Teachers' evaluations and students' achievement: a "deviation from the reference" analysis

Several studies show that teachers make use of grading practices to affect students' effort and achievement. Generally linearity is assumed in the grading equation, while it is everyone's experience that grading practices are frequently non-linear. Representing grading practices as linear can be misleading both from a descriptive and a prescriptive viewpoint. Here we propose to identify grading practices as 'deviations from a reference', which is a fully non-parametric criterion, and measure their effects on achievement based on this classification. To show the effectiveness of our approach, we apply the methodology to a data-set on Italian lower secondary school.