Exchange

Sharing ideas for Learning and Teaching

Scholarship and Resources: Mathematical Sciences

  ,

📥  Briefings

Scholarship and teaching related sources relating to mathematical sciences, recommended by colleagues at the University of Bath. Contributions welcome.

Overview

Mathematics Education is an established field with a large amount of research and theoretical work, as well as a large body of case studies, practical tips and advice. On the practical side you can find books and guides written by mathematicians in the context and language of maths. On the research/theory side, there is a body of work providing frameworks and models on mathematical thinking, learning mathematics, and specific issues such as proof.

MSOR Subject Centre: there are a number of good resources from the (now closed) Maths, Stats and OR subject centre (MSOR), written specifically for academics (archived: www.icse.xyz/mathstore/). The MSOR magazine (Connections) contained a large number of case studies of specific teaching topics, technologies, investigations and projects. Most resources are now on the HEA’s resource hub (www.heacademy.ac.uk).

Teaching University Mathematics (practical general books)

“I found the books “Teaching mathematics in higher education: the basics and beyond” by Cox and “Ideas from mathematics education” by Alcock and Simpson to be useful, as they are subject specific (and feel I would have benefited if I had come across them before I started lecturing).”

Teaching mathematics in higher education: the basics and beyond
Bill Cox
Book, but chapters in pdf form online (archive): www.icse.xyz/mathstore/node/1919.html
Recommended frequently by new lecturers as a good practical teaching guide written for mathematicians covering most of the major practical topics to consider.

Effective Learning and Teaching in Mathematics and its Applications
Kahn
371.39:510 KAH
This book covers a range of learning/teaching topics you may discuss cross-departmentally, but written for mathematics specifically and is worth a browse and a read of appropriate topics.

How to Teach Mathematics: A Personal Perspective
Steven G. Krantz
(Colleagues may have a personal copy. No University copy at the moment)

"I often make reference to the book “How to teach Mathematics” by Krantz. This subject specific reference is a useful handbook for specific queries about the practicalities of teaching mathematics as well as the broader philosophies behind common teaching practices.”

Supporting postgraduate students who teach mathematics and statistics
MSOR
Individual chapters on the HEA Hub site; full set as a book:
www.birmingham.ac.uk/Documents/college-eps/college/stem/additional/Teaching-Mathematics.pdf
A good set of practical guides originally written for the workshops for postgraduates teaching mathematics, they have good advice for academics teaching the same, as well as being a potential resource to indicate to your PhD students and GTAs.

Mathematics Education Research (theoretical topics)

Ideas from mathematics education: an introduction for mathematicians
Lara Alcock and Adrian Simpson
www.heacademy.ac.uk/resource/ideas-mathematics-education-introduction-mathematicians
This booklet provides a good introduction (for academics) to a few key theories from mathematics education research. It is a good introduction for understanding enough of some theories to think about how they may impact on your teaching.

Mathematical thinking is an important topic and a key skill for undergraduates. Understanding what this actually is, and how it can be developed can help enhance your teaching and as thinking about your own processes. The following are recommended books for exploring in more depth, but there are others written on the same topic, including ones written for undergraduates themselves:

Thinking Mathematically
John Mason
371.3:510 MAS
John Mason is a well-known expert in the field and provides a good in-depth tour of mathematical thinking.

Advanced Mathematical Thinking
David Tall (Ed.)
This book is out of print and difficult to obtain but if you are interested in the mathematics education research in more depth, this was written to provide a summary of the state of knowledge at the time covering a range of topics.

How to Think like a Mathematician
Kevin Houston
510.36 HOU
This book is aimed at undergraduate students themselves and is frequently recommended for them as a resource (you can find samples online: https://www1.maths.leeds.ac.uk/~khouston/httlam.html).

Proof

The mainstay of undergraduate mathematics and often a difficult skill to learn.

How to Solve it
Polya
510.43 POL
This is an (old) classic, but still an interesting read to start thinking about how we actually go about proof.

There is a range of research on proof, and further HEA resources on the topic (search the HEA site), and guides by researchers such as Nardi and Iannone e.g.

How to Prove it: A brief guide to teaching Proof to Year 1 mathematics undergraduates
Elena Nardi and Paola Iannone
icse.xyz/mathstore/headocs/Nardi_book.pdf

The above is by no means an exhaustive list, but examples of useful resources to start with, recommended by previous participants and the course team as more general or wider ranging texts to gain both advice and an understanding of some key ideas, to think about how your students learn and how you can teach to enable this better. For specific issues it is worth searching for articles, papers, and resources online (as well as using the reference lists in the above).

Journals

There is a wide field of published research in Mathematics Education, much of which covers all levels from primary through to tertiary education.

Research in Mathematics Education – The journal of the British Society for Research into Learning Mathematics is a good example. Other examples include:

University of Bath

“I found LITEbox incredibly useful. First, subscribing to the blog was a simple way for me to find about the events run by the Learning and Teaching unit. For example the idea of implementing  an electronically marked coursework came from an entry on that blog along with all the corresponding resources including an actual video to a presentation.  Also I have found here a good amount of information on the use of tablets (iPad) in teaching.”

LITEBox provides case studies and lessons from the early use of technologies: blogs.bath.ac.uk/litebox

Exchange provides access to case studies and projects from Bath as part of a growing collection. You can also use the Faculty or Department tags:

There are also various internal university events with a number of live case study presentations.

Journal Club (Conversation with Cake) holds monthly cross-department meetings based around suggested topics (and associated papers): wiki.bath.ac.uk/display/cake/L_and_T_journal_club.