WEAVING ASSESSMENT FOR STUDENT LEARNING IN PROBABILISTIC REASONING AT THE INTRODUCTORY TERTIARY LEVEL

For any course in a student's degree program, the assessment should be part of an integrated assessment and learning package, with the components of the package combining to meet the learning objectives in a steady development of skills and operational knowledge that take account of the students' various prior and future learnings. This paper considers such a package for an introductory course in probability and distributional modelling, including its objectives with reference to the nature of statistical thinking in probabilistic and distributional modelling, and general assessment principles. A new component of assessment to strengthen the problem-solving environment and to better address some of the objectives is described, together with student and tutor feedback and student data. INTRODUCTION Tertiary educators' complaints of previous eras that students learn only for assessment are fading with the growing understanding that assessment should be designed for, and aligned with, student learning. Assessing for student learning requires identification of the purpose of the learning, of what the students are bringing to their learning, of how they learn and manage their learning, and of their perception of the roles of this particular learning in their courses and their futures. For the tertiary teacher, the variety and extent of demands and pressures on assessment packages can appear overwhelming and sometimes even contradictory. Amidst the balancing of formative, summative, flexible, continuous, rich and authentic assessment with demands for developing generic graduate capabilities such as teamwork, problem-solving and communication skills, lurk the problems of over-assessment and the politics of pass rates and attrition. The many dimensions of the assessment challenge are complicated in introductory courses by the diversity of student cohorts in which the wide range of backgrounds, programs, motivations and study skills need consideration in designing appropriate assessment and learning packages. Perhaps it is not surprising that Garfield et al (2002), in a survey of US statistics educators, report that of all areas of statistics education, assessment practices have undergone the least reform. Calls for statistics educators to assess what they value (Chance, 2002) are reflected in general higher education literature emphasizing the role of assessment in learning (Angelo, 1999). Explicit aligning of assessment with objectives also features in both the general higher education (James et al, 2002) and statistics education literature (Gal and Garfield, 1998). Such alignment requires identification of course objectives in order to weave an integrated learning and assessment package appropriate for the student cohort and crafted to meet both statistics education goals and tertiary demands, particularly in diverse introductory course cohorts. Contrary to the fears of tertiary staff who have been exposed to only the verbal descriptors/no marks methods of criteria and standards referenced assessment, the key messages in leading research in this general area are consistent with what is regarded as best practice by staff, and most desirable by students, in assessment in statistics (and mathematics). After a summary of these key messages, the paper briefly discusses how the spirit of the statistics education reforms can guide and link with objectives in the development of probabilistic reasoning and modelling at the tertiary level. A set of objectives for an introductory course are given, and the components of the assessment for learning package are described, with selected items, criteria and student reactions outlined or given where possible. A new component of the package was introduced in 2006 to strengthen the problem-solving environment and the learning at key stages, and the paper concludes with a brief analysis of the similarities and contrasts between the reactions of the 2005 and the 2006 cohorts.