Literature Index

This 30-minute webinar is the second in a two-part series on the AP Statistics experience. The first part focused on the AP exam and its grading. This second part will focus on the teaching of the AP course. David Spohn, an experienced AP Statistics teacher, will discuss the curriculum of AP, insights on his own teaching, and resources that are available to AP Statistics teachers.

We examined how middle school students reason about results from a computer-simulated die-tossing experiment, including various representations of data, to support or refute an assumption that the outcomes on a die are equiprobable. We used students' actions with the software and their social interactions to infer their expectations and whether or not they believed their empirical data could be used to refute an assumption of equiprobable outcomes. Comparisons across students illuminate intricacies in their reasoning as they collect and analyze data from the die tosses. Overall, our research contributes to understanding how students can engage in informal hypothesis testing and use data from simulations to make inferences about a probability distribution.

When solvers have more than one strategy available for a given problem, they must make a selection. As they select and use different strategies, solvers can learn the strengths and weaknesses of each. We study how solvers learn about the relative success rates of two strategies in the Building Sticks Task and what influence this learning has on later strategy selections. A theory of how people learn from and make such selections in an adaptive way is part of the ACT-R architecture (Anderson, 1993). We develop a computational model within ACT-R that predicts individual subjects' selections based on their histories of success and failure. The model fits the selection behavior of two subgroups of subjects: those who select each strategy according to its probability of success and those who select the more successful strategy exclusively. We relate these results to probability matching, a robust finding in the probability-learning literature that occurs when people select a response (e.g., guess heads vs. tails) a proportion of the time equal to the probability that the corresponding event occurs (e.g., the coin comes up heads vs. tails).

This booklet is part of the Curriculum and Evaluation for School Mathematics Addenda Series, Grades K-6. This series was designed to illustrate the standards and to help you translate them into classroom practice. In Making Sense of Data you will find that familiar activities have been redesigned and infused with an investigative flavor. You will discover new ideas that can be easily incorporated into your mathematics program. You will also encounter a variety of problems and questions to explore with your class. Margin notes give you an additional information on the activities and on such topics as student self-confidence, evaluation, and grouping. Connections to science, language arts, social studies, and other areas in the curriculum are made throughout. Supporting statements from the Curriculum and Evaluation Standards appear as margin notes.