Using partial knowledge to inform the creation of learning progressions

The aim of this study was to show that some of the errors made by students when responding to mathematics assessment items can indicate progress in the development of conceptual understanding. By granting partial credit for specific incorrect responses by early secondary students, estimates of the difficulty of demonstrating full and partial knowledge of skills associated with the development of proportional reasoning were determined using Rasch analysis. The errors were confirmed as indicators of progress, and hence partial knowledge, when the thresholds of achievement followed a logical order: The greater the proficiency of the students, the more likely they were to receive a higher score. Consideration of this partial knowledge can enhance the descriptions of the likely behaviours of students at the various levels of learning progressions and this can be informative for teachers in their planning of learning activities.