Proceedings

  • This paper will report on outcomes observed in an investigation that involved teaching chance and data with an emphasis on understanding the part that variation plays in processes associated with chance measurement and data collection/analysis. Classes of students in grades 3, 5, 7, and 9 took part in the study but this report will focus on children in grade 3. They were taught a unit of 10 lessons over eight weeks and given pre and post tests in association with the teaching of the unit. Of interest was not only their learning about basic probability and data handling but also their developing understanding of the influence that variation has on outcomes in relation to the observation of pattern. The question of the age at which children can start appreciating the influence of variation creates special interest in this group of students.

  • Real data and statistical techniques can motivate many traditional mathematical topics at the secondary level. Collectively, the important statistical ideas and ways of reasoning can be developed in the context of studying mathematics. The study of formulas, linearity, centers, inequalities, matrices, and logarithms can be embedded in data and statistics and used to lay the foundation for the mathematics and to demonstrate the relevance of statistics to the world. Data Driven Mathematics provides teachers and students with application based activities that makes this happen and that can be used in conjunction with a standard mathematics course or to design a data based statistics course.

  • The implicit power of Statistics is that it is a tool of thinking, in particular critical thinking. The paper will clarify how can we teach statistics in order to help students to use the statistical concepts in their cognitive activities according to standards and elements of critical thinking. Some practical, interesting and different examples from secondary school statistics will be given.

  • The availability of technology opens up opportunities for students to explore larger datasets and to gain experience of the effects of random variation. We have been involved in a development project to produce materials, with a sound pedagogical basis, to support the construction of accurate conceptual understanding of key statistical concepts. This paper presents the range of materials from the project and outline the pedagogical basis for them in light of the question posed in the title.

  • The present work describes the results of a study carried out in the 1999-2000 school year in primary schools of 5 Italian provinces, which involved 145 teachers and more than 2000 pupils aged 6-10. Teaching units adopted by teachers were based on Data Oriented Approach, according to two distinct teaching strategies. One regarded the usual teaching model aiming at objectives, and the other concentrated on the learning of relationships between concepts by using a conceptual map. All the teachers involved attended a preliminary training course on statistics, pedagogy and theory of learning. Basic statistical concepts and their relationships were learnt through semi-structured interviews in class. Concept mapping gave interesting results, especially with regards to permanent acquisition of concepts. Comparison with concepts pupils had before the teaching of statistics in class and after, was carried out with entrance and exit cognitive maps.

  • The paper describes 7th graders' cooperative work on a data assessment task in a computer-assisted environment. The task was administered at the end of a carefully designed Exploratory Data Analysis (EDA) course. The purpose of the study is to assess students' ability to make sense of data and their representations: a) use of data analysis skills, and understanding of basic statistical procedures and concepts; b) if and how they adopted the dispositions and points of view of certain aspects of the EDA culture. The "local-global lens" is used to assess students' formulation of research questions and hypotheses, and use and interpretation of data representations.

  • This study examined twelve inexperienced and eleven experienced teachers' constructions of and conceptions about pedagogical representations for teaching arithmetic average. The teachers were asked to generate appropriate pedagogical representations as well as predict and evaluate the uses of different representations for solving problems involving the arithmetic average. The experienced teachers were able to predict a variety of representations as well as errors that are recognized as common among middle-school students, while the inexperienced teachers used algebraic representations almost exclusively. Additionally, the inexperienced teachers tended to value algebraic solutions over guess-and-check or visual drawing solutions, more so than did the experienced teachers. However, the differences in the experienced and inexperienced teachers' abilities to predict and evaluate the use of different representations were not clearly evident in their generation of pedagogical representations in a lesson plan context.

  • The CensusAtSchool project involves young people between the ages of 7 and 16 in gathering some simple information about themselves, which then form the basis of a national database for school children to use for data handling within many varied subject areas in school. At the very heart of the project the CensusAtSchool website http://www.censusatschool.ntu.ac.uk gives schools the opportunity to access and use the web within a learning environment. Summary data is posted on the site for schools to use along with a variety of curriculum tasks, which encourage greater use of ICT methods. South Africa and Queensland have both taking up the project within their own regions so expanding the project into providing opportunities for international comparisons to be made. The beauty of CensusAtSchool is that the data is real and the pupils themselves are fully involved.

  • This paper discusses an instructional design heuristic called "emergent modeling", with an instructional sequence on data analysis as an example. The emergent modeling approach is presented as an alternative for instructional approaches that focus on teaching ready-made representations. In relation to this, a distinction is made between modeling as "translation" and modeling as "organizing". Emergent modeling fits the latter. Within this perspective, the model and the situation modeled are mutually constituted in the course of modeling activity. This gives the label "emergent" a dual meaning. It refers to both the process by which models emerge, and the process by which these models support the emergence of more formal mathematical knowledge. This is reflected in the exemplary instructional sequence, in which the model co-evolves with the notion of distribution as an entity.

  • In most countries at the secondary school level, the statistics curriculum is a part of the mathematics curriculum. If we have a look at the papers on statistical education at the college or at the university published ten years ago, we can see that the requirements are practically adaptable to the actual secondary level. With the changes occurring in mathematical education at the secondary school level, with the development of interdisciplinary class projects especially for higher grades (9-12), with the increasing availability of computers at school, the teaching of statistics has changed. But first, we have to define the objective or more precisely the objectives, then the ways to get them and conclude with the limits and their reasons of the approach.

Pages

register