IASE /ISI Satellite, 2007: Lipson 1 ® ASSESSING UNDERSTANDING IN STATISTICS LIPSON, Kay Swinburne University of Technology, Lilydale Australia Using a framework for assessing dimensions of understanding in statistics a series of assessment tasks were developed by the researcher to address both procedural and conceptual understanding. This paper describes these tasks, together with the results of students’ performance on the tasks. It will be shown that, while some of the tasks developed did assess the dimension of knowledge which they were developed to address, and some did not, overall it was possible to develop tasks to specifically assess both procedural and conceptual knowledge in statistical inference. INTRODUCTION Assessment in statistics has become of great interest to researchers in recent years, and considerable work has been done to develop a range of assessment instruments (Gal & Garfield, 1997). In particular, educators are interested in tasks which measure both procedural understanding, a students ability to correctly perform a task, and conceptual understanding, their knowledge of what they are doing and why they are doing it (Garfield, delMas, & Chance, 2002). This paper describes a variety of tasks which were developed to measure conceptual understanding, and provides some empirical evidence that while several of the tasks do indeed measure aspects of a student’s conceptual understanding as intended, some do not. FRAMEWORK FOR MEASURING UNDERSTANDING Several researchers have developed theoretical models for thinking about the development of understanding in mathematics and statistics. Most recent is the hierarchy of statistical literacy, statistical reasoning, and statistical thinking described by Ben-Svi and Garfield (2004). The theoretical framework used in this paper is based on some earlier work by Putnam, Lampert and Peterson (1990), who described five dimensions of understanding: representation, knowledge structure, connections between types of knowledge, active construction of knowledge and situated cognition. Tasks that fall within the classification of understanding as representation are considered here to measure procedural understanding. Tasks which fall within any of the other four dimensions of understanding are considered to contribute to the measurement of conceptual understanding. Based on the application of this framework by Nitko and Lane (1990) to understanding in statistics, the following assessment framework for statistics is suggested: Procedural Understanding Understanding as representation Tasks which involve application of standard notation, representation and algorithms to solve statistical problems. This would include standard applications of the t-test or chi-square test for example. Conceptual Understanding Understanding as knowledge structure Tasks which give insight into the knowledge structures of students. That is, tasks that demonstrate that the student has made a connections between concepts, such as hypothesis-testing and confidence intervals for example. Understanding as connections between types of knowledge Tasks that require students to integrate formal knowledge with informal knowledge developed outside the class. This would include tasks requiring the interpretation of statistical concepts.