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

Learning Sciences for Computing Education

his chapter discusses potential and current overlaps between the learning sciences and computing education research in their origins, theory, and methodology. After an introduction to learning sciences, the chapter describes how both learning sciences and computing education research developed as distinct fields from cognitive science. Despite common roots and common goals, the authors argue that the two fields are less integrated than they should be and recommend theories and methodologies from the learning sciences that could be used more widely in computing education research. The chapter selects for discussion one general learning theory from each of cognition (constructivism), instructional design (cognitive apprenticeship), social and environmental features of learning environments (sociocultural theory), and motivation (expectancy-value theory). Then the chapter describes methodology for design-based research to apply and test learning theories in authentic learning environments. The chapter emphasizes the alignment between design-based research and current research practices in computing education. Finally, the chapter discusses the four stages of learning sciences projects. Examples from computing education research are given for each stage to illustrate the shared goals and methods of the two fields and to argue for more integration between them

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)

Are there any gender differences in students' emotional reactions to programming learning activities?

Novice programmers experience a wide set of emotions when they are learning to program. This exploratory study analyzes the emotions experienced by a group of students when solving diverse programming tasks. The goal was to understand if there are gender differences in the emotions reported by the students. A self-report tool to track emotions was used. The results show that, regardless of the type of learning activity, there is a tendency for women to attribute themselves negative emotions to a greater extent, which happens to be the opposite with men. It is concluded that further research is needed to understand the factors that cause these differences.Los programadores novatos experimentan un amplio conjunto de emociones cuando están aprendiendo a programar. Este estudio exploratorio analiza las emociones que experimenta un grupo de estudiantes al resolver diversas tareas de programación. El objetivo era comprender si existen diferencias de género en las emociones que reportan los estudiantes. Se utilizó una herramienta de autoinforme para rastrear las emociones. Los resultados muestran que, independientemente del tipo de actividad de aprendizaje, existe una tendencia a que las mujeres se atribuyan en mayor medida emociones negativas, lo que pasa a ser lo contrario con los hombres. Se concluye que se necesita más investigación para comprender los factores que causan estas diferencias.Universidad Nacional, Costa RicaEscuela de Informátic

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