Teaching mathematics to address fundamental human rights

Mathematics is one of the most important subjects in the curriculum, central to so many areas of life and academic disciplines. Yet students – and people widely – struggle with mathematics possibly more than with any other subject. It is the right of every human being to know and understand mathematics relative to the context and purpose for which it is needed. These statements have profound implications for the teaching of mathematics. In this short monograph (a written version of my inaugural lecture for the Donders Chair at the University of Utrecht) I address the following questions about the role of teaching: .What does it mean to teach mathematics? .What are the characteristics of “good” teaching of mathematics? .How does/can “good teaching” develop? Because it is hard to address “what is good teaching?” in a simple way at the outset, I will start with another question: How can we teach mathematics for the effective learning of our students

Developing mathematics teaching: What can we learn from the literature?

In this chapter we address the extensive literature which can inform the teaching of mathematics drawing on our own experience of using and finding value in the literature to enhance our own knowledge and practice in teaching mathematics at university level. Three areas of literature are recognised and addressed: professional literature, in which we gain insights into the ways in which other teachers/lecturers have thought about their teaching and the approaches/strategies and frameworks they have used; research literature which offers what is known, findings from research that can enable more informed approaches to teaching; and pedagogical literature that deals overtly with developing and enhancing teaching, through the lecturer engaging with new ideas (for example those offered in the professional literature), attending to research findings or using specific tactics or teaching approaches recommended by the authors. Many examples are provided, both of particular sources in the literature and of approaches to learning and teaching in mathematics, with an extensive reference list. This approach is intended to be informative to mathematics teachers at university level who look for knowledge and ideas to inform their teaching and support its development

Students as partners in complex number task design

We report on a collaborative project at university level involving students as partners in task design for a bridging mathematics module (known in the UK as a Foundation module) which is part of gaining access to first year degree studies. Three teacher-researchers met regularly with four student partners who developed a set of tasks on matrices and on complex numbers which were trialled with students on this Foundation module. We show the mediational processes by which the tasks developed from ‘static’ designs to more ‘dynamic’ designs using the software Autograph. Our analyses highlighted various tools in the mediation of the learning of mathematics, in the mediation of task development and in the mediation of the engagement of all team members in collaboration