Problems in physics and mathematics contexts with middle and high school classes: vertical and horizontal comparison

My thesis falls within the framework of physics education and teaching of mathematics. The objective of this report was made possible by using geometrical (in mathematics) and qualitative (in physics) problems. We have prepared four (resp. three) open answer exercises for mathematics (resp. physics). The test batch has been selected across two different school phases: end of the middle school (third year, 8\textsuperscript{th} grade) and beginning of high school (second and third year, 10\textsuperscript{th} and 11\textsuperscript{th} grades respectively). High school students achieved the best results in almost every problem, but 10\textsuperscript{th} grade students got the best overall results. Moreover, a clear tendency to not even try qualitative problems resolution has emerged from the first collection of graphs, regardless of subject and grade. In order to improve students' problem-solving skills, it is worth to invest on vertical learning and spiral curricula. It would make sense to establish a stronger and clearer connection between physics and mathematical knowledge through an interdisciplinary approach.

Hierarchical Multi-Label Text Classification in a Low-Resource Setting

In this thesis we address a multi-label hierarchical text classification problem in a low-resource setting and explore different approaches to identify the best one for our case. The goal is to train a model that classifies English school exercises according to a hierarchical taxonomy with few labeled data. The experiments made in this work employ different machine learning models and text representation techniques: CatBoost with tf-idf features, classifiers based on pre-trained models (mBERT, LASER), and SetFit, a framework for few-shot text classification. SetFit proved to be the most promising approach, achieving better performance when during training only a few labeled examples per class are available. However, this thesis does not consider all the hierarchical taxonomy, but only the first two levels: to address classification with the classes at the third level further experiments should be carried out, exploring methods for zero-shot text classification, data augmentation, and strategies to exploit the hierarchical structure of the taxonomy during training.