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Chapter

  • The chapter does not provide an extensive overview of the use of technology in statistics. Rather, a detailed summary is provided of how one researcher has used technology to teach and assess statistics in grade eight. Both traditonal modes of assessment as well as technology-driven methods will be described in an attempt to demonstrate how multiple mediums of assessment can be used to provide a profile of students' statistical knowledge. The research reported here is grounded in cognitive theory with an emphasis on theories of learning that emphasize learning situations that are concrete rather than abstract. In other words, students learn better by "doing" statistics rather than just computing or reciting statistical equations or definitions. This research program is designed to provide authentic learning and assessment situations (Lajoie, 1995). The term authentic refers to meaningful, realistic tasks and assessments that validly assess what the learner understands.

  • When constructing assessment instruments both the purpose of the assessment (feedback, grading) and the skills which are being assessed need to be considered. The main purpose of this chapter is to help teachers develop their own assessment instruments by giving specific examples of tasks. Unsatisfactory tasks are used to illustrate the pitfalls, and alternative versions are given as examples of good practice. Some comments on grading are included. The emphasis is on written assessment in the classroom, mainly of pupils aged about 14-19, but much is relevant also to introductory statistics courses at college and university level. Consideration is given to ways of assessing factual knowledge, the ability to use computers, understanding of concepts and application of techniques, and communication skills. The pros and cons of multiple choice and open-ended questions are discussed as are the challenges of oral assessment and assessment of group work.

  • Because many of the authentic assessment methods described in this book tend to be very demanding of teacher-time, there is still an important place for finding ways to employ inexpensive, traditoinal methods more creatively in an attempt to come closer to achieveing the same goals that those who advocate authentic assessment methods are targeting. The basic idea is to identify the elements of statistical thinking that we want to foster and then find ways of testing these elements with objective assessment methods (in particular, multiple choice). The chapter explores the extent to which objective testing can approximate the results of authentic assessment techniques and the extent to which it falls short. We provide guidelines for the writing of objective test items, together with examples.

  • Randomness and chance variation are key ideas that can function as goals in young students' understanding and application of chance. In this chapter, I examine how these key ideas involve construction of new concepts, as well as beliefs about the place of chance in the world. These ideas are considered from the perspective of the mathematics or statistics classroom culture; i.e., how the classroom culture reflects and fosters beliefs about the place of uncertainty and chance in the world.

  • In this chapter we provide some answers to the following questions: (1) What is combinatorics and what role does it play in teaching and learning probability?, (2) What components of combinatorial reasoning should we develop and assess in our students?, (3) Are there any task variables that influence students' reasoning and provoke mistakes when solving combinatorial problems?, and (4) What are the most common difficulties in the problem-solving process? How should we consider these variables in the teaching and assessment of the subject? We illustrate these points by presenting some examples and test items taken from different research work about combinatorial reasoning and samples of students' responses to these tasks.

  • While mathematics education guidelines have encouraged substantial change in the introductory probability and statistics curriculum, probability distributions still remain an important topic in a first course. In fact, just as software has made data analysis more accessible to students in introductory courses, it also offers new ways to teach probability distributions. However, these new teaching technologies, which emphasize active experimentation and interpretation of displays, also raise new questions. Just what do students see when they exmaine a display of a probability distribution? Do the displays really help students acquire a clear conceptual understanding? Can interactive exercises for related concepts like sampling distributions make good use of displays? Finally, can good assessment practices help us learn when displays are effective and when they might be confusing? This chapter will discuss some interactive, computer-based exercises that use and teach probability distributions, and consider how assessment can help address some of the important questions these new teaching technologies raise.

  • Statistics is the science of modeling the world through theory-driven interpretation of data. Models of chance and uncertainty provide powerful cognitive tools that can help in understanding certain phenomena. In this chapter, we consider the development of children's models of chance and uncertainty by considering their performance along five distinct, albeit related, components of a classical model of statistics: a) the distinction between certainty and uncertainty, b) the nature of experimental trials, c) the relationship between individual outcomes (events) and patterns of outcomes (distributions), d) the structure of events (e.g., how the sample space relates to outcomes) and e) the treatment of residuals (i.e., deviations between predictions and results). After discussing these five dimensions, we summarize and interpret the model-based performance of three groups as they solved problems involving classical randomization devices such as spinners and dice. The three groups included second-graders (age 7-8), fourth/fifth-graders (age 9-11), and adults. We compare groups by considering their interpretations of each of these five components of a classical model of chance. We conclude by discussing some of the benefits of adopting a modeling stance for integrating the teaching and learning of statistics.

  • This chapter focuses on our work in middle schools. We describe the implementation and evaluation of a three-week instructional unit that was adapted to three different subject-matter contexts (science, social studies, and mathematics). In all contexts, the purpose of the unit was to improve students' abilities to think and reason statistically about real-world issues.

  • This chapter focuses on the Authentic Statistics Project (ASP). The goal of this project is to make statistics meaningful to students in middle school, grade eight in particular, and to assess the type of progress students achieve in learning statistics.

  • This chapter explores the different paths that educators can take as they move toward a successful statistics curriculum where students are expected not only to learn but to learn key concepts.

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