Literature Index

While written comments are a popular and potentially effective method of student exam feedback, these comments are often overshadowed by students' focus on their grades. In this paper I discuss the additional use of orally recorded exam feedback in introductory statistics classes of 40 or fewer students. While grading and writing comments on a student's exam solution, I create a personalized sound file of detailed oral feedback for each question. The student can then securely access this file. The oral feedback in combination with written comments is more understandable for and motivating to the students, and accommodates a broader range of student learning styles. In support of this new feedback method, I provide and discuss classroom data collected from my students. Furthermore, I make suggestions for the use of orally recording feedback when time and resources are scarce.

"In reasoning about everyday problems, people use statistical heuristics, that is, judgmental tools that are rough intuitive equivalents of statistical principles. Statistical heuristics improved historically and they improve ontogenetically. Use of statistical heuristics is more likely when (a) the sample space and the sampling process are clear, (b) the orle of chance in producing events is clear, (c) the culture specifies statistical reasoning as normative for the events. Perhaps because statistical procedures are part of people's intuitive equipment to begin with, training in statistics has a marked impact on reasoning. Training increases both the likeli- hood that people will take a statistical approach to a given problem and the quality of the statistical solution. These empirical findings have important normative implications."

The paper analyzes the relationship between the epistemological nature of mathematical knowledge and its socially constituted meaning in classroom interaction. Epistemological investigation of basic concepts of elementary probability reveals the theoretical nature of mathematical concepts: The meaning of concepts cannot be deducted from former more basic concepts; meaning depends in a self-referent manner on the concept itself. The self-referent nature of mathematical knowledge is in conflict with the linear procedures of teaching. The micro-analysis of a short teaching episode on introducing the chance concept illustrates this conflict. The interaction between teacher and his students in everyday teaching produces a school-specific understanding of the epistemological status of mathematical concepts: the chance concept is conceived of as a concrete generalization, which takes "chance" as a fixed and universalized pattern of explanation instead of unfolding potential and variable conceptual relations of "chance" or "randomness" and developing the theoretical mature of this concept in an appropriate way for students' comprehension.

Research on human judgment demonstrates that people's theories often bias their evaluation of evidence and suggest that people might be more accurate if they were unbiased by prior beliefs. Rather than comparing people's judgments of data when they do or do not have a prior theory, most studies compare people's estimates to conventional statistical standards, even though the status of these measures as normative criteria is controversial. We propose that people's theories may have beneficial consequences not examined in previous research. In two paradigms (the covariation estimation problem and the t-test problem), we compare judgments made by people who have potentially biasing prior information. We vary the quality of the data, presenting subjects with data that are either well-behaved or contaminated with outliers. In both paradigms, people's judgments approximated robust statistical measures rather than the conventional measures typically used as normative criteria. We find the usual biasing effects of prior beliefs but also find an advantage for subjects who have prior theories - even incorrect ones - over subjects who are completely "objective." Potentially biasing beliefs both enhanced people's sensitivity to the bulk of the data and reduced the influence atypical scores had on their estimates. Evidence is provided that this robustness results from the fact that prior theories make judgment problems more meaningful. We discuss the conditions under which prior beliefs are likely to help and hinder human judgment.