Literature Index

Examines the collaborative efforts of a mathematics educator and statistician to help prospective elementary teachers develop statistical knowledge and experience through merging statistical investigation into existing elementary curricula. Offers insight into preservice teachers' statistical and pedagogical content knowledge based on their application of the process of statistical investigation themselves and with children.

The development of the understanding of average was explored through interviews with 94 students from Grades 3 to 9, follow-up interviews with 22 of these students after 3 years, and follow-up interviews with 21 others after 4 years. Six levels of response were observed based on a hierarchical model of cognitive functioning. The first four levels described the development of the concept of average from colloquial ideas into procedural or conceptual descriptions to derive a central measure of a data set. The highest two levels represented transferring this understanding to one or more applications in problem-solving tasks to reverse the averaging process and to evaluate a weighted mean. Usage of ideas associated with the three standard measures of central tendency and with representation are documented, as are strategies for problem solving. Implications for mathematics educators are discussed.

The field of Data Mining like Statistics concerns itself with "learning from data" or "turning data into<br>information". For statisticians the term "Data mining" has a pejorative meaning. Instead of finding<br>useful patterns in large volumes of data as in the case of Statistics, data mining has the connotation of<br>searching for data to fit preconceived ideas. Here we try to discuss the similarities and differences as<br>well as the relationships between statisticians and data miners. This article is intended to bridge some of<br>the gap between the people of these two communities.

Mathematicians from the Greeks on have used simple physical or visual models to understand and create new mathematics. The history of innovation in geometry, probability and calculus is full of examples of commonplace or mundane models explicating and motivating new ideas. Modern research statisticians also use the same strategies. Ask an expert in experimental design what he knows about and how he thinks about an industrial experiment. Often you will get an extraordinarily naive answer. You discover that he has cheerfully ignored important, even critical, physical details of the industrial process., and yet industry amply compensates our apparently naive experimental design colleagues. Perhaps industry has learned some lessons that we as teachers of statistics have forgotten. In this paper we argue that our undergraduate students need to be able to view, construct and manipulate mundane models and that this is a critical part of undergraduate mathematics and statistics education. All this may seem obvious, but in the past decades a number of forces have contributed to a decline of our students ability to approach statistics using visual model approaches to mathematics.