# Theory

• ### Software tools and mathematics education: The case of statistics

The overall goal of this chapter is to discuss perspectives for using technology in statistics education. For this purpose, we will analyse and illustrate new revolutionary developments in statistics itself. We intend to make sense of statistical software tools by relating them to subject matter developments and to analytical perspectives generated by the requirements of software from a didactical point of view. New developments in statistics education and curriculum dependent educational software tools will be critically related to the technological and subject matter changes outside school.

• ### Towards lean and lively courses in statistics

The present paper represents a summary of the results of a workshop on statistical education.

• ### Teaching statistics as a representable subject

In discussing the teaching of statistics, I will first show why statistics is not properly considered as a field of mathematics. Then I will illustrate the inadequacy of the theory-driven mode of teaching through discussion of a simple setting that is considered in every first course. Finally, I will make some comments on useful principles and content for teaching statistics as statistics.

• ### Experience is the best teacher

Because of the abstract nature of fundamental concepts in statistics, full understanding of the most basic concepts can be elusive for students. While some students are apt at mimicking the professor's choice of terminology or application of a particular procedure, they often lack an intuitive feel for or visualization of key concepts. As professors, we need to be aware that correct answers do not necessarily indicate understanding. We need to give students experiences that go beyond textbook exercises in order to prove their understanding of statistical concepts and then to push students to deeper levels of understanding. Group projects, based on real or simulated data, are an effective means of accomplishing these goals.

• ### Training teachers for teaching statistics

In what follows we intend to focus our attention on the cognitive-development aspects and their didactical implications of the teaching of statistics.

• ### Improving students' attitudes towards statistics

This paper looks at the question of students' attitudes towards statistics and suggests ways of improving their feelings about this subject.

• ### An authentic assessment of students' statistical knowledge

Probability and Statistics are increasingly being given an important place in the K-12 mathematics curriculum. According to the NCTM Curriculum and Evaluation Standards (1989), students should learn to apply probability and statistics concepts to solve problems and evaluate information in the world around them. The statistics standards suggest using hands-on activities involving collecting and organizing data, representing and modeling data including the use of technology, and communicating ideas verbally and in written reports. Teachers are encouraged to help students develop important ideas (for example, about distributions, randomness, and bias) and gain experience in choosing appropriate techniques to use in analyzing data. Many teachers are currently using materials from recent projects or projects in development that have developed curricula and software to implement the NCTM Standards (e.g., the Quantitative Literacy Project, the Reasoning under Uncertainty Project, and the ChancePlus Project). These new materials encourage teachers to have students work on statistical projects: formulate research questions, collect and analyze data, and write up the results. Working on statistical projects individually or in groups engages students in learning about statistics and helps them to integrate the knowledge they have learned.

• ### Reforming the introductory statistics course

This paper discusses the movements involving reform of statistical education, both at the college and precollege level. In addition, one model for a revised introductory course, based on the two reform movements is included. This course is based on the following components: Involvement with real data, emphasis on exploring data, use of new software and technology, oral and written communication, and confronting misconceptions

• ### How students learn

This paper focuses on the theme of statistical education and includes the following topics: 1. Theories of learning: how we think students learn 2. What we would like students to learn: in terms of statistical ideas, concepts, skills and beliefs 3. Research on teaching and learning statistics 4. Research on teaching and learning mathematics that relates to teaching and learning statistics 5. Implications of research for teaching statistics 6. One example: an alternative statistics course 7. What we still need to find out: a research agenda 8. Current projects

• ### The theoretical nature of probability and how to cope with it in the classroom

In this paper the role of the theoretical character of stochastics is considered for the teaching process and its organisation. The consequence of the theoretical character of stochastic knowledge - or the fact that the basic concepts cannot completely define probability theory, but are conversely only formed while developing probability theory - is that the teaching process must be organized differently. It is inappropriate to start from ready-made concepts, gradually adding further knowledge. Conversely, it is necessary to begin with meaningful situations which permit the forming and developing of concepts. Freudenthal characterizes this inversion of the teaching method by introducing mental objects.