The article I chose for this week is titled “Training Teachers to Teach Probability” and can be found at http://www.amstat.org/publications/jse/v12n1/batanero.html . I chose this article as I have been thinking about how I might approach teaching probability to future students. The article provided a way to teach probability as an introductory lesson and gave an understanding about how an instructor may miss the level of difficulty inherent in the material.
The article makes the point that math teachers at the elementary and secondary school level have a difficult time understanding probability when the concepts are counterintuitive to the way most people think. They conducted two different experiments where the teachers were asked to make some judgment calls based upon their knowledge and intuition. One was looking at two sequences of head-tail results; one real, the other made up, than decide which was which. The other was looking at one side of a two sided counter and, given certain assumptions, guessing the color of the other side. Strategies on how they decided were discussed and then participants tried again using a different strategy. If the participant got better results, their conclusions were reinforced, despite the fact that statistically there was no correlation.
The argument here was that there are rules to probability that are not going to change. But what was really eye opening to me was how even teachers with background in math and science would struggle with the counterintuitive arguments associated with probability.
From this I learned that I must be mindful about how difficult it might be for an introductory statistics course and not assume my students should grasp it easily. From the wider view of how to teach this field, it is easy to slip into the idea that just explaining concepts should be fairly clear. But through the use of problem or case studies such as shown in the article, the concepts can be taught with greater impact to the students.
I think Brian is onto something here. Though the article is addressing probability, I still see it relating to all of us. One of the things that Bain talked about was that the best teachers anticipate where their students are going to have real difficulty and preparing them for it. In other words, how to help students with new ideas and concepts by relating or connecting them to what they are familiar with. The idea of using some creative teaching activities like case studies is helpful to keep in mind. Thanks for sharing, Brian.
Bass
I’ve been teaching probability for years and frequently encounter trouble with my students preconceptions. The problem with probability is that the fundamental ideas are quite simple and intuitive, while the more advanced problems display a significant jump in difficulty.
Another interesting probability question that most students get incorrect is the classic Monty Hall problem. Here is a link describing it:
http://en.wikipedia.org/wiki/Monty_Hall_problem