Probability is arguably the area of mathematics where the concepts are most intuitively obvious while simultaneously containing some of the most counterintuitive principles. People immediately grasp the idea of the probability of drawing a specific card from a deck of fifty-two cards or drawing a red bead from a bowl where the number of different colored beads is known. Yet, as the controversy over the Monty Hall problem and the billions of dollars earned by casinos indicate, many people are confused by some of the realities of probability.
As many of the articles in this collection demonstrate, probability is a deep topic, penetrating to the level of fundamental philosophy. As I discovered, even though I have taught basic statistics over twenty times, there are aspects of probability that I have not considered or grasped. Most of those aspects have to do with the significance of the assumptions that are sometimes made when considering a problem in probability. I can say without hesitation or qualification that every person that works using or teaching probability can learn something from this book.
The papers include discussions of the teaching of probability starting from children and going through adults, the underpinnings of cognitive psychology as it applies to learning probability, the role of cultural background in the person’s understanding of probability, the history of how the concepts of probability were developed, and how effectively various people solve problems in probability. The papers are generally geared towards the teaching of probability, but given the breadth of the use of probability, there is wide applicability.
Advancements in modern societies are largely based on the proper use and understanding of probability. For example, new medical treatments are based on the effectiveness of new drugs and medical techniques, and this effectiveness is proved or disproved using probability models and reasoning. For this to work right, researchers need to have the highest levels of understanding of probability. And that is the responsibility of educators. Those educators will be able to use something from this book to make them better at their job.
Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.