Literature Index

This study was carried out as a preparation to the development of instruction material for statistics. The history of statistics was studied with special attention to the development of the average values: the arithmetic, geometric, harmonic mean; median, mode, and midrange. Also sampling and distribution are discussed. After an introduction on phenomenology, this article firstly discusses a so-called historical and then a didactical phenomenology of the average values.<br>The average values form a large family of notions that in early times were not yet strictly conceptions. It appears to be important that students discover many qualitative aspects of the average values before they learn how to calculate the arithmetic means and the median. From history, it is concluded that estimation, fair distribution and simple decision theory can be fruitful starting points for a statistical instruction sequence.

This article demonstrates that art may inspire statistical thinking in many ways, providing aesthetic pleasure, scientific enlightenment, and humorous excitement. Art can serve as a fine tool for educational purposes in statistics, presenting explicit illustrations of statistical concepts. The role of statisticians here is to find a hidden meaning of a masterpiece and to interpret it for students. This work gives some examples of such an interpretation of painting from a statistical perspective.

The focus of this chapter is on research in conditional probability and independence that uses both with- and without-replacement tasks. Probabilistic thinking about conditional occurrences as well as independence are explored. A framework postulates that middle school students' thinking in conditional probability and independence could be described and predicted across four levels that represent a continuum from subjective thinking to numerical reasoning. Then implications for teaching and learning are considered, emphasizing the fostering of understanding.

Both researchers and teachers of statistics have made considerable efforts during the last decades to re-conceptualize statistics courses in accordance with the general reform movement in mathematics education. However, students still hold misconceptions about statistical inference even after following a reformed course. The study presented in this paper addresses the need to further investigate misconceptions about hypothesis tests by (1) documenting which misconceptions are the most common among university students of introductory courses of statistics, and (2) concentrating on an aspect of research about misconceptions that has not yet received much attention thus far, namely the confidence that students have in their misconceptions. Data from 144 college students were collected by means of a questionnaire addressing the most common misconceptions found in the literature about the definitions of hypothesis test, p-value, and significance level. In this questionnaire, students were asked to select a level of confidence in their responses (from 0 to 10) for each item. A considerable number of participants seemed to hold misconceptions and lower levels of concept-specific self-perceived efficacy were found to be related to misconceptions more than to the correct answers. On average, students selected significantly lower levels of confidence for the question addressing the definition of the significance level than for the other two items. Suggestions for further research and practice that emerge from this study are proposed.