I observed that my students do not understand what a probability distribution is.
We do not treat probability axiomatically on the course, so the required level of understanding is knowing all the possible outcomes and their probability, which is good enough for discrete distributions. We do not pay too much attention as to what this might mean with continuous distributions; I would be happy if the students understood the meaning for discrete ones.
When asked about the probability distribution of, say, the sum of two dice, I am equally likely to get the expected value or the probability of a single outcome, or even the probability of getting a given result on both dice, than I am to get what I would think of as the probability distribution.
I have had students calculate some probability distributions and things based on them, but this is not a huge theme on the course. I have also given them the meaning of the term "probability distribution". We have seen different representations of probability distributions, such as trees, graphs and the area model. It is unclear whether I will cover probability distribution as a concept next year and how thoroughly.
- Is this a known issue and where can I read more about this?
- Any good ideas as to how to work with probability distribution as a theme?
Teacher education of future teachers at grades 5-10 in Norway (mostly grades 8-10 and thereby lower secondary education). The students are second year university students with 40 ECTS credits in mathematics didactics, but no previous university level education in probability. Many have only practical (low-level) mathematics from videregående (upper secondary school) and grades might not be very good.
This year we used Alfa as the main book, supplemented by QED 5-10 -books. Next year we are likely to have QED as the primary textbook. Hva er sjansen for det? does not cover the subject. Other books, preferably in Norwegian or other Scandinavian language, are possible.