Literature Index

The project will research the effectiveness of new information and communication technologies in teaching various scientific and mathematical concepts at secondary level. The project focuses in particular on the analysis of complex data. We will use and adapt innovative instructional material and analyze students' competencies by means of classroom observations and clinical interviews. The interactive constitution of meaning in classroom discourse will be analyzed by means of new interpretative methods of research into classroom interactions. Our goal is to identify and describe more precisely various conceptual barriers that make statistical reasoning difficult for secondary students and to develop and test an instructional sequence that would enable such reasoning at a rudimentary, but statistically valid, level. The project is situated in the context of interdisciplinary research in mathematics education (didactics of mathematics) with relations to the didactics of the sciences.

Evaluation, analysis and interpretation of data is an important task of all sciences. Students should be introduced to a critical relationship with numbers. As an example, the two aspects measurement of a single value and investigation of the functional interrelationship of two measured values are discussed. The current mathematical subject should be applied, practised and constantly repeated. The proposed examples are interesting experiments, which allow us to mix empirical and mathematical conclusions. (orig.)

Conceptual understanding of statistics is usually considered one of several aspects of statistical knowledge. It refers to the ability of students to tie their knowledge of statistical ideas and concepts into a network of interrelated propositions. In this study an attempt was made to analyze the theory of descriptive regression analysis into its constituent propositions. Content analysis of the work of nine students revealed that these propositions were used by the students as cognitive units in their mental representation of the statistical theory. Suggestions for a use of constituent propositions as learning tools are discussed.

In this article, I introduce a novel applet (“module”) for exploring probability distributions, their samples, and various related statistical concepts. The module is primarily designed to be used by the instructor in the introductory course, but it can be used far beyond it as well. It is a free, cross-platform, stand-alone interactive application based on Wolfram Research’s novel computable document format (CDF) technology. It features over thirty common discrete and continuous distributions and can be used to illustrate concepts such as random samples, population and sample means and medians, histograms, kernel density estimators, boxplots, and cumulative distribution, survival, and hazard functions all while dynamically linking samples and estimators to adjustable distribution parameters in real-time. Additionally, the module includes real-world datasets to aid in communicating the concept of fitting a distribution to data. It is hoped that the module will be helpful to instructors at both the high school and college levels for the conceptual understanding of distributions. A simplified version geared specifically toward out-of-class student learning in the introductory course is also made available for students’ use. Both are accessible from http://www.baylor.edu/statistics/disttool.