History of mathematics and history of science

This essay argues that the diversity of the history of mathematics community in the United Kingdom has influenced the development of the subject and is a significant factor behind the different concerns often evident in work on the history of mathematics when compared with that of historians of science. The heterogeneous nature of the community, which includes many who are not specialist historians, and the limited opportunities for academic careers open to practitioners have had a profound effect on the discipline, leading to a focus on elite mathematics and great mathematicians. More recently, reflecting earlier developments in the history of science, an increased interest in the context and culture of the practice of mathematics has become evident

Variations in duty arrangements to respond to concerns about children's welfare

Historians and philosophers of mathematics share an interest in the nature of mathematics: what it is, what features affect its growth, how it informs other disciplines. But much of the work done in history and philosophy of mathematics suggests that the two groups largely work in isolation. A reconsideration of the history of mathematical analysis in the 19th Century suggests that history and philosophy of mathematics can be done together to the advantage of both, and also how legitimately different enquiries need not drive them apart

Using the history of mathematics for mentoring gifted students: Notes for teachers

The paper presents a theoretical framework, methodology and practical implications for the work with gifted students using history of mathematics. A teaching-learning model, where history of mathematics is integrated in problem-solving activities, is described. Didactical material based on the concepts of triangle geometry is given in the scope of this model. A beautiful and intriguing piece of geometry – the Lemoine point is the focus of consideration. Its properties are investigated through appropriately designed activities for students. Different examples show the importance of history of mathematics for the development of students’ mathematical thinking

Categories without structures

The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics studies invariant forms (Awodey) categorical mathematics studies covariant transformations which, generally, don t have any invariants. In this paper I develop a non-structuralist interpretation of categorical mathematics and show its consequences for history of mathematics and mathematics education.Comment: 28 page

‘Walking in a Foreign and Unknown Landscape’ : studying the history of mathematics in initial teacher education

This article develops the argument that students in initial teacher education benefit in terms of who they are becoming from developing awareness of and engagement in the history of mathematics. Initially, current school mathematics practices in the UK are considered and challenged. Then the role of teachers’ relationship to mathematical subject knowledge and of teachers’ engagement in critical thinking are considered. Connections are made between these concerns and studying the history of mathematics in initial teacher education classrooms. I then draw on the perspectives and practices of the mathematics teacher educators at one institution to understand these connections better and to exemplify them. Issues of equity are threaded throughout

A Mathematician\u27s Overview of the Virginia Elementary Mathematics Specialist Program

This article discusses the mathematics component of the Mathematics Specialist master\u27s degree program in the Virginia Mathematics Specialist Project (VMSP). It includes my personal views on the significant mathematical knowledge and skills that Mathematics Specialists need, the mathematics that is taught in the Mathematics Specialist courses, and my thoughts on what appear to be the substantial mathematical abilities and aptitudes that are required by successful Mathematics Specialists in their work. The interpretations I present are highly personal and are undoubtedly dependent on my personal history, a short description of which is given (see Appendix A)

Mathematical motivators: using the history of mathematics to enrich the curriculum

This article provides a summary of the MSOR funded mini project Mathematical Motivators. Mathematics is usually, and of course correctly, presented ‘ready-made’ to students, with techniques and applications presented systematically and in a logical order. However, like any other academic subject, mathematics has a history which is rich in astonishing breakthroughs, false starts, misattributions, confusions and dead-ends. This history gives a narrative and human context which adds colour and context to the discipline