Vicki Steinle

A Case of the Inapplicability of the Rasch Model: Mapping Conceptual Learning

The basic theory of Rasch measurement applies to situations where a person has a certain level of a trait being investigated, and this level of ability is what determines (to within a measurement error) how well the person does on each item in a test. This paper responds to frequent suggestions from colleagues that the use of Rasch measurement would be profitable in analysing a set of data on students’ understanding of decimal notation. We demonstrate misfit to the Rasch model by showing that item difficulty estimates show important variation by year level, that there is significant deviation from expected score curves, and that success on certain splitter items does not imply a student is more likely to score well on other items. The explanation given is that conceptual learning may not always be able to be measured on a scale, which is an essential feature of the Rasch approach. Instead, students move between categories of interpretations, which do not necessarily provide more correct answers even when they are based on an improved understanding of fundamental principles. In this way, the paper serves to highlight the assumptions built into the Rasch model and to discuss its applicability to describing the progress of learning with various characteristics.

Decimal numbers and safe interpretation of clinical pathology results

Objective To determine the understanding of decimal numbers by medical laboratory scientists, doctors and nurses. Methods A Decimal Comparison Test determined the comprehension of decimals numbers. Additional questions sought the participants’ understanding of concentrations and reference ranges, and their preferences for the presentation of clinical pathology results. Results Of the 108 participants, 40% exhibited poor comprehension of decimal numbers. One-third of the medical laboratory scientists, a quarter of doctors, and half the nurses were characterised as lacking numeracy skills. The majority of participants (60%) thought it would be safer for results to be presented as whole numbers rather than as decimals with leading zeros. Conclusions The number of laboratory and clinical staff who show numeracy issues that could lead to misinterpretation of clinical pathology results and contribute to medical error strongly supports recommendations that pathology results should be presented as whole numbers.

The need to address poor numeracy skills in the emergency department environment

Substantial evidence exists for lack of numerical skills among many health professionals. Although poor numeracy has long been recognised as a contributor to medication error, other activities for which numerical literacy are required, such as interpretation of diagnostic results, have been largely ignored. Poor self‐awareness of lack of numerical literacy increases the risk, especially in the busy and hurried emergency environment. System changes, such as standardising units and improving number presentation, reduce the potential for misinterpretation; however system changes do not address the underlying deficiencies in mathematical skills. The training of doctors in numeracy has been largely ignored. In contrast, education for nurses frequently occurs during both pre‐ and post‐registration programmes. Interventions have had mixed success, although additional emphasis in increasing conceptual understanding of numbers is encouraging. The consequences of poor numerical literacy should be addressed in all clinical staff, not only by practice change to remove the potential for errors to be made, but also complemented by self‐awareness and education.

Bayesian Reasoning for Diagnosing Student Misconceptions about Decimals

Work in Bayesian student modelling is described, which draws on extensive analyses of the way that students think about the decimal numeration system. The model wiU form the basis of an adaptive tutoring system. We present an initial model and discuss issues arising.

Specific Mathematics Assessments that Reveal Thinking: An Online Tool to Build Teachers’ Diagnostic Competence and Support Teaching

In this chapter, we describe the design of an online system for the formative assessment of students’ understanding of mathematics and discuss how it develops diagnostic competence and influences teaching. The smart-test system covers many mathematics topics studied by students between about 10 and 16 years of age. It is programmed to provide teachers with an automated diagnosis of their own students’ stages of development in specific topics and to report on an individual’s errors and misconceptions, in order to inform teaching. Our claim is that teachers’ diagnostic competence increases when they have easy access to information about their own students’ thinking. In turn, this can further improve teaching, and hence learning. By drawing together evaluative data from four sources, we highlight aspects of teachers’ initial responses to formative assessment and the effect of using this system on their knowledge for teaching and the subsequent changes to teaching practice. Overall, teachers report that using the smart-tests has improved their knowledge of the thinking of individual students as well as of students in general (i.e., their pedagogical content knowledge), and that they can use this information in several ways to adjust their teaching. Paradoxically, using smart-tests reduces the demand for teachers to have specific knowledge for diagnosis and at the same time increases this knowledge and so improves their diagnostic competence.