Bruce Schneier's blog commented recently on Teaching Risk Analysis in School. He linked to a London Times article on teaching risk. Actually, the article was more about teaching probability and statistics as a way to understand risk, which isn't exactly the same thing as what we call *risk analysis* these days. In practice, risk analysis is a qualitative process in which we apply numerical estimates to risk factors. If you look at even the most applied statistics work, you find very little that's truly qualitative, except perhaps in the choice of survey questions, if you're doing a survey.

I've been trying to teach risk analysis to undergraduates. It is a very tricky topic. Some risk elements fit into a formal mathematical model, but others don't. Instead of ejecting the misfitting elements from the model, typical risk analyses incorporate estimates that try to match the structure and behavior of the formal elements. While it's important in some fields (like security) to understand and apply this technique, there's no way to prove the correctness of this type of model. It is, ultimately, an opinion.I agree with the London Times article in that primary and secondary school students should learn more about comparing risks. There are obvious examples of people focusing on silly risks, like fearing an airline flight more than the trip to the airport. I'd love to see a more mathematically literate population that was less likely to make such errors.

The problem I have with teaching "risk analysis" is that it is a scary mixture of math and opinion, whose result is intended to help sway other opinions. Math classes these days have the benefit of focusing on formal, objective techniques. We don't want to cloud students' minds with qualitative techniques while teaching them traditional math.

When teaching risk analysis, it's essential that the students distinguish between the quantitative and qualitative aspects of the work. They need to understand that the numbers may look exact, but the inputs are often estimates. This doesn't render the result worthless, but it limits its precision and accuracy.

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