Gerd Gigerenzer's Reckoning with Risk shows how traditional methods often leave people with a poor grasp of statistics.
While statistics may sound like a small area of mathematics, Gigerenzer uses examples from medicine and law to highlight the importance of ensuring that we do not misunderstand statistical information
This is best shown with an example:
The probability that a woman of age 40 has breast cancer is about 1%. If she has breast cancer, the probability that she tests positive on a mammogram is 90%. If she does not have breast cancer, the probability that she nevertheless tests positive is 9%.Presented in this format, most people suggest that the probability is about 90%, as they are confused by the framing of the situation in probabilities.
What are the chances that a woman who tests positive actually has breast cancer?
However Gigerenzer then presents the problem in natural frequencies
Think of 100 women. One has breast cancer, and she will probably test positive. Of the 99 who do not have breast cancer, 9 will also test positive. Thus, a total of 10 women will test positive.This way of presenting the numbers clearly shows that 90% of women who test positive would not actually have cancer.
How many of those who test positive will actually have breast cancer?
Which way would you prefer your doctor to have been taught?
Gigerenzer goes on to illustrate this with the example of an experiment where American and German students were taught statistics using probabilities and natural frequencies.
German students have traditionally better at understanding probability based statistical teaching, and retain that knowledge better.
However, when taught to convert probabilities into natural frequencies, both groups acheived significantly better results
Even more impressive however, is the difference on retention - in both groups students were able to continue to apply the techniques accurately on later tests, which they were unable to do when taught using traditional probabilities.
As Gigerenzer says, dealing with uncertainty is a crucial skill in today's world, and the better able people are to accurately evaluate outcomes, the better they are able to deal with reality and all its inherent challenges.
However, the more important development that comes out of teaching students in ways that 'stick', is that everyone enjoys things more when they can do them well.
This changes everything.
While the above example involves maths, the development of new teaching methods to ensure 'stickiness' means that students will face learning with a whole new outlook.
The idea of making things stick comes from the book of the same name by Chip and Dan Heath. Dan co-founded Thinkwell, a company which specialises in new media textbooks.
As Carl Tyson, the current CEO of Thinkwell says "education and learning are fundamental to making our country competitive in the world".
As detailed in my previous post, I think that education not only offers to make a country competitive, but also improves out chances of solving many of the world's problems.
Although unfortunately I wasn't taught using natural frequencies so I'm not sure how much...!