The focus of the present article will be on one variety of inductive recombination--the use of analogies (particularly analogies between situations drawn from relatively remote knowledge domains) to solve novel problems and to form generalized rules.
A key element in developing ideas associated with statistical inference involves developing concepts of sampling. The objective of this research was to understand the characteristics of students' constructions of the concept of sample. Sixty-two students in Grades 3, 6, 9 were interviewed using open-ended questions related to sampling; written responses to a questionnaire were also analyzed. Responses were characterized in relation to the content, structure, and objectives of statistical literacy. Six categories of construction were identified and described in relation to the sophistication of developing concepts of sampling. These categories illustrate helpful and unhelpful foundations for an appropriate understanding of representativeness and hence will help curriculum developers and teachers plan interventions.
This chapter reports on student performance with data and chance by examining individual 1996 NAEP items or clusters of related items and where available samples of student responses to constructed-response questions. The focus of this chapter is on four categories that are often interrelated: central tendency, reasoning with data, graphical data displays, and probability and chance. In addition to reporting and interpreting performance based on NAEP results, for some short and extended constructed-response items we also examined a set of sample student responses. This sample was not a representative sample of all responses; rather it was a convenience sample of non-blank responses. Some of the items described in this chapter were extended constructed-response tasks, a type of NAEP item that is discussed extensively in chapter 11 by Silver, Alacaci, and Stylianou.
The objective of this chapter is to consider the practical implications of the biases observed in experimental studies of human reasoning and to discuss the ways in which we might limit the potential damage that such biases inflict on real life thinking and decision making.
This paper discusses many different aspects of the concept of data handling, which is described as an holistic approach to dealing with data, involving a frame of mind as well as an environment within which one can explore data, rather than just covering a body of specific statistical content.
In this paper we will first explore some of the reasons for people's failure to solve problems, problem-solving "derailers" so to speak, and investigate the role of probabilistic misconceptions as one possible derailer. Second, we will consider the implications of what can "go wrong" when we solve probelms for research on the teaching of problem solving.
This paper explores the phenomenological and curricular dynamics of implicit mathematical structures embodied in "transparent" computer-based tools. Examples from a clinical study of students working with the Tabletop database/data analysis environment illustrate the process by which disruptions of transparency can provoke increasingly reflective use of a tool and bring students into engagement with valuable mathematical ideas. The interaction among learner, medium and curriculum is seen to have important implications for pedagogy, tool design, and evolving conceptions of mathematics.
In this chapter, we concentrate on statistics education at the college level. We summarize the literature related to women and math; women and statistics in college, including statistics performance and attitudes toward statistics; and two cognitive models relevant to learning statistics. We then discuss a number of topics relevant to teaching college statistics: the overall approach for the course, structural and organizational issues, presentation of numbers and formulas, computers and technology, process issues, recommended study strategies, counseling and advising, sexism, and classroom assessment. Finally, we provide some overall conclusions. Readers who want a more detailed review and a greatly expanded reference list are requested to contact us.
This chapter focuses on the problem of improving young adults' statistical reasoning skils, with particular emphasis on transfer outside the original learning context.
This paper will document four instruments devised to assess student understanding of statistical concepts. Two are intended for large scale administration and two are for individual differences.