Making Sense of Probability Through Paradox and Programming A Case Study in a Connected Mathematics Framework
Many scholars have argued (e.g., Cohen, 1987; Gigerenzer, 1987; Hacking, 1987) that a probabilistic revolution has occurred in our century. In this short period, the use of statistical methods has exploded from nonexistence to relative rarity to virtual ubiquity in the scientific literature. In the university, courses in probability and statistics are required for virtually all students in the natural and social sciences. Our daily newspapers are full of statistics about such matters as lung cancer risks, divorce rates, birth control failure rates, variation in temperature, the purity of soap, and so on. Beyond ubiquity, the disciplines of probability and statistics have fundamentally changed the way we think about science and the way we think about our world. Notions of randomness and uncertainty have opened up whole new areas of mathematics and science. This has released a ground swell of interest in subjects such as complexity, chaos, and artificial life.
Yet, despite the rapid infiltration of probability and statistics into our science and media, there is substantial documentation of the widespread lack of understanding of the meaning of the statistics we encounter ( Gould, 1991; Konold, 1991; Phillips, 1988; Piaget, 1975; Tversky & Kahneman, 1974). Even highly educated professionals who use probability and statistics in their daily work have great difficulty interpreting the statistics they produce ( Kahneman & Tversky, 1982).
Besides a lack of competence and understanding, students express a great deal of dislike towards courses in probability and statistics--an antipathy well captured by the oft-quoted line attributed to both Mark Twain and Benjamin Disraeli : "There are three kinds of lies: lies, damn lies and statistics" (cited in Tripp, 1970, p. 612).