Methodology of Probability Theory Instruction

elective courses
pedagogical qualifications

We will discuss teaching methodology for combinatorics and theory of probability and work on developing probabilistic intuition.

Topics:

How to present axioms of probability theory and the properties of probability? Classical probability. Elements of "college" probability. The sum rule and the product rule. The methodology of introducing notions of "college" probability. Problems with interesting numerical results. Paradoxes in probability theory. Stochastic trees - a a method for illustrating the notion of conditional probability. Explaining basic probability theorems on stochastic trees. How to introduce the notion of independent events? Bernoulli's scheme. Stochastic games as a method for introducing notions related to random variables. Applications of the theorem on the expected value of a sum of random variables. Using stochastic graphs in the analysis of some random experiments.

Literature will be given durign the course.

(Each effect is followed by the code of the corresponding requirement of the Teachers' Education Standard)

In the scope of knowledge a graduate knows:

the national curriculum of mathematics in the scope of the probability theory, the teaching objectives and the content knowledge at different education levels (D.1/E.1.W2.);

methods of teaching of probability theory - substantive and methodical solutions, good practices, how to adapt the teaching to needs and abilities of students of divirsified learning potentials, typical students' errors, their role and how to makee use of them while teaching (D.1/E.1.W6.);

the need to build a positive attitute of students towards studying, developing their curiosity, activity and coginitive independence, logical and critical thinking, to build the motivation to learn mathematics in a systematic way, to use different knowlegde sources, incuding the Internet and to prepare students for life-long learning through self-reliant learning (D.1/E.1.W15.);

In the scope of skills a graduate can:

identify typical school exercises with the learning objectives, in particular with the general requirements of the national curriculum and with the key competemces (D.1/E.1.U1.);

identify the probability theory topics with other learning content topics (D.1/E.1.U3.);

addopt the communication style to the level of development of his/her students (D.1/E.1.U4.);

create didactical situations invoking students' activity and aimed at broadening of their interests and at the knowledge popularization (D.1/E.1.U5.);

recognize typical students' errors and use them in the teaching practice (D.1/E.1.U10.).

In the scope of social competences, a graduate is ready:

to popularize knowledge among students, within and outide the school (D.1/E.1.K2.);

to encourage students to research attempts (D.1/E.1.K3.);

to promote a responsible and critical use of digital media and to obey the copyright laws (D.1/E.1.K4.);

to develop students' curiosity, activity and cognitive independence as well as the logical and critical thinking (D.1/E.1.K7.);

to stimulate students to life-long learning through self-reliant learning (D.1/E.1.K9.).

The final grade is based on the number of points gained during classes, the midterm exam and the final exam.