This book discusses the conceptual and pragmatic issues in the assessment of statistical knowledge, reasoning skills, and dispositions of students in diverse contexts of instruction, both at the college and precollege levels. It is designed primarily for academic audiences interested in the teaching and learning of statistics and mathemetics and for those involved in teacher education and training in diverse contexts.
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 describes the Mathematics in Context (MiC) project. This project involves presenting students with activities, in the middle grades, which help them understand how to reason from and make conclusions based on data, judge the quality of other people's conclusions, recognize the degree of uncertainty in any endeavor, and quantify the uncertainty.
This report covers the topic of assessment. It provides a broad overview of the definition of assessment and the different types of assessments (portfolio, authentic, performance), and it then discusses issues such as what the purposes of assessment are, what should be assessed, how assessment should proceed, and what the implications of assessment are for instructors.
Because assessment drives student learning, it can be used as a powerful tool to encourage students to adopt deep rather than surface learning strategies. Many standard assessment questions tend to reinforce the memorization of procedures rather than the understanding of concepts. To counteract this trend, some techniques for constructing questions that test understanding of concepts and that address specific goals of statistical education are described and illustrated with examples.
What can we as instructors do to improve the quality of student learning and our own teaching? A great deal of research findings that were compiled in the 1980s are available to inform teaching in the 1990s. These research findings can be used by statistics teachers to improve the quality of student learning and their own teaching. The purpose of this paper is to illustrate assessment methods that can be used by the instructor to improve student learning and hence our teaching. Principles of good teaching based on research and ways to implement these principles in statistics classes are presented, which, in turn, will assist a faculty member in gathering information about the learning of his or her students and about his or her teaching. This paper is divided into four sections. The first section addresses the question as to why assess the statistics course. In the second section, the topic is what to assess in the statistics course, whereas how to assess the statistics course follows in the third section. After all of the data are gathered, what you do with the assessment information is the focus of the last section.
Many of today's university undergraduate curricula include two seemingly conflicting themes: (1) increase the quality of teaching to include emphasis on pedagogical elements, such as active learning, in the undergraduate statistics classroom; and (2) cope with a decrease in teaching resources. In this paper, a means by which a department of mathematics or statistics can maintain and increase its standards of teaching excellence in introductory statistics while coping with ever-increasing budgetary pressures is proposed. This process involves promoting what we call cooperative teaching, applying the concepts
This paper describes an educational tool, Critiquing Statistics, that is designed to foster and facilitate reasoning about statistical investigations involving descriptive statistics (e.g., measures of central tendency and variability) in middle school. This tool is being developed as part of a large scale research project emphasizing statistical investigation where students generate a research question; collect, analyze, interpret, and represent data; and communicate results to peers. However, the objective of this particular tool is to provide students with a critiquing activity that enhances students reflection on their own statistical investigations and those of others. In this way, Critiquing Statistics is intended to promote self-assessment and learning as well as reasoning. Students are given opportunities to enhance their reasoning skills by critiquing statistical investigations performed by former students, after having conducted their own research. Discussions about what could be done better in the statistics projects is facilitated through technology that allows students to view digitized videotapes as well as appropriate data and graphics files. These discussions are guided by an understanding of assessment criteria for investigations, which the Critiquing Statistics environment opens up for public viewing. Students engage in small group discussions of these criteria and apply them to the projects they are required to assess. This activity thereby promotes dialogue about the appropriateness of statistical methods, data collection procedures, graphical representations, analyses, and interpretation of data. Such discussions can be used to build a community of scientific reasoners who share their knowledge, reasoning, and argumentation.
Curriculum recommendations in mathematics at international and national levels have advocated increased attention to probability instruction K-8 (Australian Education Curriculum Corporation, 1994; Department of Education and Science and the Welsh Office, 1991; National Council of Teachers of Mathematics, 1989). In response to these recommendations, current curriculum materials have placed increased emphasis on the teaching and learning of probability (Berle-Carman, Economopoulos, Rubin, Russell, & Corwin, 1995; Chandler & Brosnon, 1994). With respect to teaching and learning, numerous studies (Fennema, Franke, Carptenter, & Carey, 1993; Fuys, Geddes, & Tischler, 1988; Lamon, 1996; Mack, 1995), advocate the use of research-based knowledge of students' thinking to inform instruction. Although there has been considerable research on students' probabilistic reasoning (e.g., Falk, 1983; Fischbein, Nello, & Marino, 1991; Hawkins & Kapadia, 1984; Piaget & Inhelder, 1975; Shaughnessy, 1992), none of this research has generated a framework for systematically describing and predicting students thinking in probability. Moreover, research has not generated or evaluated instructional programs at the elementary and middle school levels that are guided by research-based knowledge of students probabilistic thinking (Shaughnessy, 1992). This paper reports on a program of four research studies on probability in the elementary and middle grades. In particular, it examines: a) a research-based framework for describing and predicting how elementary and middle grades' students think in probability; b) an instructional program in probability for the elementary level that was informed by the research-based framework on students probabilistic thinking; and c) two instructional programs in the middle grades, one emphasizing conditional probability and independence, the other focusing on probabilistic thinking and writing in the context of probability.
We highlight one interpretation of Pearson's r (largely unknown to behavioral scientists), inspired by the genetic measurement of inbreeding. The coefficient of inbreeding, defined as the probability that two paired alleles originate from common descent, equals the correlation between the uniting gametes. We specify the statistical conditions under which r can be interpreted as probability of identity by descent and explore the possibility of generalizing that meaning of correlation beyond the inbreeding context. Extensions to the framework of agreement between judges and to that of sequential dependencies are considered. Viewing correlation as probability is heuristically promising. We examine the implications of this approach in the case of three types of bivariate distributions and discuss potential insights and risks.