900.212 (19S) AusgewählteThemen der Mathematikdidaktik: Didaktik der Wahrscheinlichkeitsrechnung
- LV-Titel englisch
- Selected Topics in Didactics of Mathematics: Didactics of Probability Calculation
- Seminar (prüfungsimmanente LV )
- 3 (35 max.)
Zeit und Ort
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.
There will be a course of lectures given in an interactive format whereby students are also expected to take some initiative themselves and engage in the ideas discussed. Then, the students will get a manuscript or a paper to prepare a seminar lecture, which has also to be delivered in written form after the presentation.
- The history of probability has seen the basic ideas emerging rather late, compared to geometry and number. An axiomatic approach had to await the 20th century. Some presentations explore the reasons for this 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. Some will be presented at the beginning of the course for students to consider. Others will be integrated into the presentations.
- Amongst the ideas studied will be the normal axioms (basic notions) of probability and the simple laws.
- 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, there is a place for discussing ideas to further pupils’ understanding; this may be more prevalent in probability than in mathematics.
- 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 course covers a range of stimulating ideas. The expectation is for active participation of students in the discussion and the presentation of the other participants.
- 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.
It is expected that students are familiar with the basic ideas of probability. No prior knowledge of psychology or didactics will be required. The lectures will be in English which should help you with your future work and studies.
LiteraturReferences will be given in a hand-out.
Initial Assignment and Reading (not assessed).
Do task 1 if your birthday is January to June; do task 2 if your birthday is July to December. Discuss with other students and be prepared to present your ideas to the rest of the group.
1 Monty Hall Challenge.There are three boxes, one of which contains a prize of gold, and the other two boxes contain booby prizes of base metal. The host, Monty Hall asks you to choose a box. You select one and then Monty Hall opens a box which is shown to contain the booby prize. Would you switch boxes or not? Ask four friends the same question.
Explain the reasons for your answer and discuss how this compares with the results of the five people (including yourself) as a whole. You do not need to write more than a page.
2 Division of Stakes. Peter and Paul are playing a series of games. How should they share the stakes if the series is ended at a time when Peter needs two points and Paul needs three more points to win? Suppose, for example, in a series of 11 games Peter has 4 points while Paul has 3 points and the stake is £100. Ask four people the same question.
Explain the reasons for your answerand discuss how this compares with the results of the five people (includingyourself) as a whole. You do not need to write more than a page.
The assessment will be by the presentation of the written essay.
There will also be assessment based on participation in the discussion on other presentations.
Position im Curriculum
- Besonderer Studienbereich Themenbereich "Didaktik der Mathematik"
(SKZ: 102, Version: 15W)
Fach: Themenbereich "Didaktik der Mathematik"
Ausgewählte Themen der Didaktik der Mathematik (
1.0h / 2.0 ECTS)
- 900.212 AusgewählteThemen der Mathematikdidaktik: Didaktik der Wahrscheinlichkeitsrechnung (2.0h SE / 4.0 ECTS)
- Ausgewählte Themen der Didaktik der Mathematik ( 1.0h / 2.0 ECTS)
- Fach: Themenbereich "Didaktik der Mathematik" (Pflichtfach)