Mathematical Explanation: Examining Approaches to the Problem of Applied Mathematics

The problem of applied mathematics is to account for the ’unreasonable effectiveness’ of mathematics in empirical science. A related question is, are there mathematical explanations of scientific facts, in the same way there are empirical explanations of scientific facts? Philosophers are interested in the problem of applied mathematics for two main reasons. They are interested in whether the use of mathematics in empirical science is sufficient to motivate ontological conclusions. The indispensability argument suggests that the widespread application of mathematics obligates us to accept mathematical entities into our ontology. The second primary philosophical question concerns the details of the applications of mathematics. Philosophers are interested in what sort of relationship between mathematics and the physical world allows mathematics to play the role that it does. In this thesis, I examine both areas of literature in detail. I begin by examining the details of the indispensability argument as well as some significant critiques of the argument and the methodological conclusions that it gives rise to. I then examine the work of those philosophers who debate whether the widespread application of mathematics in science motivates accepting mathematical entities into our ontology. This debate centers on whether there are mathematical explanations of scientific facts, which is to say, scientific explanations which have an essential mathematical component. Both sides agree that the existence of mathematical explanations would motivate realism, and they debate the acceptability of various examples to this end. I conclude that there is a strong case that there are mathematical explanations. Next I examine the work of the philosophers who focus on the formal relationship between mathematics and the physical world. Some philosophers argue that mathematical explanations obtain because of a structure preserving ’mapping’ between mathematical structures and the physical world. Others argue that mathematics can play its role without such a relationship. I conclude that the mapping view is correct at its core, but needs to be expanded to account for some contravening examples. In the end, I conclude that this second area of literature represents a much more fruitful and interesting approach to the problem of applied mathematics

Computer Science Education Needs Survey for Grades K-8 Teachers

This survey is an integral part of a broader community-engaged project working with K-8 teachers across Tennessee in order to understand their needs concerning teaching CS. The survey includes open-ended and closed-ended items, including questions from the National Survey of Science and Mathematics Education (NSSME)+ (Banilower et al.,2018)

Review and Use of Learning Theories within Computer Science Education Research: Primer for Researchers and Practitioners

Computing education research is built on the use of suitable methods within appropriate theoretical frameworks to provide guidance and solutions for our discipline, in a way that is rigorous and repeatable. However, the scale of theory covered extends well beyond the computing discipline and includes educational theory, behavioural psychology, statistics, economics, and game theory, among others. The use of appropriate and discipline relevant theories can be challenging, and it can be easy to return to reuse familiar theory rather than investigate a new, more appropriate, area. To assist researchers in understanding how computing theory is currently used in the discipline and what theories might become of interest, we present in this paper a quantitative analysis of how learning theories are adapted in the computing education research communities. We search computing education venues for specific theory related keywords as well as for the citation of the influential paper describing each individual theory to identify popular theories and highlight gaps in use. We propose a template categorization of theories based on three main perspectives, namely, individual, group, and artefact, with several modifiers, and use this template to visualize general and computing education learning theories. To better understand theory connections we visualize the co-occurrence of learning theories in computing education research papers. Our analysis identifies three main theory communities focused respectively on social theories, experiential theories, and theories of mind. We also identify the strongest links within these communities, highlighting several avenues for further research