Literature Index

Confidence intervals are an attractive means of conveying experiemental results, as they contain a considerable amount of information in a concise format. Two competing metaphors that arise from students' speech and gestures during interviews are examined for their impact on understanind, statistical problem solving, and future learning of mathematics. In the Changing Ring Aroung a Fixed Point metaphor, confidence intervals are moving disks of various diameters covering a fixed but unknown point, like pitching horseshoes of varying widths to capture a fixed stake. Key to this correct conceptual metaphor is that the interval is a property of a sample but not of the population. Here, the diameter of the disk (i.e., the length of the confidence interval) changes from sample to sample, while the location of the stake (i.e., the population paramet, or population mean) is fixed across samples, but generally unknown. In contrast, the Changing Point on a Fixed Disk metaphor conceptualizes confidence intervals as fixed-diameter disks onto which changing points are placed. In this incorrect metaphor, the population parameter can change from sample to sample. The interval is of fixed length and each experiment results in placing a new parameter somwhere onto the fixed-diameter disk. One possible source of this second metaphor is a suspected confusion between acceptance regions in hypothesis testing and confidence intervals, which tend to be taught in close proximity to one another in the statistics textbooks. The Changing Point on a Fixed Disk metaphor will generally support a misinterpretation of the confidence interval that leads to inaccurate problem solving. By better understanding students' mental representations of confidence intervals, and appealing to the metaphors they convey, we can hope to improve both statistics instruction and educational researchers' uses of statistical tests.

In this paper, I will report and summarize some preliminary results of two ongoing studies. The aim is to identify problem areas and difficulties of students in elementary data analysis based on preliminary results from the two ongoing studies. The general idea of the two projects is similar. Students took a course in data analysis where they learned to use a software tool, used the tool during the course, and worked on a data analysis project with this tool at the end of the course. The course covered elementary data analysis tools, such as variables and variable types, box plots, frequency tables and graphs, two-way frequency tables, summary measures (median, mean, quartiles, interquartile range, range), scatterplots, and line plots. The grouping of data and the comparison of distributions in the subgroups defined by a grouping variable was an important idea related to studying the dependence of two variables. The methods for analyzing dependencies differed according to the type of variables: for example, scatterplots were used in the case of two numerical variables, and two-way frequency tables and related visualizations were used in the case of two categorical variables.

The purpose of this phenomenological study was to talk to students about their experiences taking introductory statistics. The author met with eleven students individually for four interviews throughout the semester, followed by a member-checking focus group during the last week of classes. One of the most salient themes to emerge was the students' reliance on their instructor for feedback about performance, directions on taking notes, and the creation of a classroom environment that motivated them to study. As part of the phenomenological tradition, the author presents his own reflections based on these students' comments. Conclusions include the encouragement of instructors to be more mindful of students' reactions to course content, and suggestions for developing a more learner-centered learning environment.