Theoretical linguistics postulates abstract structures that successfully explain key aspects of language. However, the precise relation between abstract theoretical ideas and empirical data from language use is not always apparent. Here, we propose to empirically test abstract semantic theories through the lens of probabilistic pragmatic modelling. We consider the historically important case of quantity words (e.g., `some', `all'). Data from a large-scale production study seem to suggest that quantity words are understood via prototypes. But based on statistical and empirical model comparison, we show that a probabilistic pragmatic model that embeds a strict truth-conditional notion of meaning explains the data just as well as a model that encodes prototypes into the meaning of quantity words.

Research on analogical processing and reasoning has provided strong evidence that the use of adequate educational analogies has strong and positive effects on the learning of mathematics. In this talk I will show some experimental results suggesting that analogies based on spatial representations might be particularly effective to improve mathematics learning. Since fostering mathematics learning also involves addressing psychosocial factors such as the development of mathematical anxiety, providing social incentives to learn, and fostering engagement and motivation, I will argue that one area to explore with great potential to improve math learning is applying analogical research in the development of learning games aimed to improve math learning. Finally, I will show some early prototypes of an educational project devoted to developing games designed to foster the learning of early mathematics in kindergarten children.