Conference Paper

• Probabilistic thinking, statistical reasoning and the search for causes: Do we need a probabilistic revolution after we have thought data analysis?

My interest is in the relationship between probability and statistics (data analysis) with regard to teaching and learning. Ideas for teaching (exploratory) data analysis with no preparation in probability emphasize, among other things, finding relationships in sets of variables, identifying relevant variables, interpreting data with regard to sources of variation, possible explaining factors and causes. Probability is often introduced as an antithesis to deterministic situations. Some empirical research even blames children for looking for causes where there is "really" randomness. There is other research taking positions against stochastics.

• Combinatorics and its teaching: Analysis of teachers' responses to a survey

In this work teachers' responses to a survey about combinatorics and its teaching are analyzed. Participants were 22 in service teachers and 14 trainee teachers who respond to questions concerning actual teaching methodology, suggestions for change, and students' difficulties and interest in combinatorics. We present information about the following aspects: content being taught, time spend for it and its planning, types of problems proposed to students and their relative difficulty in opinion of those teachers and suggested changes for teaching of the subject.

• Identifying and Alleviating Problems Novices Have While Learning Formulae

In this study I investigate what elements of statistical formulae cause people to perceive said formulae as difficult. The perception of difficulty is important because it affects how and what people study as well as the amount of time they devote to study. By understanding how people perceive formulae we can design our instruction to accommodate these perceptions. I approach this investigation from three major theoretical bases. The first theoretical base will concern cognitive load. Are students intimidated by certain formulae because the formulae contain to much information to be held in working memory? The second theoretical base will concern motivational perceptions. Are there aspects of certain formulae which cause students to perceive certain formulae as more difficult and thereby stimulate negative emotions that interfere with the efficient use of working memory. The third theoretical base involves impasse drive learning. When learners reach a cognitive impasse, are they able work around it. If learners can work around certain impasses and not others, how do the impasses they can work around and those they cannot work around differ?

• The Affective Component of Attitude in Statistics Instruction

Suggestions from the literature for dealing with students' statistics anxiety are listed in this paper. The role of motion in learning is reviewed and results of a small correlational study are used to illustrate the association between the affective component of attidude as a measure of anxiety and statistics performance for classes of education students. Strategies the author has found helpful are presented.

• Authentic Assessment of Statistical Reasoning in Cooperative Learning Environments

This paper describes two case studies that examined statistical reasoning skills in an authentic environment in which learning occurred in small groups. Multiple forms of assessments were developed to obtain a detailed profile of reasoning demonstrated by individual students and groups of students on projects. Two conditions were developed by individual students and groups of students on projects. Two conditions were developed to exemplify assessment criteria on such projects: a library of exemplars condition and a text condition. Qualitative analyses of verbal protocols during group discussions and presentations indicated that the library of exemplars was effective in promoting (a) reasoning about data analysis and data presentation issues (b) planning and (c) aligning students ratings of projects with experimenter ratings. The importance of student participation and request for assistance in group situations was highlighted in this study. Moreover, information about the reasoning demonstrated by individual students is required to ensure that group assessments do not overestimate student performance.

• How does Group Composition and Gender Influence the Learning of Statistics?

The purpose of this study was to examine how group composition and gender influences the learning of statistics for eighth grade mathematics students. Students participated in an extended grup project where they designed a research question, collected, analyzed, and interpreted data using the computer. Same-gender mixed ability groups were randomly assigned to two exemplar conditions (text vs. video and text). Assessment criteria were described to students prior to their project development through exemplar conditions, video and text was thought to be more explict. An Analysis of Variance of Condition (text or text and video) by Gender (male or female) by Test (pre, post) revealed no condition effect, but females performed higher than males on a post-test of statistical knowledge. Gender differences were also noted in journal keeping. Implications of these results are discussed.

• Lesson transcripts and their role in the in-service training of mathematics teachers

This paper discusses the dilemma in the cooperation between teachers and scientists and introduces the cooperative project which should help to improve the understanding between them.

• The practice of teaching and research in didactics

The traditional role of educational research and theory for the mathematical teaching practice has been increasingly and extensively questioned during the last decade. There is something wrong with the usual understanding of the theory-practice-relation. Theories - be they as detailed and comprehensive as possible - cannot be transferred directly into the teacher's practice nor can they be applied immediately. Educational research cannot automatically improve teaching practice. Research results cannot be disseminated into teacher's practice simply in a strategy "from the top down". In one word, the old idea that the relationship of theory to practice is of a linear nature in a way that the theoretical results developed in research - if they are only adequately elaborated and made explicit - can be handed over to practice for immediate use will not longer work.

• Proposal of curriculum for teaching probability and statistics

Described here is the project for the teaching of elements of Probability and Statistics at the ages of 11-14. It is the result of the work of the Didactic Research Group of Pavia (1); formed of 5 university researchers and about 20 in-service teachers.

• Computer simulations of probability challenges: From data to theory

In this paper we will briefly address the use of microcomputers in the classroom to enhance data collection and data analysis for stochastic experiments. The approach that we have in mind is appropriate for middle school (lower secondary) students, secondary school students, preservice teachers at the college and university level, and inservice teachers doing post-baccalaureate work.