A particular issue on my mind recently is the sheer quantity of ‘in-house’ resources that departments create to either do away with textbooks, or at least supplement them with materials tailored to their schemes of work and students’ abilities. For some, photocopying costs must be paralleling the purchase price of textbooks!

I raised this issue in some recent tweets, wishing that there was a way to share this work and its products – in some parallel to the ‘open source’ software movement. The barriers to that are typically quality control; choosing the right platform for collaborative authoring; and keeping a generally consistent format throughout. None of these problems is necessarily insurmountable but the solutions come with the costs of inconvenience, learning curves, or simply time. (For examples of so-called open textbooks, take a look at Stitz and Zeagers’ Pre-calculus book or the ‘approved’ lists collated by the American Institute for Mathematics.)

## Nor any drop to drink?

The main product I envisage being most useful is simply a ‘problem book’ for A level Maths: minimal (if any) theory or worked examples, but masses of questions at different levels. Something along the lines of Drill, Exam Standard and Extension.

The more I think about this kind of project, the more I realise how many resources I’m surrounded by. I have textbooks of every style from every decade; past papers from every board for the past decade or more; papers from STEP, AEA and MAT exams which are great for extension problems; worksheets, packs of questions, and even more papers from Solomon, T. Madas, Delphis, Zigzag; the exercises and quizzes from Integral maths… The list feels almost infinite.

Las year I almost drowned my students during the summer revision period with huge packs of past papers from every source, supplemented with topic practice too!

## […] is this indeed, The light-house top I see?

Just the other day, I rediscovered the book Graded Exercises in Pure Mathematics which I’d forgotten I even owned. This is the closest approximation to what I think would be my ideal resource: chapters are focussed on each pure topic and the exercises are graded as Basic, Intermediate, Revision and Advanced – almost exactly the same gradings as I had considered.

But there’s a downside: published in 2001, this book has missed out on a couple of curriculum reforms and the (mis)ordering of the topics from our current perspective renders it almost as difficult to use as the usual cutting and sticking I do from every other book on my shelf.

## A speck, a mist, a shape, I wist!

I’ve been a big fan of Elmwood press‘s textbooks for a long while now: they contain some theory and examples but then great sets of exercises of increasing difficulty, exam standard questions and some review. I’ve been in contact with them and they have confirmed that new editions are being produced to match the 2017 specification.

I think I’ll hold out hope on these new editions, otherwise I’ll have a big project for myself in the coming academic year, creating what (for me at least) would be the ideal practice and problem book!

### Think, Pair, Share…

- Does your department systematically produce a large number of ‘custom’ resources for teaching A level Maths? (More than just the occasional photocopied exercise from another book?)
- Is most of your supplementary material geared towards giving students questions to work on? Or explaining aspects of theory in a way you prefer over the textbook approach for example?
- Do particular advantages come from having in-house resources, or might it be possible (over several iterations) to agree on a common ‘best practice’ resource?

Do share your own thoughts and experiences in the comments!

I have just this year (after 10 years of teaching) started to make/ collate my own resources for a level (mainly for further maths) as we do Aqa spec and I focuses on challenge sheets, have also thought a lot about next year, did the teach further maths course at kings maths school (which was amazing) and they create/collate their own exercises, would be very interested to collaborate with a few people to create collate this style of questions, I use lots of questions from bostock and chandler, amongst others, Agree with the wealth of resources but feel the same about never quite being right! Although theory I find mei notes pretty good for students, as I just want them to have worked examples them we go deeper in class

Thanks for your comments, Anne. Perhaps another difficulty is pitching this material at the right level: it sounds like you (as am I) are keen to challenge your students whereas others with weaker groups might want more resources that reinforce the groundwork.

I did visit Kings school a couple of years ago and was very impressed with their approach, especially their discussions about teaching topics in department meeting time. As with many other schools, it sounds like they’ve invested a lot of initial time to prepare a valuable set of resources.

Ultimately this feels like a huge project: even focussing on, say, the new AS core topics, we would need to compile at least 3 levels of exercises (basic, exam standard, extension). Plus incorporating plenty of cross-topic work later on (eg finding a tangent to a curve but rationalising the denominator of surds is involved). And I don’t know what format the finished product should be: a book? A collection of separate documents? Just an online resource?

I’m very keen to crack this nut, but I’m also very aware that I want to go about it in the right way from the outset!

I guess it could start small, a collection of individual resources, developed as time goes by next year for the new spec and online, that way you can edit if needs be! I teach further maths kids so pretty bright but they still need practice, like the idea of confidence building, standard and challenging, (my kids like these terms) if we got a few people on board could be manageable

That’s true, and the new spec feels like the perfect time to begin such a project. My latest idea is to look into ‘Wikibooks’ as a potential route to collaborative writing. But at the same time, many of my students like a physical copy to work from. Will keep investigating and hopefully the idea and process will distil over time.

I’ve never seen the Elmwood books, but I am intrigued. Will wait for the new editions and get samples I think.