Probability distributions, assessment and instructional software: Lessons learned from an evaluation of curricular software

While mathematics education guidelines have encouraged substantial change in the introductory probability and statistics curriculum, probability distributions still remain an important topic in a first course. In fact, just as software has made data analysis more accessible to students in introductory courses, it also offers new ways to teach probability distributions. However, these new teaching technologies, which emphasize active experimentation and interpretation of displays, also raise new questions. Just what do students see when they exmaine a display of a probability distribution? Do the displays really help students acquire a clear conceptual understanding? Can interactive exercises for related concepts like sampling distributions make good use of displays? Finally, can good assessment practices help us learn when displays are effective and when they might be confusing? This chapter will discuss some interactive, computer-based exercises that use and teach probability distributions, and consider how assessment can help address some of the important questions these new teaching technologies raise.