
Perhaps at school you liked mathematics for a while but were then put off because you missed a key idea and kept getting stuck. Perhaps you always liked mathematics but gave it up because your main interest was music or languages or science or philosophy. Or perhaps you studied mathematics to advanced levels, but have now forgotten most of what you once knew. Whichever is the case, this book is for you. It aims to build on what you know, revisiting basic ideas with a focus on meaning. Each chapter starts with an idea from school mathematics - often primary school mathematics - and gradually builds up a network of links to more advanced material. It explores fundamental ideas in depth, using insights from research in mathematics education and psychology to explain why people often get confused, and how to overcome that confusion. For nervous readers, it will build confidence by clarifying basic ideas. For more experienced readers, it will highlight new connections to more advanced material. Throughout, the book explains how mathematicians think, and how ordinary people can understand and enjoy mathematical ideas and arguments.
- At the Open University in the UK you can get degree in "Mathematics and its Learning": https://www.open.ac.uk/courses/maths/degrees/bsc-mathematics... There is a reasearch group at the OU behind this.
- Department of Mathematics Education at Loughborough University: https://www.lboro.ac.uk/departments/maths-education/
- Mathematics Rebooted by Lara Alcock: https://global.oup.com/academic/product/mathematics-rebooted... (She's at Loughbourgh, linked above. She has also written some books for University level mathematics.)
- Frank Farris' gorgeous book "Creating Symmetry" (https://press.princeton.edu/books/hardcover/9780691161730/cr...), which has this brilliant passage:
This belief that my motivation deserves mention moves me to call this a postmodern mathematics book. By contrast, modern mathematics books were written in the twentieth century by intentionally voiceless authors for an intended audience of "the hypothetical anybody", which made the books feel cold and inaccessible, at least to me. Postmodern books are situated in time and place, taking into account the identities of both reader and author. Here I am, writing to reach you: please join me.
“The future is already here. It's just not evenly distributed yet”
Mathematics for the curious - Peter Higgins
Mathematics rebooted - Lara Alcock
Mathematics: a very short introduction - Timothy Gowers
The Essence of Mathematics Through Elementary Problems
https://open.umn.edu/opentextbooks/textbooks/the-essence-of-...