# Teaching

• ### Analysis of didactic situations suggested to distinguish disjunctive events and independent events.

The concepts of disjunctive events and independent events are didactic ideas that are daily used in the classroom. Previous observations of attitudes and assessment given to students at university level who attend the introductory Statistics course have helped detect the confusion between disjunctive events and independent events, and indicate the spontaneous ideas that students tend to elaborate about both concepts in the different situations in which these notions have to be considered. However the relation between these ideas and their formal definitions is not known in detail. In this work, we use Didactic Engineering as methodology to analyze students' misconceptions, their persistence, and the process by which the student confronts his misconceptions by applying theoretical concepts. The aim is to improve the teaching of these topics.

• ### Does viewing video of statistics in action affect student attitudes?

Recent studies have indicated that student attitudes can assist or impede learning and that students tend to have negative attitudes towards mathematics and statistics. We used a treatment-control experimental design to explore the effects of using video clips, showing applications of statistics in real world settings, on student attitudes toward statistics. Students with higher scores on standardized tests of mathematical and verbal ability, who were exposed to the video treatment, had more positive attitudes toward statistics than video exposed students with lower ability scores and more than students who were not exposed to the video treatment.

• ### The total probability theorem, the "depends" argument and simulation.

As an alternative to the Total Probability Theorem, the "depends" argument that students use to calculate marginal probabilities is studied. We discuss an experience with undergraduate engineering students who took a computed aided basic probability course based on the frequency approach. The result of this experience shows that an adequate interpretation of the outcomes of simulated random experiments allows conjecturing and arguing algebraic results of the theory of probability.

• ### Statistics education applied to agroforestry area (2005).

Basic subjects play an important role in engineering education. Applied Statistics may be regarded as a basic subject as well as a technical subject, and occupies therefore a central place in agro-forestry engineer professional curriculum. Statistics is present in some proportion in our whole life. With the purpose of implementing new methods for statistical learning, in the framework of European Higher Education Area, an experimental proof has been started during a quarter of academic year 2004/05 of the third class in the Faculty of Forestry Engineers from Polytechnic University of Madrid. Methodology was oriented for students to improve capacities of oral expression, information search, use of recent technologies and experience in knowledge analysis and synthesis, together with acquisition of minimum knowledge required in the subject.

• ### Designing statistical learning opportunities for industry.

Our interest in the techno-mathematical literacies employees need in their jobs has led us to do case studies in different industrial sectors and to design learning opportunities for improving employees' techno-mathematical literacies. We conceptualise the learning opportunities not as training or transfer, but as forms of "boundary crossing" between employees from a company and us as researchers. Two examples are given in which packaging managers explore and discuss a realistic problem using TinkerPlots, an educational software tool. The results emphasise how important it is to allow managers to bring their ideas and concerns to the problem situation so they can connect these to statistical theory that is relevant in statistical process control (SPC). This approach is contrasted with SPC training we have observed in two industrial sectors.

• ### Postgraduate teaching performance evaluation system.

A postgraduate teaching performance evaluation methodology is presented starting with the design of a questionnaire applied to enrolled in the Master's in Sciences program. The evaluation instrument was divided into four sections and programmed in informatics language. Regular students answered 543 questionnaires, one per course taken during 2003 and 2004. The information was studied statistically course-by-course from a point of view both educational and psychological. The results were analyzed course-by-course taught and on an overall basis.

• ### Computing probabilities from two way tables: An exploratory study with future teachers.

Being able of correctly read and interpret two ways tables is a basic component of statistical literacy for every citizen. Therefore, future teachers who will be responsible to teach statistics to children at school level should acquire these abilities along their training. However, this capacity is taken for granted in Spain and its teaching is not usually included in the curriculum for training teachers. In this study present the results of a small exploratory study that describe the future teachers' semiotic conflicts in solving elementary probability problems when data re given in a two-way table.

• ### Project work in statistics: Statistics learning as a tool to help students' knowledge about their educational community.

The development of students' competencies expressed in current curricular documents is a complex task that teachers have to perform (Brocardo, 2005). Project work is a practice that can allow for this development (Abrantes, 1994). According to the Portuguese Department of Basic Education (2001), project work, namely in statistics, is one of the learning experiences that all students should have the opportunity to engage in. This study is a part of the research project Interaction and Knowledge, whose main goal is to study and implement collaborative work within classrooms. We discuss how students from two 7th grade classes (compulsory education, 12/13 years old) used project work in statistics to learn more about statistical contents, about their colleagues, and to develop social, cognitive and affective competencies.