# Chapter

• ### Mere literacy is not enough

As computers enhance the value of verbal, visual, and logical skills needed to reason with data, more than ever citizens and employees need skills in quantitative reasoning that create a tapestry of meaning blending context with structure.

• ### Probability concepts: Putting research into practice

The Chance and Probability Concepts Project, directed by the author at Loughborough University from 1978-81 (Green, 1982a) revealed the very limited understanding which 11-16 year old English School pupils have of probability concepts. A previous article in Teaching Statistics (Green, 1983) presented a general report of the research findings and made some recommendations. This article describes an attempt to follow up the research with practical class based activities using the computer to improve pupils' understanding.

• ### Session Seven--Lab Activity

A common experiment in investigating consumer preferences is to give a sample of potential customers two competing products and ask them which they prefer. The statistical inference involves the proportion of the population of potential consumers who prefer a particular product.

• ### Assessing statistical knowledge as it relates to students' interpretation of data

The chapter examines the nature of interpretive skills that students need to acquire in statistics education, with a special focus on the role of students' opinions about data. Issues in the elicitation and evaluation of students' opinions are examined, and implications for assessment practices and teacher training are discussed.

• ### Aligning everyday and mathematical reasoning: The case of sampling assumptions

In this chapter, we present results from three studies that examined and supported 5th- and 6th-grade children's evolving notions of sampling and statistical inference. Our primary finding has been that the context of a statistical problem exerts a profound influence on children's assumptions about the purpose and validity of a sample. A random sample in the context of drawing marbles, for example, is considered acceptable, whereas a random sample in the context of an opinion survey is not. In our design of instructional and assessment materials, we have tried to acknowledge and take advantage of the role that context plays in statistical understanding.

Statistics is not about numbers, statistics is about numbers in context. Statistics is not the same as probability. But some probability is necessary to understand certain statistical topics, while other statistical topics do not depend on probability. Statistics is not the same as mathematics. But an appropriate level of mathematics is needed to understand any statistical topic, and understanding statistics can contribute to an understanding of mathematics. Statistics is not the same as the scientific method. Yet statistics helps solve problems in science, engineering, medicine, business, and many other fields. Using statistics is inherently interdisciplinary. While using statistics demands that one understand the problem, the reason that statistics is so powerful is that key statistical concepts, methods and ideas are applicable in so many different problem contexts. This paper discusses the key concepts in statistics that students must learn in the K-12 curriculum so that all high school graduates can become productive citizens and use quantitative information effectively. The topics are organized and discussed in terms of number sense, planning studies, data analysis, probability, and statistical or inferential reasoning.

• ### Emergent ideas of chance and probability in primary grade children

The National Council of Teachers of Mathematics has recommended that we incorporate chance and probability as a thematic strand throughout children's formal schooling, beginning at the kindergarten level. This recommendation comes at a time when there is little agreement concerning the psychology of chance and probability. This is particularly disconcerting, given the importance now given to building on children's intuitions in the instructional process. The chapter addresses these issues as they involve the successful implementation of the K-4 statistics and probability standard, through an analysis of releveant research literatures. These literatures indicate that primary grade children have a number of intuitions that are directly relevant to statistical instruction. These include intuitions about relative magnitude and part/whole relations, incertitude and indeterminancy, the likelihood of a given event and, much more limited, intuitions about expected distrubutions of outcomes. The chapter also considers challenges to primary grade children's reasoning in this sphere that instruction needs to address, including conceptual gaps such as the idea of patterns in outcomes over the long haul, the restructuration and elaboration of children's intuitions, raising the meta-level of children's knowledge, and the issue of appropriate application.

• ### Curricular goals and assessment challenges in statistics education

This chapter frames the main issues with which this volume deals. The chapter examines common goals for statistics education at both precollege (school) and college levels, describes the resulting challenges for assessment in statistics education, and outlines the main issues addressed by each of the chapters in this volume. Finally, needs for future research and development are discussed.

• ### Some emerging influences underpinning assessment in statistics

A number of influences impinge on statistics education. This chapter focuses on three of these that are especially noticeable at the K-12 level but also operate to some extent at the college level: a) the changing place of statistics in the curriculum, b) the emphasis on processes in the mathematics curriculum, and c) new ideas about learning and the ways that assessment is viewed in education in general. These, together with the purposes and principles of assessment, are explored because they underpin aspects of assessment in statistics education.

• ### Authentic assessment models for statistics education

Authentic assessment is an emerging field within assessment models. It claims to measure by direct means the student performance on tasks that are relevant to the student outside of the school setting. Most educators will agree with the need to assess learning within the context of applications. This chapter will address the following issues: (1) a vision of an effective assessment system must be articulated--what are the standards (visions) for an effective assessment system?, (2) a well-thought-out plan for designing an effective program must be constructed--what are the components of a process for designing an effective authentic assessment program?, (3) classroom teachers readiness to change assessment plans is crucial to any program of assessment--how do you determine the degree of readiness of classroom teachers for a new assessment plan?, and (4) promises abound in the assessment field but limitations can strangle an assessment program at conception--what are the promises and limitations of recent assessment reforms? A crucial aspect of teaching and learning is knowing what and how much is learned. Assessment should be the source of this information. This chapter will give a glimpse of how to design an authentic assessment plan in statistics education.