Research

  • This paper develops insights into how to deal with the arithmetic mean in the initial phases of statistics instruction. It focuses on one of the various ways in which the mean can be used in statistics: as a normalized ratio. The paper analyzes individual interviews of 12 12-year-old students prior to their participation in a classroom teaching experiment. These interviews were used to test and develop instructional conjectures about how to support students' understanding of the mean and other normalized ratios. Three differences where detected in how students seemed to make sense of proportional comparison problems in which the use of the mean as a ratio is pertinent. The paper explains how these findings can be capitalized upon in designing and conducting instruction.

  • This paper focuses on 6-8 year-old children's thinking about randomness. It reports the findings of a study in which the children engaged with a game-like environment to construct for themselves spatial representations of sample space. The system was designed so that the rules governing the relationships between the selection of elements of the sample space and the outcomes of the game were available for inspection and reconstruction by the children. In response to a range of tasks, the children manipulated the sample space in ways that generated corresponding outcomes in the game. We present a case study of children's activities, which illustrates how the novel medium mediates the children's expression and understanding of chance events.

  • 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.

  • 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.

  • This paper describes the main results of a research project carried out in Italy at every school level to compare how different teaching approaches influence the students' learning process. The experiment involved more than 6000 pupils (age 6-19) at every school level and 338 teachers.

  • The sociocultural perspective draws attention to students' development of a sense of who they are in relation to statistics as an integral aspect of their learning. This focus on students' construction of identities as doers of statistics relates directly to a number of issues that are of immediate concern to most teachers including students' interest in and motivations for studying statistics. We present the results of a classroom design experiment in which a group of 12-year-old students developed identities as people who chose to engage in, saw value in, and viewed themselves as competent at developing data-based arguments. We also discuss aspects of the design experiment that appeared to play an important role in supporting the students' development of these positive orientations towards statistics.

  • We report the findings of a detailed study of the ways in which a group of paediatric nurses think about the notion of average and variation. We describe some continuities and discontinuities between mathematical and nursing epistemologies, and draw some general conclusions about the ways in which more general mathematical meanings are constructed and 'transferred' that takes account of both cognitive and sociocultural perspectives.

  • The role of Statistics is becoming increasingly important in today's society. According to several authors, collaborative work has shown to be one of the most adapted forms of facilitating knowledge appropriation and the mobilisation of competencies. The project Interaction and Knowledge has studied and encouraged peer interactions in the Mathematics class, in association with a new didactic or experimental contract, as a way of promoting pupils' performances, allowing them to reach relational knowledge. By analysing excerpts of these interactions we can understand the facilitating character of this working method.

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