Mathematics Teachers' Diagnostic Skills and Their Impact on Students' Achievements

The present study investigates diagnostic skills of mathematics teachers and the way they relate to instructional quality and students' achievements. Longitudinal data were obtained from a sample of 155 teachers and their classes (3483 students) in the context of the German national extension to the PISA study (measurement points: end of 9th and 10th grade). Diagnostic skills were investigated using two indicators: the accuracy of teachers in judging the difficulty levels of mathematics tasks in their own class and the accuracy in estimating the rank order of students' achievement outcomes in their classes (rank component). In average, teachers underestimated the difficulty level of mathematics tasks in their own classes, the median of the rank component was r=0.32. The accuracy of judging difficulty levels of mathematics tasks was related to the instructional quality. Multilevel analyses showed further that both indicators were related to students' achievements, controlling for students' background and prior attainment.