MULTIVARIATE ANALYSIS FOR OVERALL ASSESSMENT OF STUDENT LEARNING BASED ON SEVERAL INDIVIDUAL SCORES OBTAINED IN DIFFERENT ACTIVITIES

Almost all teaching activities, especially in official settings (primary, secondary/middle, high school or university) end up in the need of reducing the overall assessment of student learning to a single number.

Continuous assessment trough different activities to evaluate student‘s progress in the development of various skills provides several scores that together define student’s performance.

For several reasons, each teacher/professor should outline their grading policies before effectively applying any of the planned learning activities. In general, it means that the weights are defined ‘a priori’, and then a weighted average of the scores is computed that reduces the multivariate information we have about each student to a single score, or the corresponding quantile.

In this work, we present an alternative method for the assessment that takes into account the multivariate information the different activities provide. This is done with a Principal Component Analysis of the scores (the vector of all individual scores) obtained for a group of 33 students in the first semester of a first university course (Chemistry degree). The scores come from the evaluation of the performance of every student in different learning activities: solving real-life cases (adapted to the level, of course) through group or individual analyses; or in an assisted or self-learning environment (inside or outside the classroom).

The first principal component is indeed a weighted average of the scores, but that takes into account the performance of the group of students. The second and third principal components describe the performance of students in the different situations: those who work better alone, those that work better in a self-learning context, that is, outside the classroom with time to think, consult references, etc.
In this way, we have information about the skills in which each student is better, and which one we should encourage.

At the end of the course, the first principal component could be used to define a single ‘overall’ score, although the drawback is, of course, that these weights cannot be defined before the course begins (in the syllabus).