Using Rasch models to reveal contours of teachers' knowledge

Teachers' knowledge is usually categorised into subject matter (SMK) and pedagogical content knowledge (PCK). Previously, measurement instruments and consequent cognitive scales have been developed to assess students' and teachers' subject knowledge. A number of qualitative studies have explored teachers' pedagogical content knowledge. This study developed a means to investigate one aspect of PCK--teachers' awareness of their students' knowledge--using a combination of measurement and qualitative interpretation. We asked teachers to estimate on a Likert scale (and also describe qualitatively) the difficulty their pupils would have with test items which we had already scaled using data from their pupils. We then constructed, using various models, a "Teacher's collective Perception of Item Difficulty" (TPID) scale and contrasted this with the student's ability scale by comparing the two sets of item-difficulty parameters. The results were triangulated with qualitative data. We suggest the methodology is best supported by an Inverse Partial Credit Model (IPCM) but we compare the results across alternative Rasch models.