This dissertation is about a particular style of research. The philosophy of this style is that in order to scientifically understand deep learning, it is fruitful to investigate what happens when neural networks are trained on simple, mathematically well-defined tasks. Even though the training data is simple, the training algorithm can end up…

The field of Data Science has seen rapid growth over the past two decades, with a high demand for people with skills in data analytics, programming, statistics, and ability to visualize, predict from, and otherwise make sense of data. Alongside the rise of various artificial intelligence (AI) and machine learning (ML) applications, we have also…

Probabilistic machine learning increasingly informs critical decisions in medicine, economics, politics, and beyond. To aid the development of trust in these decisions, we develop a taxonomy delineating where trust in an analysis can break down: (1) in the translation of real-world goals to goals on a particular set of training data, (2) in the…

Immediacy is one of the necessary criteria to show strong evidence of treatment effect in single case experimental designs (SCEDs). With the exception of Natesan and Hedges (2017) no inferential statistical tool has been used to demonstrate or quantify it until now. We investigate and quantify immediacy by treating the change-points between the…

In our investigation of university students' knowledge about real numbers in relation to computer algebra systems (CAS) and how it could be developed in view of their future activity as teachers, we used a computer algorithm as a case to explore the relationship between CAS and the knowledge of real numbers as decimal representations. Our work was…

Language is one of the hallmarks of intelligence, demanding explanation in a theory of human cognition. However, language presents unique practical challenges for quantitative empirical research, making many linguistic theories difficult to test at naturalistic scales. Artificial neural network language models (LMs) provide a new tool for studying…

As we move further into the digital age, the acquisition of digital literacy (DL) and computational thinking (CT) skills is emerging internationally as an essential goal for students in contemporary school curricula. As the world becomes more uncertain and volatile due to impacts of artificial intelligence (AI), international unrest, climate…