If you are applying for teacher-training in England, you have to pass QTS skills tests in numeracy and literacy. I’ve used several books with students preparing for QTS numeracy — some very good, but others are really poor and should be avoided. A planned change to the test syllabus was reversed without ever being implemented, yet some books have been published advertising they are suitable for the “new” exam! This means they include things you don’t need, and have less focus on what you do. Here are the better books I’ve found.
I think Mark Patmore’s “Passing the Numeracy Skills Test” is the most impressive book on the market. Patmore is actively involved with the setting of the QTS tests, and the sample questions he includes are very similar to those in the real thing. This book is excellent preparation for your test. His explanations of the material are brief, but clear.
If you’re rusty and need a quick refresher, and a lot of practice, Patmore is an ideal choice. However, if you didn’t understand basic maths concepts well at school in the first place, you’d struggle to learn them by self-study from this book as its coverage of the syllabus is more like a revision guide. (If so, Patmore’s questions would still be useful once you’re nearing the exam, but try working through a thorough “back to basics” book first. One of my top tips to pass the QTS numeracy test is to work through as many book questions as possible before starting using up the practice tests.) Older editions are available cheaply second-hand — more recent versions have added extra questions, and I’d recommend not to go earlier than the 5th edition. Prior editions had several mistakes in the answers section, which can sow confusion.
Teacher’s Skills Tests For Dummies is a “back to basics” book, which is quite hefty (though note it includes both Numeracy and Literacy) and spends a lot of time on explanation. If you just want practice, you can jump straight to the questions, which are quite representative of the real exam. Someone struggling with key concepts would gain from carefully reading and working through the whole text.
One caution about this book: ratio and proportion is a vital idea in the QTS Numeracy test. The author teaches it by a “chequerboard” method he found effective in one-on-one tuition. It’s a traditional technique seen in manuals of instruction many centuries ago (catchily renamed the “Grid of Joy” here) but barely used at all in UK schools in the last few decades. It does work, yet it will almost certainly be strange and unfamiliar, particularly with nobody talking you through it. You might prefer to re-learn the method you were taught at school. Whichever route you take, you must master ratio and proportion before taking this exam — ensure you have a clear idea of what’s going on and how it works, not just a “magic trick” that gives you the answer, since this gives you the best chance of adapting quickly when a new question is put in front of you.
Finally, some older books are worth considering. Pass the QTS Numeracy Skills Test with Ease by Vali Nasser is used by many people. The book is self-published, so the design, layout and print quality is noticeably worse than the books above. It seems to be reprinted annually with the current year in the title, but I’ve never seen any changes in content — feel free to buy a cheaper second-hand version! Nasser worked on the launch of the QTS tests over a decade ago, but unlike Patmore no longer seems to be actively involved: oddly, from its first editions, this book has got the syllabus wrong. Explanations of algebra, or how to find the area of a circle, can be safely ignored. Some of my students found the explanations confusing or unclear. Having said that, lots of students seem to like this book and plenty pass by using it: the questions it includes are okay for extra practice, though not as close to the real thing as Patmore’s.
There’s also How to Pass the QTS Numeracy and Literacy Skills Tests by Chris Tyreman. This is an adequate book that many people pass with, but again is more useful for the practice questions than the quality of explanations (at least for numeracy: I can’t comment on the literacy half of the book). Students I’ve worked with who used both Tyreman and Nasser generally preferred Tyreman, but those using Tyreman and Patmore mostly favoured Patmore. Beware: the publisher originally posted audio files for the mental questions online, which was a nice feature, but the link advertised in the book is now dead. This is still a much better book than Tyreman’s more recent How to Pass the Professional Skills Tests for Initial Teacher Training (ITT): 1000 + Practice Questions, which suffers from overly repetitive questions and errors in the text (which hopefully will be fixed in later editions).
My usual advice to people is to buy Passing the Numeracy Skills Test by Patmore and, if they feel they lack confidence on the basics and have the time for a good read, consider supplementing it with the Teacher’s Skills Tests For Dummies. If you come across an old copy of Tyreman or Nasser from a friend or colleague, this should still be adequate to pass your test, but may not be worth purposefully seeking out unless you are desperate for extra practice material, or found the other books hard to get on with and you want to try a different approach. If I tutor you then there will be a plentiful supply of worksheets, so seeking out extra practice questions is less important! See also my suggestions for websites where you can practise QTS Numeracy online.