HMSO.

Chiesi, F.& Primi, C. (2009). Recency effects in primary-age children and college students. International Electronic Journal of Mathematics Education, 4(3), 259-274. Online: www.iejme.com.

David, F.N. (1962). Games, gods and gambling. London: Griffin.

Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Dordrecht: Reidel.

Gigerenzer, G. (2002). Reckoning with risk: learning to live with uncertainty. London: Penguin Books.

Hacking, I (1975) The emergence of chance CUP

Hacking, I. (1990). The taming of chance. Cambridge: Cambridge University Press.

Kahneman, D. (2011). Thinking, fast and slow. London: Penguin.

Kapadia, R. & Borovcnik, M. (Eds.) (1991). Chance encounters: probability in education. Dordrecht: Kluwer Academic Publishers.

Kolmogorov, A.N (1933/1956). Foundations of the theory of probability. Chelsea, London.

Piaget, J. & Inhelder, B. (1951/1975). The origin of the idea of chance in children. Routledge and Kegan Paul, English translation).

Schools Council (1980), Teaching statistics 11-16. London, Foulsham Educational.

Székely, G.J. (1986). Paradoxes in probability and mathematical statistics. Dordrecht/Boston: D. Reidel.

Prüfungsinformationen

Prüfungsmethode/n

Course Assessment

The assessment will be by an examination based on essays rather than solely mathematical problems. There will also be assessment during the course, based on participation, and a presentation/ project.

Beurteilungsschema

Note/Grade Benotungsschema

Position im Curriculum

  • Bachelor-Lehramtsstudium Bachelor Unterrichtsfach Mathematik (SKZ: 420, Version: 15W.2)
    • Fach: Freie Wahlfächer (Freifach)
      • Freie Wahlfächer ( 0.0h XX / 5.0 ECTS)
        • 313.902 Didaktische Aspekte der Wahrscheinlichkeitsrechnung (2.0h VU / 2.0 ECTS)
  • Lehramtsstudium Unterrichtsfach Mathematik (SKZ: 406, Version: 04W.7)
    • 2.Abschnitt
      • Fach: Freies Wahlfach gem. § 5 (LM 2.7.) (Freifach)
        • Empfohlene Freie Wahlfächer (zweistündig) ( 2.0h VO / 4.0 ECTS)
          • 313.902 Didaktische Aspekte der Wahrscheinlichkeitsrechnung (2.0h VU / 2.0 ECTS)

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