# Chapter

• ### Monitoring attitudes and beliefs in statistics education

Students' attitudes and beliefs can impede (or assist) learning statistics, and may affect the extent to which students will develop useful statistical thinking skills and apply what they have learned outside the classroom. This chapter alerts educators to the importance of assessing student attitudes and beliefs regarding statistics, describes and evaluates different methods developed to assess where students stand in this regard, provides suggestions for using and extending existing assessments, and outlines future research and instructional needs.

• ### A framework for assessing knowledge and learning in statistics (K-8)

This chapter provides an overview for thinking about what teachers and students should know and be able to do with respect to learning statistics at the K-8 levels. Given the number of concepts to be considered and our limited knowledge about the complexities of learning these concepts, we focus on the understanding of graphical representations, examine examples of "good tasks" that may be used to assess graph knowledge, and reflect on what we have learned about the complexities of assessing students' graph knowledge, when using these tasks.

• ### Using "real-life" problems to prompt students to construct conceptual models for statistical reasoning

The purpose of this chapter is to examine a "model-eliciting activity", based on a "real-life" problem situation, in which students were provided with an opportunity to construct powerful ideas relating to data analysis and statistics, without explicitly being taught. Student results of this activity will be examined that reveal the somewhat surprising fact that children, even those who traditionally do not perform well in mathematics, can invent more powerful ideas relating to trends, averages, and graphical representations of data than their teacers ever anticipated. The student results shared in this chapter are not unique. In classrooms where we have piloted and refined problems (including the ones presented), one common observation is that many of the children who emerge as "most productive" are often those whose mathematical abilities had not been recognized or rewarded by their teachers in the past.

• ### Simple approaches to assessing underlying understanding of statistical concepts

Statistics should be introduced with clear linkages to the mathematics that students already understand and within contexts that students find meaningful. Otherwise, students may learn statistics in rote fashion or apply statistics in a merely instrumental fashion and draw erroneous conclusions from data. In this chapter we present two examples of the use of simple assessment techniques that uncovered students' poor understanding of statistical concepts.

• ### Assessing students' connected understanding of statistical relationships

We believe that connected understanding among concepts is necessary for successful statistical reasoning and problem solving. Two of our major instructional goals in teaching statistics at any level are to assist students in gaining connected understanding and to assess their understanding. In this chapter, we will explore the following questions: (1) Why is connected understanding important in statistics education?, (2) What models of connected understanding are useful in thinking about statistics education?, (3) How can connected understanding be represented visually?, and (4) What approaches exist for assessing connected understanding?

• ### Assessing statistical thinking using the media

The goals of this chapter are (a) to address the need to assess statistical thinking as it occurs in social settings outside the classroom, (b) to suggest a hierarchy for judging outcomes, (c) to provide examples of viable assessment based on items from the media, and (d) to discuss the implications for classroom practice.

• ### Assessing students' statistical problem-solving behaviors in a small group setting

The ability to interpret and predict from data presented in graphical form is a higher-order thinking skill that is a necessity in our highly technological society. Recent recommendations for the mathematics and science education communities have therefore stressed the importance of engaging learners in real life statistical tasks given in a setting that will promote effective problem solving. Since the small-group setting has been shown to be a fertile environment in which problem solving can occur, we have used that setting for engaging students in data analysis tasks. However, there is a dearth of ideas related to how to assess students' behavior, thinking, and performance in such a setting. The purpose of this chapter is to describe a framework for assessing students' problem solving behaviors on a graph task as they work within a small-group setting.

• ### Assessing student projects

The main purpose of this chapter is to offer practical advice to teachers who want to use projects in their courses. In this chapter some examples of projects are given, two assessment models are explained, and teachers' experiences are described. The project models and examples described have been used with students of 14 to 18 years of age, but can be adapted for younger or older students as well.

• ### Assessing project work by external examiners

Over a number of years the external examiners of a regional statistics course for 18-year-old students in schools and colleges in the United Kingdom became aware that the method of assessment was distorting the teaching and learning process, that the things being assessed were not the things that the examiners thought most important for the students to know. This chapter shows how the assessment methods were changed by adding in a compulsory project and reflects on the impact of this change on the teaching and learning of statistics.

• ### Portfolio assessment in graduate level statistics courses

In this chapter, the process of developing a form of alternative assessment, the portfolio, will be described. The portfolio is a purposeful collection of student work that exhibits the student's efforts, progress and achievements over time. Portfolio develpment supports the assessment of long-term projects, encourages student-initiated revision and provides a context for presentation, guidance, and critique. The purpose of portfolio development is the same no matter the course or age of the students, to display the products of instruction in a way which challenges teachers and students to focus on meaningful outcomes. The context in which the use of portfolios is described here is a graduate level statistics course where an additional purpose is to provide students with an organized reference on statistical programming, analylsis, and interpretation. However, the process used in developing portfolios and the important issues surrounding portfolio assessment can easily be generalized to different educational levels and subject areas. Some of the questions addressed in this chapter are 1) What is the underlying belief concerning knowledge construction which guides portfolio assessment?, 2) How do you develop and use portfolios?, 3) What does a portfolio look like?, and 4) What are the major considerations in deciding to use portfolio assessment?