Easier analysis and better reporting : modelling ordinal data in mathematics education research

This article presents an examination of the use of Rasch modelling in a major research project, 'Improving Middle Years Mathematics and Science' (IMYMS). It is unarguable that it is important to take students' perceptions, or views, into account when planning learning and teaching for them. The IMYMS student perceptions survey is an attempt to make visible these student viewpoints, and report them in a way that is accessible to teachers and researchers involved in the project. The project involves four clusters of schools from urban and regions of Victoria to investigate the role of mathematics and science knowledge and subject cultures in mediating change processes in the middle years of schooling. There are five secondary and twenty-eight primary schools. The project has generated both qualitative and quantitative data, with much of the qualitative data being ordinal in nature. Reporting the results of analyses for a range of audiences necessitates careful, well-designed report formats. Some useful new report formats based on Rasch modeling -the Modified Variable Map, the Ordinal Map, the Threshold Map, and the Annotated Ordinal Map - are illustrated using data from the IMYMS project. The Rasch analysis and the derived reporting formats avoid the pitfalls that exist when working with ordinal data and provide insights into the respondents' views about their experiences in schools unavailable by other approaches.